[{"data":1,"prerenderedAt":73482},["ShallowReactive",2],{"blog-layout-count-es":3,"blog-post-ai-capabilities-and-limitations-es":70640,"blog-post-adjacent-ai-capabilities-and-limitations-es":71766},[4,2273,3629,3678,12733,19777,33014,40499,44595,46290,63551,64192],{"id":5,"title":6,"author":7,"body":8,"date":2249,"description":14,"extension":2250,"image":2251,"lastmod":2252,"meta":2253,"navigation":208,"order":2254,"path":2255,"seo":2256,"sitemap":2257,"slug":2260,"stem":2261,"summary":2262,"tags":2263,"__hash__":2272},"content_es\u002Fblog\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013.md","Modelo de Predicción de Riesgo en Adolescentes (SV 2013)","David Deras",{"type":9,"value":10,"toc":2221},"minimark",[11,15,29,39,42,45,50,53,62,65,70,75,79,82,100,103,106,109,113,116,138,141,156,163,322,327,330,344,355,396,403,407,429,446,457,460,520,538,542,545,549,560,627,630,641,644,651,655,658,661,705,712,816,819,824,828,839,894,905,911,915,921,935,1044,1152,1218,1221,1228,1232,1239,1254,1258,1272,1283,1418,1434,1445,1449,1453,1460,1541,1545,1611,1616,1619,1720,1850,1853,1859,1863,1866,1925,1936,1942,1952,1963,1972,1975,1979,1986,1993,2103,2114,2118,2121,2193,2196,2217],[12,13,14],"p",{},"Sería de mayor utilidad si tuviésemos datos más recientes pero desafortunadamente, el conjunto de datos más reciente disponible para El Salvador es del año 2013. A pesar de esto, haremos este ejercicio con el fin de ejemplificar como la inteligencia artificial puede ser un gran apoyo en la resolución de problemas críticos para la sociedad, como lo es la salud de los adolescentes. En este artículo, crearemos dos modelos dentro de un mismo pipeline:",[16,17,18],"blockquote",{},[12,19,20,21],{},"El código completo de este proyecto está disponible en el repositorio: ",[22,23,28],"a",{"href":24,"rel":25,"target":27},"https:\u002F\u002Fgithub.com\u002Fdaiv05\u002Fmodel-risk-factors-adolescents-sv-2013",[26],"nofollow","_blank","model-risk-factors-adolescents-sv-2013",[30,31,32,36],"ul",{},[33,34,35],"li",{},"Uno para predecir el IMC (Índice de Masa Corporal) basado en los hábitos de alimentación y actividad física de los adolescentes.",[33,37,38],{},"Otro para predecir el riesgo de salud mental basado en factores de riesgo psicosociales y de comportamiento.",[40,41],"table-of-contents",{},[43,44],"hr",{},[46,47,49],"h2",{"id":48},"la-investigación-de-la-salud-en-adolescentes","La investigación de la salud en adolescentes",[12,51,52],{},"La Global School-based Student Health Survey (GSHS) es una encuesta desarrollada por la Organización Mundial de la Salud (OMS), mide los factores de riesgo conductuales y los factores de protección en 10 áreas clave entre jóvenes de 13 a 17 años.",[12,54,55,56,61],{},"Toda la investigación y reportes se puede encontrar en el sitio web de la OMS, específicamente en la sección de ",[22,57,60],{"href":58,"rel":59},"https:\u002F\u002Fextranet.who.int\u002Fncdsmicrodata\u002Findex.php\u002Fcatalog\u002F97",[26],"El Salvador - Global School-based Student Health Survey 2013",".",[12,63,64],{},"Tambien se puede acceder a otras investigaciones en el mismo sitio web.",[16,66,67],{},[12,68,69],{},"Los datos de esta investigación de GSHS son de acceso público y pueden ser utilizados para fines de investigación. Sin embargo, es importante tener en cuenta los términos y condiciones establecidos en la website de la OMS, y se recomienda revisar y cumplir con dichos términos antes de utilizar los datos para cualquier propósito.",[16,71,72],{},[12,73,74],{},"El dataset NO se incluye en este repositorio ni en el repositorio principal de la investigación, debido a restricciones de la plataforma de la OMS.",[46,76,78],{"id":77},"los-datos","Los datos",[12,80,81],{},"La encuesta tiene varias preguntas relacionadas con la salud de los adolescentes, incluyendo hábitos de alimentación, actividad física, salud mental, consumo de sustancias y factores de riesgo psicosociales, en total son 52 preguntas, identificadas con códigos específicos: Q1 hasta Q58, saltandose Q28-Q33.",[12,83,84,85,89,90,93,94,93,97,61],{},"A parte de estas preguntas, se incluyen variantes derivadas con respuestas en un rango de ",[86,87,88],"span",{},"1, 2",", donde 1 representa la respuesta \"Sí\" y 2 representa la respuesta \"No\", para las preguntas ",[86,91,92],{},"Q6-Q27",", ",[86,95,96],{},"Q34-Q40",[86,98,99],{},"Q44-Q58",[12,101,102],{},"Por último, se incluyen otros indicadores derivados, como de obesidad, sobrepeso, bajo peso, actividad física, consumo de frutas, entre otros, para un total de 11 indicadores derivados.",[12,104,105],{},"En total, el conjunto de datos contiene 104 variables, incluyendo las preguntas originales, las variantes derivadas y los indicadores derivados.",[12,107,108],{},"Algunas respuestas contienen el valor de: 1.7976931348623157E+308, que representa un valor faltante o desconocido. En esta investigación (en el pipeline), reemplazaremos estos valores con NaN (Not a Number) para su manejo.",[46,110,112],{"id":111},"objetivos","Objetivos",[12,114,115],{},"Dividiremos los objetivos en 3 puntos principales:",[117,118,119,126,132],"ol",{},[33,120,121,125],{},[122,123,124],"strong",{},"Limpieza y análisis de datos",": Se hará un análisis exploratorio de los datos para seleccionar las variables más relevantes para cada modelo, así como tener en cuenta la colinealidad entre las variables y la importancia de cada una en los modelos de predicción.",[33,127,128,131],{},[122,129,130],{},"Modelo de predicción del IMC (Índice de Masa Corporal)",": Utilizando los hábitos de alimentación y actividad física de los adolescentes, construiremos (o intentaremos crear) un modelo de regresión para predecir el IMC, pero, sin usar las variables de peso y altura directamente.",[33,133,134,137],{},[122,135,136],{},"Modelo de predicción del riesgo de salud mental",": Utilizando algúnos factores de riesgo, como ideas de suicidio, consumo de sustancias, violencia, entre otros, construiremos un modelo de clasificación para predecir el riesgo de salud mental en los adolescentes.",[46,139,124],{"id":140},"limpieza-y-análisis-de-datos",[12,142,143,144,148,149,155],{},"Antes de entrenar cualquier modelo, necesitamos entender y preparar los datos. El primer obstáculo es el valor centinela que mencionamos: ",[145,146,147],"code",{},"1.7976931348623157E+308",". Este número es el ",[122,150,151,152],{},"máximo valor representable por un ",[145,153,154],{},"float64"," según el estándar IEEE 754, y el software de la OMS lo usa para marcar respuestas faltantes o no aplicables.",[12,157,158,159,162],{},"Por eso, lo primero que hacemos al cargar los datos es reemplazarlo por ",[145,160,161],{},"NaN",":",[164,165,170],"pre",{"className":166,"code":167,"language":168,"meta":169,"style":169},"language-python shiki shiki-themes vitesse-light vitesse-dark","import numpy as np\nimport pandas as pd\n\nSENTINEL_VALUE = 1.79769313486232e+308\n\ndef load_raw(path):\n    df = pd.read_csv(path)\n    df.replace(SENTINEL_VALUE, np.nan, inplace=True)\n    return df\n","python","",[145,171,172,190,203,210,225,230,250,274,313],{"__ignoreMap":169},[86,173,176,180,184,187],{"class":174,"line":175},"line",1,[86,177,179],{"class":178},"sTPum","import",[86,181,183],{"class":182},"s8w-G"," numpy ",[86,185,186],{"class":178},"as",[86,188,189],{"class":182}," np\n",[86,191,193,195,198,200],{"class":174,"line":192},2,[86,194,179],{"class":178},[86,196,197],{"class":182}," pandas ",[86,199,186],{"class":178},[86,201,202],{"class":182}," pd\n",[86,204,206],{"class":174,"line":205},3,[86,207,209],{"emptyLinePlaceholder":208},true,"\n",[86,211,213,217,221],{"class":174,"line":212},4,[86,214,216],{"class":215},"sfsYZ","SENTINEL_VALUE",[86,218,220],{"class":219},"si6no"," =",[86,222,224],{"class":223},"sqbOQ"," 1.79769313486232e+308\n",[86,226,228],{"class":174,"line":227},5,[86,229,209],{"emptyLinePlaceholder":208},[86,231,233,237,241,244,247],{"class":174,"line":232},6,[86,234,236],{"class":235},"s5TCs","def",[86,238,240],{"class":239},"s_xSY"," load_raw",[86,242,243],{"class":219},"(",[86,245,246],{"class":182},"path",[86,248,249],{"class":219},"):\n",[86,251,253,256,259,262,264,267,269,271],{"class":174,"line":252},7,[86,254,255],{"class":182},"    df ",[86,257,258],{"class":219},"=",[86,260,261],{"class":182}," pd",[86,263,61],{"class":219},[86,265,266],{"class":182},"read_csv",[86,268,243],{"class":219},[86,270,246],{"class":182},[86,272,273],{"class":219},")\n",[86,275,277,280,282,285,287,289,292,295,297,300,302,306,308,311],{"class":174,"line":276},8,[86,278,279],{"class":182},"    df",[86,281,61],{"class":219},[86,283,284],{"class":182},"replace",[86,286,243],{"class":219},[86,288,216],{"class":215},[86,290,291],{"class":219},",",[86,293,294],{"class":182}," np",[86,296,61],{"class":219},[86,298,299],{"class":182},"nan",[86,301,291],{"class":219},[86,303,305],{"class":304},"s9nN2"," inplace",[86,307,258],{"class":219},[86,309,310],{"class":178},"True",[86,312,273],{"class":219},[86,314,316,319],{"class":174,"line":315},9,[86,317,318],{"class":178},"    return",[86,320,321],{"class":182}," df\n",[323,324,326],"h3",{"id":325},"análisis-exploratorio","Análisis exploratorio",[12,328,329],{},"Con los datos ya limpios de centinelas, hacemos un análisis exploratorio (EDA) para entender qué tenemos entre manos. Aquí buscamos dos cosas:",[117,331,332,338],{},[33,333,334,337],{},[122,335,336],{},"Análisis univariado",": la distribución de cada variable por separado. ¿Cómo se reparten las edades? ¿Cuál es la proporción de hombres y mujeres? ¿Cómo se ve la distribución del IMC?",[33,339,340,343],{},[122,341,342],{},"Análisis bivariado",": cómo se relacionan las variables entre sí y con lo que queremos predecir. Por ejemplo, ¿los estudiantes más activos físicamente tienen un IMC menor? ¿El bullying se asocia con mayor riesgo de salud mental?",[12,345,346,347,350,351,354],{},"Un punto importante del EDA es el ",[122,348,349],{},"análisis de valores faltantes",". Algunas columnas ",[145,352,353],{},"QN"," son sub-muestras condicionales: solo aplican a quien respondió \"sí\" a una pregunta previa, como por ejemplo: \"entre los estudiantes que bebieron alcohol, ¿cuántos lo hicieron antes de los 14 años?\" solo tiene sentido para quienes bebieron, y esto provoca que estas columnas tengan más del 65% de datos faltantes.",[16,356,357],{},[12,358,359,93,362,93,365,93,368,93,371,93,374,93,377,93,380,93,383,93,386,93,389,392,393,61],{},[145,360,361],{},"QN18",[145,363,364],{},"QN19",[145,366,367],{},"QN21",[145,369,370],{},"QN34",[145,372,373],{},"QN36",[145,375,376],{},"QN37",[145,378,379],{},"QN40",[145,381,382],{},"QN45",[145,384,385],{},"QN47",[145,387,388],{},"QN48",[145,390,391],{},"qnc1g"," y ",[145,394,395],{},"qnc2g",[12,397,398,399,402],{},"Por eso las vamos a ",[122,400,401],{},"excluir"," de nuestras variables predictoras. Usar una variable con un 80% de ausencias introduce más ruido que señal, a parte de que su naturaleza condicional rompería un poco la interpretación del modelo.",[323,404,406],{"id":405},"usamos-las-preguntas-q-o-las-variantes-qn","¿Usamos las preguntas Q o las variantes QN?",[12,408,409,410,412,413,416,417,420,421,424,425,428],{},"Si haz analizado el dataset, esta es probablemente la decisión más importante que se debe tomar, porque NO puedes simplemente usar todas columnas relacionadas \"porque asi tengo más información\", cada columna ",[145,411,353],{}," es una ",[122,414,415],{},"dicotomización"," de su pregunta ",[145,418,419],{},"Q"," correspondiente: por ejemplo, ",[145,422,423],{},"QN7"," vale 1 (\"Sí\") si el estudiante come fruta dos o más veces al día (",[145,426,427],{},"Q7 ≥ 4","), y 2 (\"No\") en caso contrario.",[12,430,431,432,392,435,437,438,441,442,445],{},"Esto significa que ",[145,433,434],{},"Q7",[145,436,423],{}," están ",[122,439,440],{},"casi perfectamente correlacionadas",". Si incluyéramos a ambas en el mismo modelo, introduciríamos ",[122,443,444],{},"colinealidad",", que distorsiona los coeficientes de los modelos y además, no aporta información nueva.",[12,447,448,449,61],{},"Asi que antes de seguir, tenemos que definir una regla: ",[122,450,451,452,392,454,456],{},"nunca mezclar ",[145,453,419],{},[145,455,353],{}," del mismo dominio",[12,458,459],{},"Pero tampoco podemos hacerlo de manera global para todo el pipeline, recordemos que tenemos 2 modelos, entonces:",[461,462,463,479],"table",{},[464,465,466],"thead",{},[467,468,469,473,476],"tr",{},[470,471,472],"th",{},"Modelo",[470,474,475],{},"Familia",[470,477,478],{},"Por qué",[480,481,482,498],"tbody",{},[467,483,484,490,495],{},[485,486,487],"td",{},[122,488,489],{},"Regresión (IMC)",[485,491,492,494],{},[145,493,419],{}," (ordinales)",[485,496,497],{},"La escala ordinal conserva información que una binarización pierde. Comer fruta 1 vez al día no es lo mismo que comerla 5 veces, y esa diferencia importa para predecir un valor continuo como el IMC.",[467,499,500,505,510],{},[485,501,502],{},[122,503,504],{},"Clasificación (salud mental)",[485,506,507,509],{},[145,508,353],{}," + demográficas",[485,511,512,513,515,516,519],{},"Los ",[145,514,353],{}," representan los umbrales clínicos ",[122,517,518],{},"validados por la OMS",". Aquí la binarización sí es significativa: haber consumido alcohol es un factor de riesgo, sin importar la cantidad exacta.",[12,521,522,523,526,527,530,531,534,535,537],{},"Las variables demográficas (",[145,524,525],{},"Q1"," edad, ",[145,528,529],{},"Q2"," sexo, ",[145,532,533],{},"Q3"," grado) las usamos en ambos modelos, ya que no tienen una variante ",[145,536,353],{}," equivalente.",[46,539,541],{"id":540},"nuevas-variables","Nuevas variables",[12,543,544],{},"Para cumplir con nuestros objetivos, necesitamos construir algunas variables nuevas.",[323,546,548],{"id":547},"imc","IMC",[12,550,551,552,555,556,559],{},"Para la tarea de regresión, calculamos el IMC a partir del peso (",[145,553,554],{},"Q5",", en kg) y la estatura (",[145,557,558],{},"Q4",", en metros) con la fórmula estándar:",[164,561,563],{"className":166,"code":562,"language":168,"meta":169,"style":169},"df[\"bmi\"] = df[\"Q5\"] \u002F (df[\"Q4\"] ** 2)\n",[145,564,565],{"__ignoreMap":169},[86,566,567,570,573,577,581,583,586,588,591,593,595,597,599,601,604,607,609,611,613,615,617,619,622,625],{"class":174,"line":175},[86,568,569],{"class":182},"df",[86,571,572],{"class":219},"[",[86,574,576],{"class":575},"scnC2","\"",[86,578,580],{"class":579},"spP0B","bmi",[86,582,576],{"class":575},[86,584,585],{"class":219},"]",[86,587,220],{"class":219},[86,589,590],{"class":182}," df",[86,592,572],{"class":219},[86,594,576],{"class":575},[86,596,554],{"class":579},[86,598,576],{"class":575},[86,600,585],{"class":219},[86,602,603],{"class":235}," \u002F",[86,605,606],{"class":219}," (",[86,608,569],{"class":182},[86,610,572],{"class":219},[86,612,576],{"class":575},[86,614,558],{"class":579},[86,616,576],{"class":575},[86,618,585],{"class":219},[86,620,621],{"class":235}," **",[86,623,624],{"class":223}," 2",[86,626,273],{"class":219},[12,628,629],{},"Con esto ya tenemos la etiqueta para nuestro modelo.",[12,631,632,633,61],{},"Sin embargo, aqui debemos aclarar algo, ",[122,634,635,636,392,638,640],{},"usaremos ",[145,637,558],{},[145,639,554],{}," solo para construir el target, NO los incluiremos como variables predictoras",[12,642,643],{},"Si los usáramos, predecir el IMC sería trivial (es literalmente su fórmula).",[12,645,646,647,650],{},"Lo interesante, y lo que queremos averiguar, es cuánto del IMC podemos explicar únicamente con el ",[122,648,649],{},"estilo de vida"," de los estudiantes: alimentación, actividad física y sedentarismo.",[323,652,654],{"id":653},"la-variable-de-riesgo-de-salud-mental","La variable de riesgo de salud mental",[12,656,657],{},"El dataset no tiene una única columna de \"riesgo grave de salud mental\", así que tenemos que construirla.",[12,659,660],{},"Analizando las preguntas, encontramos tres indicadores que nos dan señales de riesgo de salud mental:",[461,662,663,673],{},[464,664,665],{},[467,666,667,670],{},[470,668,669],{},"Columna",[470,671,672],{},"Significado",[480,674,675,685,695],{},[467,676,677,682],{},[485,678,679],{},[145,680,681],{},"QN24",[485,683,684],{},"Consideró seriamente el suicidio en los últimos 12 meses (ideación)",[467,686,687,692],{},[485,688,689],{},[145,690,691],{},"QN25",[485,693,694],{},"Hizo un plan sobre cómo intentar suicidarse (plan)",[467,696,697,702],{},[485,698,699],{},[145,700,701],{},"QN26",[485,703,704],{},"Intentó suicidarse en los últimos 12 meses (intento)",[12,706,707,708,711],{},"Elegir sólo una podría ser un poco restrictivo, y elegir todas podría ser demasiado amplio. Por eso definimos el target como ",[122,709,710],{},"1 si el estudiante respondió \"Sí\" a cualquiera de estas tres preguntas",", y 0 en caso contrario:",[164,713,715],{"className":166,"code":714,"language":168,"meta":169,"style":169},"suicidality = [\"QN24\", \"QN25\", \"QN26\"]\ndf[\"mental_health_risk\"] = (df[suicidality] == 1).any(axis=1).astype(int)\n",[145,716,717,753],{"__ignoreMap":169},[86,718,719,722,724,727,729,731,733,735,738,740,742,744,746,748,750],{"class":174,"line":175},[86,720,721],{"class":182},"suicidality ",[86,723,258],{"class":219},[86,725,726],{"class":219}," [",[86,728,576],{"class":575},[86,730,681],{"class":579},[86,732,576],{"class":575},[86,734,291],{"class":219},[86,736,737],{"class":575}," \"",[86,739,691],{"class":579},[86,741,576],{"class":575},[86,743,291],{"class":219},[86,745,737],{"class":575},[86,747,701],{"class":579},[86,749,576],{"class":575},[86,751,752],{"class":219},"]\n",[86,754,755,757,759,761,764,766,768,770,772,774,776,779,781,784,787,790,793,795,798,800,803,805,808,810,814],{"class":174,"line":192},[86,756,569],{"class":182},[86,758,572],{"class":219},[86,760,576],{"class":575},[86,762,763],{"class":579},"mental_health_risk",[86,765,576],{"class":575},[86,767,585],{"class":219},[86,769,220],{"class":219},[86,771,606],{"class":219},[86,773,569],{"class":182},[86,775,572],{"class":219},[86,777,778],{"class":182},"suicidality",[86,780,585],{"class":219},[86,782,783],{"class":235}," ==",[86,785,786],{"class":223}," 1",[86,788,789],{"class":219},").",[86,791,792],{"class":182},"any",[86,794,243],{"class":219},[86,796,797],{"class":304},"axis",[86,799,258],{"class":219},[86,801,802],{"class":223},"1",[86,804,789],{"class":219},[86,806,807],{"class":182},"astype",[86,809,243],{"class":219},[86,811,813],{"class":812},"sHLBJ","int",[86,815,273],{"class":219},[12,817,818],{},"Ya sea que el estudiante mostró ideación, plan o intento de suicidio, cualquiera es una definición interpretable de riesgo de salud mental.",[16,820,821],{},[12,822,823],{},"No olvidemos que al hacer esto, estas mismas variables deben excluirse de las features (si no, le estaríamos filtrando la respuesta al modelo)",[46,825,827],{"id":826},"preprocesamiento-dentro-del-pipeline","Preprocesamiento dentro del pipeline",[12,829,830,831,838],{},"Antes de entrenar, los datos pasan por tres transformaciones: imputación de faltantes, codificación de categóricas y escalado. La clave es que ",[122,832,833,834,837],{},"todas viven dentro de un ",[145,835,836],{},"Pipeline"," de scikit-learn",", no se aplican \"a mano\" por separado.",[461,840,841,854],{},[464,842,843],{},[467,844,845,848,851],{},[470,846,847],{},"Tipo de columna",[470,849,850],{},"Imputación",[470,852,853],{},"Transformación",[480,855,856,877],{},[467,857,858,868,871],{},[485,859,860,861,93,863,93,865,867],{},"Categóricas (",[145,862,525],{},[145,864,529],{},[145,866,533],{},")",[485,869,870],{},"Moda (valor más frecuente)",[485,872,873,874,867],{},"One-Hot Encoding (",[145,875,876],{},"drop='first'",[467,878,879,886,889],{},[485,880,881,882,392,884,867],{},"Ordinales (resto de ",[145,883,419],{},[145,885,353],{},[485,887,888],{},"Mediana",[485,890,891],{},[145,892,893],{},"StandardScaler",[12,895,896,897,606,900,904],{},"¿Por qué dentro del pipeline y no antes? Si imputáramos y escaláramos sobre todo el dataset antes de la validación cruzada, los parámetros (la mediana, la media, la varianza) se calcularían usando también los datos de validación. Eso es ",[122,898,899],{},"fuga de datos",[901,902,903],"em",{},"data leakage","): el modelo \"vería\" información del conjunto de prueba durante el entrenamiento, y sus métricas estarían infladas. Al estar dentro del pipeline, scikit-learn recalcula estos parámetros en cada fold usando solo los datos de entrenamiento de ese fold.",[12,906,907,908,910],{},"Usamos One-Hot Encoding con ",[145,909,876],{}," para las categóricas: convierte cada categoría en una columna binaria y elimina una de referencia, evitando multicolinealidad en los modelos lineales.",[46,912,914],{"id":913},"modelo-de-predicción-del-imc","Modelo de predicción del IMC",[12,916,917,918,162],{},"Para la regresión entrenamos y comparamos ",[122,919,920],{},"dos modelos",[30,922,923,929],{},[33,924,925,928],{},[122,926,927],{},"Regresión Lineal",": nuestra línea base, simple e interpretable.",[33,930,931,934],{},[122,932,933],{},"Random Forest Regressor",": un ensemble de árboles que captura relaciones no lineales e interacciones entre variables.",[12,936,937,938,941,942,945,946,949,950,1043],{},"Ambos se evalúan con ",[122,939,940],{},"validación cruzada de 5 folds",", y medimos su desempeño con tres métricas: el ",[122,943,944],{},"RMSE"," (raíz del error cuadrático medio) y el ",[122,947,948],{},"MAE"," (error absoluto medio) que queremos minimizar, y el ",[122,951,952],{},[86,953,956,986],{"className":954},[955],"katex",[86,957,960],{"className":958},[959],"katex-mathml",[961,962,964],"math",{"xmlns":963},"http:\u002F\u002Fwww.w3.org\u002F1998\u002FMath\u002FMathML",[965,966,967,981],"semantics",{},[968,969,970],"mrow",{},[971,972,973,977],"msup",{},[974,975,976],"mi",{},"R",[978,979,980],"mn",{},"2",[982,983,985],"annotation",{"encoding":984},"application\u002Fx-tex","R^2",[86,987,991],{"className":988,"ariaHidden":990},[989],"katex-html","true",[86,992,995,1000],{"className":993},[994],"base",[86,996],{"className":997,"style":999},[998],"strut","height:0.8141em;",[86,1001,1004,1009],{"className":1002},[1003],"mord",[86,1005,976],{"className":1006,"style":1008},[1003,1007],"mathnormal","margin-right:0.0077em;",[86,1010,1013],{"className":1011},[1012],"msupsub",[86,1014,1017],{"className":1015},[1016],"vlist-t",[86,1018,1021],{"className":1019},[1020],"vlist-r",[86,1022,1025],{"className":1023,"style":999},[1024],"vlist",[86,1026,1028,1033],{"style":1027},"top:-3.063em;margin-right:0.05em;",[86,1029],{"className":1030,"style":1032},[1031],"pstrut","height:2.7em;",[86,1034,1040],{"className":1035},[1036,1037,1038,1039],"sizing","reset-size6","size3","mtight",[86,1041,980],{"className":1042},[1003,1039]," (coeficiente de determinación) que queremos maximizar.",[164,1045,1047],{"className":166,"code":1046,"language":168,"meta":169,"style":169},"from sklearn.model_selection import cross_validate\n\nscores = cross_validate(\n    pipeline, X, y, cv=5,\n    scoring=[\"r2\", \"neg_mean_absolute_error\", \"neg_root_mean_squared_error\"],\n)\n",[145,1048,1049,1067,1071,1084,1112,1148],{"__ignoreMap":169},[86,1050,1051,1054,1057,1059,1062,1064],{"class":174,"line":175},[86,1052,1053],{"class":178},"from",[86,1055,1056],{"class":182}," sklearn",[86,1058,61],{"class":219},[86,1060,1061],{"class":182},"model_selection ",[86,1063,179],{"class":178},[86,1065,1066],{"class":182}," cross_validate\n",[86,1068,1069],{"class":174,"line":192},[86,1070,209],{"emptyLinePlaceholder":208},[86,1072,1073,1076,1078,1081],{"class":174,"line":205},[86,1074,1075],{"class":182},"scores ",[86,1077,258],{"class":219},[86,1079,1080],{"class":182}," cross_validate",[86,1082,1083],{"class":219},"(\n",[86,1085,1086,1089,1091,1094,1096,1099,1101,1104,1106,1109],{"class":174,"line":212},[86,1087,1088],{"class":182},"    pipeline",[86,1090,291],{"class":219},[86,1092,1093],{"class":182}," X",[86,1095,291],{"class":219},[86,1097,1098],{"class":182}," y",[86,1100,291],{"class":219},[86,1102,1103],{"class":304}," cv",[86,1105,258],{"class":219},[86,1107,1108],{"class":223},"5",[86,1110,1111],{"class":219},",\n",[86,1113,1114,1117,1120,1122,1125,1127,1129,1131,1134,1136,1138,1140,1143,1145],{"class":174,"line":227},[86,1115,1116],{"class":304},"    scoring",[86,1118,1119],{"class":219},"=[",[86,1121,576],{"class":575},[86,1123,1124],{"class":579},"r2",[86,1126,576],{"class":575},[86,1128,291],{"class":219},[86,1130,737],{"class":575},[86,1132,1133],{"class":579},"neg_mean_absolute_error",[86,1135,576],{"class":575},[86,1137,291],{"class":219},[86,1139,737],{"class":575},[86,1141,1142],{"class":579},"neg_root_mean_squared_error",[86,1144,576],{"class":575},[86,1146,1147],{"class":219},"],\n",[86,1149,1150],{"class":174,"line":232},[86,1151,273],{"class":219},[12,1153,1154,1155,1213,1214,1217],{},"Un detalle a anticipar: el ",[86,1156,1158,1175],{"className":1157},[955],[86,1159,1161],{"className":1160},[959],[961,1162,1163],{"xmlns":963},[965,1164,1165,1173],{},[968,1166,1167],{},[971,1168,1169,1171],{},[974,1170,976],{},[978,1172,980],{},[982,1174,985],{"encoding":984},[86,1176,1178],{"className":1177,"ariaHidden":990},[989],[86,1179,1181,1184],{"className":1180},[994],[86,1182],{"className":1183,"style":999},[998],[86,1185,1187,1190],{"className":1186},[1003],[86,1188,976],{"className":1189,"style":1008},[1003,1007],[86,1191,1193],{"className":1192},[1012],[86,1194,1196],{"className":1195},[1016],[86,1197,1199],{"className":1198},[1020],[86,1200,1202],{"className":1201,"style":999},[1024],[86,1203,1204,1207],{"style":1027},[86,1205],{"className":1206,"style":1032},[1031],[86,1208,1210],{"className":1209},[1036,1037,1038,1039],[86,1211,980],{"className":1212},[1003,1039]," de este modelo será ",[122,1215,1216],{},"modesto por diseño",". Predecir el IMC solo con comportamiento autorreportado, sin peso ni estatura, es intrínsecamente difícil - el estilo de vida explica una fracción pequeña de la variabilidad del IMC en adolescentes. Y precisamente ese es el hallazgo interesante: nos dice cuánto (o cuán poco) determina el comportamiento al IMC.",[46,1219,136],{"id":1220},"modelo-de-predicción-del-riesgo-de-salud-mental",[12,1222,1223,1224,1227],{},"Esta es una tarea de clasificación binaria, y tiene un reto particular: los datos están ",[122,1225,1226],{},"desbalanceados",". Hay muchos más estudiantes sin riesgo detectado que estudiantes en riesgo. Si entrenáramos sin cuidado, el modelo aprendería el atajo de predecir siempre \"sin riesgo\" y tendría una exactitud alta pero sería inútil.",[323,1229,1231],{"id":1230},"eligiendo-las-métricas-correctas","Eligiendo las métricas correctas",[12,1233,1234,1235,1238],{},"Por eso ",[122,1236,1237],{},"no usamos accuracy como métrica principal",". En su lugar nos enfocamos en:",[30,1240,1241,1248],{},[33,1242,1243,1244,1247],{},"El ",[122,1245,1246],{},"F1-Score de la clase minoritaria"," (los estudiantes en riesgo), que balancea precisión y recall sobre la clase que realmente nos importa.",[33,1249,1243,1250,1253],{},[122,1251,1252],{},"AUC-ROC",", que mide la capacidad del modelo de distinguir entre las dos clases independientemente del umbral.",[323,1255,1257],{"id":1256},"manejando-el-desbalance","Manejando el desbalance",[12,1259,1260,1261,1264,1265,606,1268,1271],{},"Combinamos dos estrategias. La primera es ",[145,1262,1263],{},"class_weight='balanced'",", que hace que el modelo penalice más los errores sobre la clase minoritaria. La segunda es ",[122,1266,1267],{},"SMOTE",[901,1269,1270],{},"Synthetic Minority Over-sampling Technique","), que genera ejemplos sintéticos de la clase minoritaria.",[12,1273,1274,1275,1278,1279,1282],{},"Aquí hay un detalle crítico sobre ",[122,1276,1277],{},"dónde"," aplicar SMOTE. Lo insertamos dentro de un pipeline de ",[145,1280,1281],{},"imbalanced-learn",", en este orden:",[164,1284,1286],{"className":166,"code":1285,"language":168,"meta":169,"style":169},"from imblearn.pipeline import Pipeline as ImbPipeline\nfrom imblearn.over_sampling import SMOTE\n\nImbPipeline([\n    (\"preprocessor\", preprocessor),    # imputa, codifica y escala\n    (\"smote\", SMOTE(random_state=42)),  # sobremuestrea SOLO en entrenamiento\n    (\"model\", model),\n])\n",[145,1287,1288,1310,1326,1330,1338,1362,1394,1413],{"__ignoreMap":169},[86,1289,1290,1292,1295,1297,1300,1302,1305,1307],{"class":174,"line":175},[86,1291,1053],{"class":178},[86,1293,1294],{"class":182}," imblearn",[86,1296,61],{"class":219},[86,1298,1299],{"class":182},"pipeline ",[86,1301,179],{"class":178},[86,1303,1304],{"class":182}," Pipeline ",[86,1306,186],{"class":178},[86,1308,1309],{"class":182}," ImbPipeline\n",[86,1311,1312,1314,1316,1318,1321,1323],{"class":174,"line":192},[86,1313,1053],{"class":178},[86,1315,1294],{"class":182},[86,1317,61],{"class":219},[86,1319,1320],{"class":182},"over_sampling ",[86,1322,179],{"class":178},[86,1324,1325],{"class":215}," SMOTE\n",[86,1327,1328],{"class":174,"line":205},[86,1329,209],{"emptyLinePlaceholder":208},[86,1331,1332,1335],{"class":174,"line":212},[86,1333,1334],{"class":182},"ImbPipeline",[86,1336,1337],{"class":219},"([\n",[86,1339,1340,1343,1345,1348,1350,1352,1355,1358],{"class":174,"line":227},[86,1341,1342],{"class":219},"    (",[86,1344,576],{"class":575},[86,1346,1347],{"class":579},"preprocessor",[86,1349,576],{"class":575},[86,1351,291],{"class":219},[86,1353,1354],{"class":182}," preprocessor",[86,1356,1357],{"class":219},"),",[86,1359,1361],{"class":1360},"snYqZ","    # imputa, codifica y escala\n",[86,1363,1364,1366,1368,1371,1373,1375,1378,1380,1383,1385,1388,1391],{"class":174,"line":232},[86,1365,1342],{"class":219},[86,1367,576],{"class":575},[86,1369,1370],{"class":579},"smote",[86,1372,576],{"class":575},[86,1374,291],{"class":219},[86,1376,1377],{"class":182}," SMOTE",[86,1379,243],{"class":219},[86,1381,1382],{"class":304},"random_state",[86,1384,258],{"class":219},[86,1386,1387],{"class":223},"42",[86,1389,1390],{"class":219},")),",[86,1392,1393],{"class":1360},"  # sobremuestrea SOLO en entrenamiento\n",[86,1395,1396,1398,1400,1403,1405,1407,1410],{"class":174,"line":252},[86,1397,1342],{"class":219},[86,1399,576],{"class":575},[86,1401,1402],{"class":579},"model",[86,1404,576],{"class":575},[86,1406,291],{"class":219},[86,1408,1409],{"class":182}," model",[86,1411,1412],{"class":219},"),\n",[86,1414,1415],{"class":174,"line":276},[86,1416,1417],{"class":219},"])\n",[12,1419,1420,1421,1423,1424,1426,1427,1429,1430,1433],{},"¿Por qué usar el ",[145,1422,836],{}," de ",[145,1425,1281],{}," y no el de scikit-learn? Porque el de ",[145,1428,1281],{}," aplica SMOTE ",[122,1431,1432],{},"únicamente en los folds de entrenamiento"," durante la validación cruzada, nunca en los de validación. Si sobremuestreáramos todo el dataset antes de la CV, habría muestras sintéticas derivadas de los datos de validación filtrándose al entrenamiento - otra forma de fuga de datos que inflaría las métricas.",[12,1435,1436,1437,1440,1441,1444],{},"Para esta tarea también comparamos dos modelos: ",[122,1438,1439],{},"Regresión Logística"," (lineal, interpretable) y ",[122,1442,1443],{},"Random Forest Classifier"," (ensemble de árboles).",[46,1446,1448],{"id":1447},"optimización-y-evaluación","Optimización y evaluación",[323,1450,1452],{"id":1451},"ajuste-de-hiperparámetros","Ajuste de hiperparámetros",[12,1454,1455,1456,1459],{},"Cada modelo tiene hiperparámetros que ajustar. Usamos ",[122,1457,1458],{},"GridSearchCV"," integrado directamente en el pipeline de entrenamiento, de modo que cada vez que se entrena un modelo se buscan automáticamente los mejores hiperparámetros. La regresión lineal, al no tener hiperparámetros, se entrena directamente.",[461,1461,1462,1474],{},[464,1463,1464],{},[467,1465,1466,1468,1471],{},[470,1467,472],{},[470,1469,1470],{},"Hiperparámetros explorados",[470,1472,1473],{},"Mejores encontrados",[480,1475,1476,1503,1521],{},[467,1477,1478,1483,1500],{},[485,1479,1480],{},[145,1481,1482],{},"RandomForestRegressor",[485,1484,1485,93,1488,93,1491,93,1494,93,1497],{},[145,1486,1487],{},"n_estimators",[145,1489,1490],{},"max_depth",[145,1492,1493],{},"min_samples_split",[145,1495,1496],{},"min_samples_leaf",[145,1498,1499],{},"max_features",[485,1501,1502],{},"max_depth=10, max_features=sqrt, min_samples_leaf=2, n_estimators=100",[467,1504,1505,1510,1518],{},[485,1506,1507],{},[145,1508,1509],{},"LogisticRegression",[485,1511,1512,93,1515],{},[145,1513,1514],{},"C",[145,1516,1517],{},"l1_ratio",[485,1519,1520],{},"C=0.1, l1_ratio=1.0",[467,1522,1523,1528,1538],{},[485,1524,1525],{},[145,1526,1527],{},"RandomForestClassifier",[485,1529,1530,93,1532,93,1534,93,1536],{},[145,1531,1487],{},[145,1533,1490],{},[145,1535,1496],{},[145,1537,1499],{},[485,1539,1540],{},"max_depth=10, max_features=sqrt, min_samples_leaf=4, n_estimators=200",[323,1542,1544],{"id":1543},"evaluando-los-resultados","Evaluando los resultados",[12,1546,1547,1548,1606,1607,1610],{},"Para la regresión reportamos MAE, RMSE y ",[86,1549,1551,1568],{"className":1550},[955],[86,1552,1554],{"className":1553},[959],[961,1555,1556],{"xmlns":963},[965,1557,1558,1566],{},[968,1559,1560],{},[971,1561,1562,1564],{},[974,1563,976],{},[978,1565,980],{},[982,1567,985],{"encoding":984},[86,1569,1571],{"className":1570,"ariaHidden":990},[989],[86,1572,1574,1577],{"className":1573},[994],[86,1575],{"className":1576,"style":999},[998],[86,1578,1580,1583],{"className":1579},[1003],[86,1581,976],{"className":1582,"style":1008},[1003,1007],[86,1584,1586],{"className":1585},[1012],[86,1587,1589],{"className":1588},[1016],[86,1590,1592],{"className":1591},[1020],[86,1593,1595],{"className":1594,"style":999},[1024],[86,1596,1597,1600],{"style":1027},[86,1598],{"className":1599,"style":1032},[1031],[86,1601,1603],{"className":1602},[1036,1037,1038,1039],[86,1604,980],{"className":1605},[1003,1039],". Para la clasificación, además del F1 de la clase minoritaria y el AUC-ROC, generamos una ",[122,1608,1609],{},"matriz de confusión"," normalizada que nos muestra dónde se equivoca el modelo: cuántos estudiantes en riesgo detecta correctamente y cuántos se le escapan.",[1612,1613,1615],"h4",{"id":1614},"regresión-del-imc","Regresión del IMC",[12,1617,1618],{},"Las métricas sobre el conjunto de prueba, son, bastante reveladoras:",[461,1620,1621,1691],{},[464,1622,1623],{},[467,1624,1625,1627,1629,1631],{},[470,1626,472],{},[470,1628,948],{},[470,1630,944],{},[470,1632,1633],{},[86,1634,1636,1653],{"className":1635},[955],[86,1637,1639],{"className":1638},[959],[961,1640,1641],{"xmlns":963},[965,1642,1643,1651],{},[968,1644,1645],{},[971,1646,1647,1649],{},[974,1648,976],{},[978,1650,980],{},[982,1652,985],{"encoding":984},[86,1654,1656],{"className":1655,"ariaHidden":990},[989],[86,1657,1659,1662],{"className":1658},[994],[86,1660],{"className":1661,"style":999},[998],[86,1663,1665,1668],{"className":1664},[1003],[86,1666,976],{"className":1667,"style":1008},[1003,1007],[86,1669,1671],{"className":1670},[1012],[86,1672,1674],{"className":1673},[1016],[86,1675,1677],{"className":1676},[1020],[86,1678,1680],{"className":1679,"style":999},[1024],[86,1681,1682,1685],{"style":1027},[86,1683],{"className":1684,"style":1032},[1031],[86,1686,1688],{"className":1687},[1036,1037,1038,1039],[86,1689,980],{"className":1690},[1003,1039],[480,1692,1693,1706],{},[467,1694,1695,1697,1700,1703],{},[485,1696,927],{},[485,1698,1699],{},"2.95",[485,1701,1702],{},"3.89",[485,1704,1705],{},"−0.00",[467,1707,1708,1711,1714,1717],{},[485,1709,1710],{},"Random Forest (tuneado)",[485,1712,1713],{},"3.04",[485,1715,1716],{},"3.94",[485,1718,1719],{},"−0.03",[12,1721,1243,1722,1783,1784,1842,1843,1846,1847,61],{},[122,1723,1724,1782],{},[86,1725,1727,1744],{"className":1726},[955],[86,1728,1730],{"className":1729},[959],[961,1731,1732],{"xmlns":963},[965,1733,1734,1742],{},[968,1735,1736],{},[971,1737,1738,1740],{},[974,1739,976],{},[978,1741,980],{},[982,1743,985],{"encoding":984},[86,1745,1747],{"className":1746,"ariaHidden":990},[989],[86,1748,1750,1753],{"className":1749},[994],[86,1751],{"className":1752,"style":999},[998],[86,1754,1756,1759],{"className":1755},[1003],[86,1757,976],{"className":1758,"style":1008},[1003,1007],[86,1760,1762],{"className":1761},[1012],[86,1763,1765],{"className":1764},[1016],[86,1766,1768],{"className":1767},[1020],[86,1769,1771],{"className":1770,"style":999},[1024],[86,1772,1773,1776],{"style":1027},[86,1774],{"className":1775,"style":1032},[1031],[86,1777,1779],{"className":1778},[1036,1037,1038,1039],[86,1780,980],{"className":1781},[1003,1039]," es prácticamente cero (o incluso negativo)",". Un ",[86,1785,1787,1804],{"className":1786},[955],[86,1788,1790],{"className":1789},[959],[961,1791,1792],{"xmlns":963},[965,1793,1794,1802],{},[968,1795,1796],{},[971,1797,1798,1800],{},[974,1799,976],{},[978,1801,980],{},[982,1803,985],{"encoding":984},[86,1805,1807],{"className":1806,"ariaHidden":990},[989],[86,1808,1810,1813],{"className":1809},[994],[86,1811],{"className":1812,"style":999},[998],[86,1814,1816,1819],{"className":1815},[1003],[86,1817,976],{"className":1818,"style":1008},[1003,1007],[86,1820,1822],{"className":1821},[1012],[86,1823,1825],{"className":1824},[1016],[86,1826,1828],{"className":1827},[1020],[86,1829,1831],{"className":1830,"style":999},[1024],[86,1832,1833,1836],{"style":1027},[86,1834],{"className":1835,"style":1032},[1031],[86,1837,1839],{"className":1838},[1036,1037,1038,1039],[86,1840,980],{"className":1841},[1003,1039]," negativo significa que el modelo predice ",[901,1844,1845],{},"peor"," que simplemente usar siempre el IMC promedio. En otras palabras: los hábitos de alimentación, higiene y actividad física que reportaron los estudiantes ",[122,1848,1849],{},"no contienen información suficiente para predecir su IMC",[12,1851,1852],{},"Recordemos que deliberadamente excluimos el peso y la estatura. El IMC de un adolescente depende fuertemente de factores que no están en estas variables: genética, etapa de desarrollo puberal, composición corporal, y la imprecisión inherente del comportamiento que ellos mismos reportan. El error medio (MAE ≈ 3 puntos de IMC) es grande considerando que la desviación del IMC en la muestra ronda los 4 puntos.",[12,1854,1855,1856,61],{},"El modelo nos confirma, con datos, que ",[122,1857,1858],{},"el estilo de vida autorreportado explica muy poco de la variabilidad del IMC",[1612,1860,1862],{"id":1861},"clasificación-del-riesgo-de-salud-mental","Clasificación del riesgo de salud mental",[12,1864,1865],{},"Aquí los resultados son mucho más útiles:",[461,1867,1868,1885],{},[464,1869,1870],{},[467,1871,1872,1874,1877,1880,1883],{},[470,1873,472],{},[470,1875,1876],{},"Accuracy",[470,1878,1879],{},"F1 (clase en riesgo)",[470,1881,1882],{},"Recall (clase en riesgo)",[470,1884,1252],{},[480,1886,1887,1910],{},[467,1888,1889,1892,1895,1900,1905],{},[485,1890,1891],{},"Regresión Logística (tuneada)",[485,1893,1894],{},"0.78",[485,1896,1897],{},[122,1898,1899],{},"0.54",[485,1901,1902],{},[122,1903,1904],{},"0.62",[485,1906,1907],{},[122,1908,1909],{},"0.81",[467,1911,1912,1914,1917,1920,1923],{},[485,1913,1710],{},[485,1915,1916],{},"0.82",[485,1918,1919],{},"0.43",[485,1921,1922],{},"0.32",[485,1924,1909],{},[12,1926,1927,1928,1931,1932,1935],{},"Aunque el Random Forest tiene mayor ",[901,1929,1930],{},"accuracy"," (0.82), eso es engañoso: alcanza esa cifra prediciendo bien la clase mayoritaria (sin riesgo) pero fallando en la que importa — su recall sobre la clase en riesgo es apenas 0.32 (solo detecta 1 de cada 3 estudiantes en riesgo). La ",[122,1933,1934],{},"Regresión Logística es el mejor modelo"," para nuestro objetivo, con un recall de 0.62 sobre la clase en riesgo y un AUC-ROC de 0.81. Este es justo el caso donde elegir la métrica correcta cambia qué modelo consideramos \"mejor\".",[12,1937,1938,1939,1941],{},"La ",[122,1940,1609],{}," del modelo logístico muestra el balance entre detectar verdaderos casos de riesgo y las falsas alarmas:",[12,1943,1944,1949],{},[1945,1946],"img",{"alt":1947,"src":1948},"Matriz de confusión - Regresión Logística","\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013\u002Fshared\u002Fconfusion_matrix_logistic.webp",[901,1950,1951],{},"Matriz de confusión",[12,1953,1954,1955,1958,1959,1962],{},"También analizamos la ",[122,1956,1957],{},"importancia de características",", que nos dice qué factores pesan más en cada predicción. Para Random Forest usamos su atributo ",[145,1960,1961],{},"feature_importances_","; para los modelos lineales, el valor absoluto de los coeficientes.",[12,1964,1965,1969],{},[1945,1966],{"alt":1967,"src":1968},"Importancia de características - Riesgo de salud mental","\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013\u002Fshared\u002Ffeature_importance_mental_health.webp",[901,1970,1971],{},"Importancia de características",[12,1973,1974],{},"Los factores afectivos (soledad frecuente e insomnio por preocupación) y el consumo de sustancias aparecen entre los predictores más fuertes del riesgo de suicidalidad, mientras que el apoyo familiar y escolar actúa en la dirección opuesta, como factor protector.",[323,1976,1978],{"id":1977},"análisis-de-ablación","Análisis de ablación",[12,1980,1981,1982,1985],{},"Como análisis complementario hacemos un estudio de ",[122,1983,1984],{},"ablación leave-one-group-out",". Agrupamos las variables por dominio (demografía, dieta, violencia, sustancias, apoyo social, etc.) y entrenamos el modelo quitando un grupo a la vez. Comparando la caída de desempeño respecto al modelo completo, medimos cuánto aporta cada dominio.",[12,1987,1988,1989,1992],{},"Partiendo de un F1 base de ",[122,1990,1991],{},"0.498",", esto fue lo que pasó al retirar cada grupo:",[461,1994,1995,2008],{},[464,1996,1997],{},[467,1998,1999,2002,2005],{},[470,2000,2001],{},"Grupo retirado",[470,2003,2004],{},"F1 resultante",[470,2006,2007],{},"Δ vs. base",[480,2009,2010,2022,2038,2049,2060,2071,2081,2092],{},[467,2011,2012,2017,2019],{},[485,2013,2014],{},[901,2015,2016],{},"(ninguno - base)",[485,2018,1991],{},[485,2020,2021],{},"-",[467,2023,2024,2030,2033],{},[485,2025,2026,2029],{},[122,2027,2028],{},"affective"," (soledad, insomnio)",[485,2031,2032],{},"0.444",[485,2034,2035],{},[122,2036,2037],{},"−0.054",[467,2039,2040,2043,2046],{},[485,2041,2042],{},"substance_use (alcohol, drogas, sexo)",[485,2044,2045],{},"0.479",[485,2047,2048],{},"−0.019",[467,2050,2051,2054,2057],{},[485,2052,2053],{},"violence_bullying",[485,2055,2056],{},"0.495",[485,2058,2059],{},"−0.003",[467,2061,2062,2065,2068],{},[485,2063,2064],{},"diet_nutrition",[485,2066,2067],{},"0.497",[485,2069,2070],{},"−0.001",[467,2072,2073,2076,2078],{},[485,2074,2075],{},"demographics (edad, sexo, grado)",[485,2077,1991],{},[485,2079,2080],{},"+0.000",[467,2082,2083,2086,2089],{},[485,2084,2085],{},"physical_activity",[485,2087,2088],{},"0.503",[485,2090,2091],{},"+0.005",[467,2093,2094,2097,2100],{},[485,2095,2096],{},"social_support",[485,2098,2099],{},"0.507",[485,2101,2102],{},"+0.009",[12,2104,2105,2106,2109,2110,2113],{},"El resultado más claro: el grupo ",[122,2107,2108],{},"afectivo"," (soledad e insomnio por preocupación) es con diferencia el más valioso, quitarlo hace caer el F1 en 0.054. Esto valida que a pesar de que usamos (y por ende ignoramos después para evitar data leakage) las variables de suicidalidad, dejamos libres la soledad y el insomnio para usarlas como predictores, y resultaron ser justo las más informativos. El consumo de sustancias también aporta. En cambio, retirar actividad física o apoyo social ",[901,2111,2112],{},"mejora"," ligeramente el modelo, lo que sugiere que esos grupos aportan más ruido que señal para predecir riesgo.",[46,2115,2117],{"id":2116},"conclusión","Conclusión",[12,2119,2120],{},"A lo largo de este pipeline construimos dos modelos sobre los mismos datos pero con propósitos muy distintos, y obtuvimos dos resultados muy diferentes:",[30,2122,2123,2187],{},[33,2124,1243,2125,606,2128,2186],{},[122,2126,2127],{},"modelo de IMC fracasó en predecir",[86,2129,2131,2148],{"className":2130},[955],[86,2132,2134],{"className":2133},[959],[961,2135,2136],{"xmlns":963},[965,2137,2138,2146],{},[968,2139,2140],{},[971,2141,2142,2144],{},[974,2143,976],{},[978,2145,980],{},[982,2147,985],{"encoding":984},[86,2149,2151],{"className":2150,"ariaHidden":990},[989],[86,2152,2154,2157],{"className":2153},[994],[86,2155],{"className":2156,"style":999},[998],[86,2158,2160,2163],{"className":2159},[1003],[86,2161,976],{"className":2162,"style":1008},[1003,1007],[86,2164,2166],{"className":2165},[1012],[86,2167,2169],{"className":2168},[1016],[86,2170,2172],{"className":2171},[1020],[86,2173,2175],{"className":2174,"style":999},[1024],[86,2176,2177,2180],{"style":1027},[86,2178],{"className":2179,"style":1032},[1031],[86,2181,2183],{"className":2182},[1036,1037,1038,1039],[86,2184,980],{"className":2185},[1003,1039]," ≈ 0), y nos hace concluir que el comportamiento autorreportado de alimentación e higiene no basta para inferir el IMC de un adolescente.",[33,2188,1243,2189,2192],{},[122,2190,2191],{},"modelo de riesgo de salud mental funcionó razonablemente bien"," (AUC-ROC de 0.81, recall de 0.62 sobre la clase en riesgo), y la ablación nos mostró que los síntomas afectivos son sus predictores más fuertes.",[12,2194,2195],{},"También resaltar algunas decisiones técnicas que tomamos en el camino:",[30,2197,2198,2201,2204,2211],{},[33,2199,2200],{},"Tratar los valores faltantes (y los centinelas disfrazados de números válidos) antes que nada.",[33,2202,2203],{},"Detenerse a analizar y elegir entre variables correlacionadas para evitar colinealidad.",[33,2205,2206,2207,2210],{},"Encapsular todo el preprocesamiento ",[122,2208,2209],{},"dentro"," del pipeline.",[33,2212,2213,2214,2216],{},"Elegir métricas honestas cuando las clases están desbalanceadas: el modelo con mayor ",[901,2215,1930],{}," no fue el mejor para nuestro objetivo.",[2218,2219,2220],"style",{},"html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .sfsYZ, html code.shiki .sfsYZ{--shiki-default:#A65E2B;--shiki-dark:#C99076}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}html pre.shiki code .s5TCs, html code.shiki .s5TCs{--shiki-default:#AB5959;--shiki-dark:#CB7676}html pre.shiki code .s_xSY, html code.shiki .s_xSY{--shiki-default:#59873A;--shiki-dark:#80A665}html pre.shiki code .s9nN2, html code.shiki .s9nN2{--shiki-default:#B07D48;--shiki-dark:#BD976A}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .scnC2, html code.shiki .scnC2{--shiki-default:#B5695977;--shiki-dark:#C98A7D77}html pre.shiki code .spP0B, html code.shiki .spP0B{--shiki-default:#B56959;--shiki-dark:#C98A7D}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}",{"title":169,"searchDepth":205,"depth":205,"links":2222},[2223,2224,2225,2226,2230,2234,2235,2236,2240,2248],{"id":48,"depth":192,"text":49},{"id":77,"depth":192,"text":78},{"id":111,"depth":192,"text":112},{"id":140,"depth":192,"text":124,"children":2227},[2228,2229],{"id":325,"depth":205,"text":326},{"id":405,"depth":205,"text":406},{"id":540,"depth":192,"text":541,"children":2231},[2232,2233],{"id":547,"depth":205,"text":548},{"id":653,"depth":205,"text":654},{"id":826,"depth":192,"text":827},{"id":913,"depth":192,"text":914},{"id":1220,"depth":192,"text":136,"children":2237},[2238,2239],{"id":1230,"depth":205,"text":1231},{"id":1256,"depth":205,"text":1257},{"id":1447,"depth":192,"text":1448,"children":2241},[2242,2243,2247],{"id":1451,"depth":205,"text":1452},{"id":1543,"depth":205,"text":1544,"children":2244},[2245,2246],{"id":1614,"depth":212,"text":1615},{"id":1861,"depth":212,"text":1862},{"id":1977,"depth":205,"text":1978},{"id":2116,"depth":192,"text":2117},"2026-06-25","md","\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013\u002Fshared\u002Frisk-prediction-model.webp","2026-06-26",{},21,"\u002Fblog\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013",{"title":6,"description":14},{"loc":2258,"priority":2259,"lastmod":2252},"\u002Fes\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013",0.7,"risk-prediction-model-adolescents-sv-2013","blog\u002Fblog\u002Frisk-prediction-model-adolescents-sv-2013","En este artículo, crearemos modelos de predicción de riesgo en adolescentes utilizando el conjunto de datos del Global School-Based Student Health Survey 2013 para El Salvador.",[2264,2265,2266,2267,2268,2269,2270,2271],"machine learning","data science","predicción de riesgo","adolescentes","salud pública","global school-based student health survey","gshs 2013","el salvador","Yw90E_xF3OtFwwP9_yDB6PVZYgmITN7aZF41BnJgkxc",{"id":2274,"title":2275,"author":7,"body":2276,"date":3610,"description":3611,"extension":2250,"image":3612,"lastmod":3613,"meta":3614,"navigation":208,"order":3615,"path":3616,"seo":3617,"sitemap":3618,"slug":3620,"stem":3621,"summary":3622,"tags":3623,"__hash__":3628},"content_es\u002Fblog\u002Fblog\u002Fai-capabilities-and-limitations.md","Capacidades y Limitaciones de la Inteligencia Artificial",{"type":9,"value":2277,"toc":3603},[2278,2287,2289,2291,2295,2306,2315,2319,2322,2339,2342,2347,2360,2363,2389,2394,2398,2401,2446,2449,2454,2465,2469,2472,2475,2489,2495,2996,2999,3007,3013,3016,3024,3027,3035,3038,3046,3049,3056,3062,3065,3070,3073,3078,3081,3088,3095,3103,3106,3109,3116,3119,3126,3133,3136,3144,3147,3161,3167,3170,3271,3274,3358,3361,3364,3370,3373,3399,3405,3414,3417,3424,3427,3438,3441,3452,3455,3462,3465,3538,3540,3580,3583,3586,3592,3595,3598],[12,2279,2280,2281,2286],{},"Mientras exploraba los cursos de Anthropic me encontré con un artículo que me llamó la atención: ",[22,2282,2285],{"href":2283,"rel":2284},"https:\u002F\u002Fanthropic.skilljar.com\u002Fai-capabilities-and-limitations",[26],"Capabilities and Limitations of AI",". Asi que quise hacer un recorrido sobre las bases y lo que es actualmente la inteligencia artificial.",[40,2288],{},[43,2290],{},[46,2292,2294],{"id":2293},"cómo-sabe-un-modelo-que-responder","¿Cómo sabe un modelo que responder?",[12,2296,2297,2298,2301,2302,2305],{},"Los modelos de IA que se han hecho tan virales, son modelos de IA generativa, estos generan salidas basadas en patrones aprendidos a partir de grandes cantidades de datos, no tienen comprensión real del mundo, sino que ",[122,2299,2300],{},"predicen la siguiente palabra o secuencia de palabras"," basándose en las ",[122,2303,2304],{},"probabilidades"," derivadas de su entrenamiento. Por lo tanto, la salida de un modelo de IA es una combinación de patrones estadísticos y asociaciones aprendidas, sin una verdadera comprensión semántica o contextual.",[16,2307,2308],{},[12,2309,2310,2311,2314],{},"Entender que la IA es un motor de ",[122,2312,2313],{},"PREDICCIÓN"," es fundamental para entender sus capacidades y limitaciones. No es un ser consciente ni tiene intenciones propias, sino que simplemente genera respuestas basadas en patrones aprendidos.",[323,2316,2318],{"id":2317},"el-carácter-de-un-modelo","El carácter de un modelo",[12,2320,2321],{},"Todos hemos notado que cada modelo tiene su \"forma\" de responder.\nCuando se entrena un modelo de IA, se le proporciona una gran cantidad de datos para que aprenda a reconocer patrones y asociaciones, y se lleva a cabo en 2 etapas:",[30,2323,2324],{},[33,2325,2326,2327,2330,2331,2334,2335,2338],{},"En el ",[122,2328,2329],{},"pre-entrenamiento (pretraining)",": el modelo aprende a predecir la siguiente palabra en una secuencia de texto. Es dónde aprende lo que se conoce como ",[122,2332,2333],{},"Next Token Prediction",". En este es un ",[122,2336,2337],{},"completador de texto",", no tiene una tarea específica, simplemente aprende a generar texto coherente basado en los datos de entrenamiento, no sabe sobre \"ayudarte a escribir código\" o \"responder preguntas\".",[12,2340,2341],{},"En el curso de Anthropic se menciona como ejemplo que si en este punto se le pregunta al modelo \"¿Cuál es la capital de Francia?\", el modelo podría responder \"París\" y luego continuar con ¿Cuál es la capital de Alemania? \"Berlín\", ¿Cuál es la capital de España? \"Madrid\", y así sucesivamente, porque es un caso común en quizes de geografía, pero no tiene una comprensión real de lo que es una capital o un país, simplemente ha aprendido a asociar ciertas \"palabras\" con otras.",[16,2343,2344],{},[12,2345,2346],{},"Está completando texto, de la forma más estadísticamente probable",[30,2348,2349],{},[33,2350,2351,2352,2355,2356,2359],{},"Luego sigue el ",[122,2353,2354],{},"ajuste fino (fine-tuning)",": en esta etapa, el modelo se entrena con datos más específicos y se le muestra cómo responder a ciertas preguntas o realizar tareas específicas. Aquí es donde el modelo aprende como debería ser una \"buena respuesta\" a una pregunta, y se le da un marco de referencia para entender lo que se espera de él. Aqui se suelen utilizar técnicas de ",[122,2357,2358],{},"Reforzamiento con Retroalimentación Humana (RLHF)",", donde se le da retroalimentación al modelo sobre la calidad de sus respuestas, lo que ayuda a mejorar su rendimiento en tareas específicas.",[12,2361,2362],{},"En este camino de convertirse en un \"asistente\" el modelo pasa a tener ciertos \"problemas\":",[30,2364,2365,2371,2377,2383],{},[33,2366,2367,2370],{},[122,2368,2369],{},"Sycophancy",": el modelo puede aprender a ser complaciente y a generar respuestas que son agradables para el usuario, esto más de una vez lo hemos notado, y tiene mucho que ver con su entrenamiento.",[33,2372,2373,2376],{},[122,2374,2375],{},"Verbosity",": el modelo puede generar respuestas largas y detalladas, incluso cuando no es necesario.",[33,2378,2379,2382],{},[122,2380,2381],{},"Overcaution",": el modelo puede ser demasiado cauteloso y evitar responder a ciertas preguntas o realizar ciertas tareas, incluso cuando es capaz de hacerlo.",[33,2384,2385,2388],{},[122,2386,2387],{},"Lose confidence calibration",": el modelo puede perder la capacidad de calibrar su confianza en sus respuestas, lo que puede llevar a generar respuestas incorrectas con alta confianza.",[16,2390,2391],{},[12,2392,2393],{},"La manera en la que se realiza el fine-tuning impacta en que tan complaciente, detallado, confidente o cauteloso puede ser un modelo.",[323,2395,2397],{"id":2396},"la-línea-entre-capacidades-y-limitaciones","La línea entre capacidades y limitaciones",[12,2399,2400],{},"El proceso generativo dentro del modelo siempre es el mismo, lo que cambia es que tan bien \"conoce\" sobre lo que se le pregunta, si se le pregunta sobre un tema extremadamente específico, dará una respuesta con el mismo tono y seguridad que cualquier otra pregunta, pero la calidad de la respuesta será muy baja.",[30,2402,2403,2426],{},[33,2404,2405,2408,2409],{},[122,2406,2407],{},"La zona de capacidad"," es el área donde el modelo tiene un buen conocimiento y puede generar respuestas de alta calidad. En esta zona, el modelo puede responder preguntas con precisión y coherencia, y puede realizar tareas específicas de manera efectiva:",[30,2410,2411,2414,2417,2420,2423],{},[33,2412,2413],{},"Hacer resúmenes",[33,2415,2416],{},"Reformular texto",[33,2418,2419],{},"Escribir sobre conceptos comunes",[33,2421,2422],{},"Redactar en un estilo familiar",[33,2424,2425],{},"Programar en un lenguaje de programación común",[33,2427,2428,2431,2432],{},[122,2429,2430],{},"La zona de limitación"," es el área donde el modelo tiene un conocimiento limitado o nulo, y puede generar respuestas de baja calidad:",[30,2433,2434,2437,2440,2443],{},[33,2435,2436],{},"Territorios nuevos: temas nuevos que no han sido ampliamente cubiertos en los datos de entrenamiento del modelo (como preguntarle sobre la nueva versión de ese framework que salió hace 2 días).",[33,2438,2439],{},"Temas poco conocidos: temas que son raros o poco comunes, como un paper académico muy específico o un tema de nicho que no ha sido ampliamente discutido en los datos de entrenamiento del modelo.",[33,2441,2442],{},"Temas cambiantes: temas que están en constante evolución o cambio, como la tecnología o las noticias actuales, donde la información puede volverse obsoleta rápidamente.",[33,2444,2445],{},"Sesgos y estereotipos: el modelo puede reflejar sesgos presentes en los datos de entrenamiento, lo que puede llevar a generar respuestas que son inapropiadas o ofensivas.",[12,2447,2448],{},"La calidad de la respuesta dependerá de a qué zona esté más cerca la pregunta.",[16,2450,2451],{},[12,2452,2453],{},"No importa que tan confidente o detallada sea la respuesta, el tono no es una señal de calidad.\nSiempre trata las respuestas como borradores a verificar.",[12,2455,2456,2457,2460,2461,2464],{},"Para ayudar a reducir el riesgo de obtener respuestas de baja calidad existen algunas estrategias como el ",[122,2458,2459],{},"Web searching"," (el modelo puede buscar información en la web para obtener datos más actualizados o específicos) o el uso de ",[122,2462,2463],{},"MCPs"," (Model Context Protocols, para interactuar con otros modelos o herramientas).",[323,2466,2468],{"id":2467},"next-token-prediction","Next token prediction",[12,2470,2471],{},"Veámos un ejemplo de cómo funciona el proceso de predicción de la siguiente \"palabra\" utilizando cadenas de Markov simples, que es una forma de modelar la probabilidad de que una palabra siga a otra.",[12,2473,2474],{},"Supongamos que entrenamos un modelo con estas frases:",[30,2476,2477,2480,2483,2486],{},[33,2478,2479],{},"\"me gusta programar en python\"",[33,2481,2482],{},"\"me gusta aprender inteligencia artificial\"",[33,2484,2485],{},"\"programar en equipo es divertido\"",[33,2487,2488],{},"\"aprender cosas nuevas es útil\"",[12,2490,2491,2492,61],{},"A partir de esas frases, contamos qué palabra aparece después de otra.\nCon eso construye una ",[122,2493,2494],{},"matriz de transición",[461,2496,2497,2545],{},[464,2498,2499],{},[467,2500,2501,2504,2507,2510,2513,2516,2518,2521,2524,2527,2530,2533,2536,2539,2542],{},[470,2502,2503],{},"Palabra",[470,2505,2506],{},"me",[470,2508,2509],{},"gusta",[470,2511,2512],{},"programar",[470,2514,2515],{},"en",[470,2517,168],{},[470,2519,2520],{},"aprender",[470,2522,2523],{},"inteligencia",[470,2525,2526],{},"artificial",[470,2528,2529],{},"equipo",[470,2531,2532],{},"es",[470,2534,2535],{},"divertido",[470,2537,2538],{},"cosas",[470,2540,2541],{},"nuevas",[470,2543,2544],{},"útil",[480,2546,2547,2580,2612,2644,2676,2708,2740,2772,2804,2836,2868,2900,2932,2964],{},[467,2548,2549,2551,2554,2556,2558,2560,2562,2564,2566,2568,2570,2572,2574,2576,2578],{},[485,2550,2506],{},[485,2552,2553],{},"0",[485,2555,980],{},[485,2557,2553],{},[485,2559,2553],{},[485,2561,2553],{},[485,2563,2553],{},[485,2565,2553],{},[485,2567,2553],{},[485,2569,2553],{},[485,2571,2553],{},[485,2573,2553],{},[485,2575,2553],{},[485,2577,2553],{},[485,2579,2553],{},[467,2581,2582,2584,2586,2588,2590,2592,2594,2596,2598,2600,2602,2604,2606,2608,2610],{},[485,2583,2509],{},[485,2585,2553],{},[485,2587,2553],{},[485,2589,802],{},[485,2591,2553],{},[485,2593,2553],{},[485,2595,802],{},[485,2597,2553],{},[485,2599,2553],{},[485,2601,2553],{},[485,2603,2553],{},[485,2605,2553],{},[485,2607,2553],{},[485,2609,2553],{},[485,2611,2553],{},[467,2613,2614,2616,2618,2620,2622,2624,2626,2628,2630,2632,2634,2636,2638,2640,2642],{},[485,2615,2512],{},[485,2617,2553],{},[485,2619,2553],{},[485,2621,2553],{},[485,2623,980],{},[485,2625,2553],{},[485,2627,2553],{},[485,2629,2553],{},[485,2631,2553],{},[485,2633,2553],{},[485,2635,2553],{},[485,2637,2553],{},[485,2639,2553],{},[485,2641,2553],{},[485,2643,2553],{},[467,2645,2646,2648,2650,2652,2654,2656,2658,2660,2662,2664,2666,2668,2670,2672,2674],{},[485,2647,2515],{},[485,2649,2553],{},[485,2651,2553],{},[485,2653,2553],{},[485,2655,2553],{},[485,2657,802],{},[485,2659,2553],{},[485,2661,2553],{},[485,2663,2553],{},[485,2665,802],{},[485,2667,2553],{},[485,2669,2553],{},[485,2671,2553],{},[485,2673,2553],{},[485,2675,2553],{},[467,2677,2678,2680,2682,2684,2686,2688,2690,2692,2694,2696,2698,2700,2702,2704,2706],{},[485,2679,168],{},[485,2681,2553],{},[485,2683,2553],{},[485,2685,2553],{},[485,2687,2553],{},[485,2689,2553],{},[485,2691,2553],{},[485,2693,2553],{},[485,2695,2553],{},[485,2697,2553],{},[485,2699,2553],{},[485,2701,2553],{},[485,2703,2553],{},[485,2705,2553],{},[485,2707,2553],{},[467,2709,2710,2712,2714,2716,2718,2720,2722,2724,2726,2728,2730,2732,2734,2736,2738],{},[485,2711,2520],{},[485,2713,2553],{},[485,2715,2553],{},[485,2717,2553],{},[485,2719,2553],{},[485,2721,2553],{},[485,2723,2553],{},[485,2725,802],{},[485,2727,2553],{},[485,2729,2553],{},[485,2731,2553],{},[485,2733,2553],{},[485,2735,802],{},[485,2737,2553],{},[485,2739,2553],{},[467,2741,2742,2744,2746,2748,2750,2752,2754,2756,2758,2760,2762,2764,2766,2768,2770],{},[485,2743,2523],{},[485,2745,2553],{},[485,2747,2553],{},[485,2749,2553],{},[485,2751,2553],{},[485,2753,2553],{},[485,2755,2553],{},[485,2757,2553],{},[485,2759,802],{},[485,2761,2553],{},[485,2763,2553],{},[485,2765,2553],{},[485,2767,2553],{},[485,2769,2553],{},[485,2771,2553],{},[467,2773,2774,2776,2778,2780,2782,2784,2786,2788,2790,2792,2794,2796,2798,2800,2802],{},[485,2775,2526],{},[485,2777,2553],{},[485,2779,2553],{},[485,2781,2553],{},[485,2783,2553],{},[485,2785,2553],{},[485,2787,2553],{},[485,2789,2553],{},[485,2791,2553],{},[485,2793,2553],{},[485,2795,2553],{},[485,2797,2553],{},[485,2799,2553],{},[485,2801,2553],{},[485,2803,2553],{},[467,2805,2806,2808,2810,2812,2814,2816,2818,2820,2822,2824,2826,2828,2830,2832,2834],{},[485,2807,2529],{},[485,2809,2553],{},[485,2811,2553],{},[485,2813,2553],{},[485,2815,2553],{},[485,2817,2553],{},[485,2819,2553],{},[485,2821,2553],{},[485,2823,2553],{},[485,2825,2553],{},[485,2827,802],{},[485,2829,2553],{},[485,2831,2553],{},[485,2833,2553],{},[485,2835,2553],{},[467,2837,2838,2840,2842,2844,2846,2848,2850,2852,2854,2856,2858,2860,2862,2864,2866],{},[485,2839,2532],{},[485,2841,2553],{},[485,2843,2553],{},[485,2845,2553],{},[485,2847,2553],{},[485,2849,2553],{},[485,2851,2553],{},[485,2853,2553],{},[485,2855,2553],{},[485,2857,2553],{},[485,2859,2553],{},[485,2861,802],{},[485,2863,2553],{},[485,2865,2553],{},[485,2867,802],{},[467,2869,2870,2872,2874,2876,2878,2880,2882,2884,2886,2888,2890,2892,2894,2896,2898],{},[485,2871,2535],{},[485,2873,2553],{},[485,2875,2553],{},[485,2877,2553],{},[485,2879,2553],{},[485,2881,2553],{},[485,2883,2553],{},[485,2885,2553],{},[485,2887,2553],{},[485,2889,2553],{},[485,2891,2553],{},[485,2893,2553],{},[485,2895,2553],{},[485,2897,2553],{},[485,2899,2553],{},[467,2901,2902,2904,2906,2908,2910,2912,2914,2916,2918,2920,2922,2924,2926,2928,2930],{},[485,2903,2538],{},[485,2905,2553],{},[485,2907,2553],{},[485,2909,2553],{},[485,2911,2553],{},[485,2913,2553],{},[485,2915,2553],{},[485,2917,2553],{},[485,2919,2553],{},[485,2921,2553],{},[485,2923,2553],{},[485,2925,2553],{},[485,2927,2553],{},[485,2929,802],{},[485,2931,2553],{},[467,2933,2934,2936,2938,2940,2942,2944,2946,2948,2950,2952,2954,2956,2958,2960,2962],{},[485,2935,2541],{},[485,2937,2553],{},[485,2939,2553],{},[485,2941,2553],{},[485,2943,2553],{},[485,2945,2553],{},[485,2947,2553],{},[485,2949,2553],{},[485,2951,2553],{},[485,2953,2553],{},[485,2955,802],{},[485,2957,2553],{},[485,2959,2553],{},[485,2961,2553],{},[485,2963,2553],{},[467,2965,2966,2968,2970,2972,2974,2976,2978,2980,2982,2984,2986,2988,2990,2992,2994],{},[485,2967,2544],{},[485,2969,2553],{},[485,2971,2553],{},[485,2973,2553],{},[485,2975,2553],{},[485,2977,2553],{},[485,2979,2553],{},[485,2981,2553],{},[485,2983,2553],{},[485,2985,2553],{},[485,2987,2553],{},[485,2989,2553],{},[485,2991,2553],{},[485,2993,2553],{},[485,2995,2553],{},[12,2997,2998],{},"Ahora imaginemos que queremos generar texto comenzando con:",[16,3000,3001],{},[12,3002,3003,3004,576],{},"\"me gusta ",[122,3005,3006],{},"_",[12,3008,3009,3010,61],{},"El modelo revisa la fila de ",[122,3011,3012],{},"\"gusta\"",[12,3014,3015],{},"Ve que después de \"gusta\" aparecieron:",[30,3017,3018,3021],{},[33,3019,3020],{},"\"programar\" - 1 vez",[33,3022,3023],{},"\"aprender\" - 1 vez",[12,3025,3026],{},"Entonces ambas palabras tienen la misma probabilidad:",[30,3028,3029,3032],{},[33,3030,3031],{},"P(programar | gusta) = 50%",[33,3033,3034],{},"P(aprender | gusta) = 50%",[12,3036,3037],{},"El modelo podría continuar de cualquiera de estas maneras:",[30,3039,3040,3043],{},[33,3041,3042],{},"\"me gusta programar...\"",[33,3044,3045],{},"\"me gusta aprender...\"",[12,3047,3048],{},"Si el modelo elige:",[16,3050,3051],{},[12,3052,3053,3054,576],{},"\"me gusta programar ",[122,3055,3006],{},[12,3057,3058,3059,61],{},"Entonces revisa la fila de ",[122,3060,3061],{},"\"programar\"",[12,3063,3064],{},"Observa que después de \"programar\" aparecieron:",[30,3066,3067],{},[33,3068,3069],{},"\"en\" - 2 veces",[12,3071,3072],{},"Por lo que es 100% probable que la siguiente palabra sea \"en\":",[30,3074,3075],{},[33,3076,3077],{},"P(en | programar) = 100%",[12,3079,3080],{},"Ahora tenemos:",[16,3082,3083],{},[12,3084,3085,3086,576],{},"\"me gusta programar en ",[122,3087,3006],{},[12,3089,3090,3091,3094],{},"Revisamos la fila de ",[122,3092,3093],{},"\"en\""," y vemos que después de \"en\" aparecieron:",[30,3096,3097,3100],{},[33,3098,3099],{},"\"python\" - 1 vez",[33,3101,3102],{},"\"equipo\" - 1 vez",[12,3104,3105],{},"De nuevo, ambas tienen 50% de probabilidad.",[12,3107,3108],{},"El texto podría continuar como:",[30,3110,3111,3113],{},[33,3112,2479],{},[33,3114,3115],{},"\"me gusta programar en equipo\"",[12,3117,3118],{},"Entonces, estamos aprendiendo patrones observando textos, y luego usamos probabilidades para decidir la siguiente palabra hasta formar una oración completa.",[12,3120,3121,3122,3125],{},"Para el caso de los LLMs, el proceso podríamos decir que es similar pero mucho más complejo, ya que no solo consideran la \"palabra\" anterior, sino todo el contexto disponible dentro de su ",[122,3123,3124],{},"ventana de contexto"," (todo lo que puede ver), además de no ser solo \"palabras\", si no tokens, que pueden ser palabras, partes de palabras o incluso caracteres.",[12,3127,3128,3129,3132],{},"Y tampoco trabajan directamente con esas palabras o caracteres como texto plano, cada token primero se convierte en un ",[122,3130,3131],{},"vector numérico"," dentro de un espacio de muchas dimensiones.",[12,3134,3135],{},"Por ejemplo:",[164,3137,3142],{"className":3138,"code":3140,"language":3141},[3139],"language-text","\"python\" --> [0.12, -0.44, 1.03, ..., 0.91]\n","text",[145,3143,3140],{"__ignoreMap":169},[12,3145,3146],{},"Ese vector puede tener X dimensiones dependiendo del modelo:",[30,3148,3149,3152,3155,3158],{},[33,3150,3151],{},"768 dimensiones",[33,3153,3154],{},"1024 dimensiones",[33,3156,3157],{},"4096 dimensiones",[33,3159,3160],{},"8192 dimensiones",[12,3162,3163,3164,3166],{},"Por ejemplo cuando decimos que un modelo usa un espacio de ",[122,3165,3154],{}," significa que cada token es representado mediante un vector de 1024 números.",[12,3168,3169],{},"Matemáticamente sería algo como:",[86,3171,3174],{"className":3172},[3173],"katex-display",[86,3175,3177,3205],{"className":3176},[955],[86,3178,3180],{"className":3179},[959],[961,3181,3183],{"xmlns":963,"display":3182},"block",[965,3184,3185,3202],{},[968,3186,3187,3190,3194],{},[974,3188,3189],{},"x",[3191,3192,3193],"mo",{},"∈",[971,3195,3196,3199],{},[974,3197,976],{"mathvariant":3198},"double-struck",[978,3200,3201],{},"1024",[982,3203,3204],{"encoding":984},"x \\in \\mathbb{R}^{1024}",[86,3206,3208,3230],{"className":3207,"ariaHidden":990},[989],[86,3209,3211,3215,3218,3223,3227],{"className":3210},[994],[86,3212],{"className":3213,"style":3214},[998],"height:0.5782em;vertical-align:-0.0391em;",[86,3216,3189],{"className":3217},[1003,1007],[86,3219],{"className":3220,"style":3222},[3221],"mspace","margin-right:0.2778em;",[86,3224,3193],{"className":3225},[3226],"mrel",[86,3228],{"className":3229,"style":3222},[3221],[86,3231,3233,3237],{"className":3232},[994],[86,3234],{"className":3235,"style":3236},[998],"height:0.8641em;",[86,3238,3240,3244],{"className":3239},[1003],[86,3241,976],{"className":3242},[1003,3243],"mathbb",[86,3245,3247],{"className":3246},[1012],[86,3248,3250],{"className":3249},[1016],[86,3251,3253],{"className":3252},[1020],[86,3254,3256],{"className":3255,"style":3236},[1024],[86,3257,3259,3262],{"style":3258},"top:-3.113em;margin-right:0.05em;",[86,3260],{"className":3261,"style":1032},[1031],[86,3263,3265],{"className":3264},[1036,1037,1038,1039],[86,3266,3268],{"className":3267},[1003,1039],[86,3269,3201],{"className":3270},[1003,1039],[12,3272,3273],{},"Donde:",[30,3275,3276,3279],{},[33,3277,3278],{},"(x) es el embedding del token",[33,3280,3281,3357],{},[86,3282,3284,3307],{"className":3283},[955],[86,3285,3287],{"className":3286},[959],[961,3288,3289],{"xmlns":963},[965,3290,3291,3304],{},[968,3292,3293,3296,3302],{},[3191,3294,243],{"stretchy":3295},"false",[971,3297,3298,3300],{},[974,3299,976],{"mathvariant":3198},[978,3301,3201],{},[3191,3303,867],{"stretchy":3295},[982,3305,3306],{"encoding":984},"(\\mathbb{R}^{1024})",[86,3308,3310],{"className":3309,"ariaHidden":990},[989],[86,3311,3313,3317,3321,3353],{"className":3312},[994],[86,3314],{"className":3315,"style":3316},[998],"height:1.0641em;vertical-align:-0.25em;",[86,3318,243],{"className":3319},[3320],"mopen",[86,3322,3324,3327],{"className":3323},[1003],[86,3325,976],{"className":3326},[1003,3243],[86,3328,3330],{"className":3329},[1012],[86,3331,3333],{"className":3332},[1016],[86,3334,3336],{"className":3335},[1020],[86,3337,3339],{"className":3338,"style":999},[1024],[86,3340,3341,3344],{"style":1027},[86,3342],{"className":3343,"style":1032},[1031],[86,3345,3347],{"className":3346},[1036,1037,1038,1039],[86,3348,3350],{"className":3349},[1003,1039],[86,3351,3201],{"className":3352},[1003,1039],[86,3354,867],{"className":3355},[3356],"mclose"," representa un espacio de 1024 dimensiones",[12,3359,3360],{},"¿Por qué usar dimensiones? Porque los modelos necesitan representar relaciones complejas entre conceptos.",[12,3362,3363],{},"En una cadena de Markov simple:",[164,3365,3368],{"className":3366,"code":3367,"language":3141},[3139],"\"gusta\" -- \"programar\"\n",[145,3369,3367],{"__ignoreMap":169},[12,3371,3372],{},"Solo estamos considerando la palabra anterior, pero en un LLM, el vector puede capturar simultáneamente:",[30,3374,3375,3378,3381,3384,3387,3390,3393,3396],{},[33,3376,3377],{},"Significado semántico",[33,3379,3380],{},"Contexto",[33,3382,3383],{},"Gramática",[33,3385,3386],{},"Relaciones entre palabras",[33,3388,3389],{},"Tono",[33,3391,3392],{},"Idioma",[33,3394,3395],{},"Patrones estadísticos",[33,3397,3398],{},"Intención",[164,3400,3403],{"className":3401,"code":3402,"language":3141},[3139],"\"python\" --> embedding --> [0.12, -0.44, 1.03, ..., 0.91]\n",[145,3404,3402],{"__ignoreMap":169},[16,3406,3407],{},[12,3408,3409,3410,3413],{},"En términos técnicos primero existe un ",[145,3411,3412],{},"embedding table",", cada token obtiene un vector inicial a partir de esa tabla, y luego ese vector se transforma a través de múltiples capas del modelo, cada una con sus propias operaciones matemáticas, hasta llegar a la salida final.",[12,3415,3416],{},"¿Que significa cada valor de ese vector?",[12,3418,3419,3420,3423],{},"Pedagógicamente podríamos verlo como que el primer valor (0.12) podría representar la relación de \"python\" con el concepto de \"programación\", el segundo valor representar su relación con \"lenguaje de programación\", etc., PERO, realmente no existe una dimensión que ",[122,3421,3422],{},"represente directamente un concepto humano específico",", el significado emerge de patrones distribuidos entre muchas dimensiones.",[12,3425,3426],{},"Mientras más grande es la dimensionalidad:",[30,3428,3429,3432,3435],{},[33,3430,3431],{},"Más información puede representar el modelo",[33,3433,3434],{},"Más complejas son las operaciones matemáticas",[33,3436,3437],{},"Más parámetros necesita",[12,3439,3440],{},"Por eso modelos grandes como:",[30,3442,3443,3446,3449],{},[33,3444,3445],{},"Llama 3.3 70B",[33,3447,3448],{},"GPT-4",[33,3450,3451],{},"Gemini",[12,3453,3454],{},"Usan espacios internos enormes y muchos parámetros.",[12,3456,3457,3458,3461],{},"Todo esto potencia lo que llamamos ",[145,3459,3460],{},"atención",": en vez de mirar solo la palabra anterior, el modelo compara cada token con los demás tokens del contexto.",[12,3463,3464],{},"La atención utiliza operaciones entre vectores como:",[86,3466,3468],{"className":3467},[3173],[86,3469,3471,3493],{"className":3470},[955],[86,3472,3474],{"className":3473},[959],[961,3475,3476],{"xmlns":963,"display":3182},[965,3477,3478,3490],{},[968,3479,3480,3482],{},[974,3481,419],{},[971,3483,3484,3487],{},[974,3485,3486],{},"K",[974,3488,3489],{},"T",[982,3491,3492],{"encoding":984},"QK^T",[86,3494,3496],{"className":3495,"ariaHidden":990},[989],[86,3497,3499,3503,3506],{"className":3498},[994],[86,3500],{"className":3501,"style":3502},[998],"height:1.0858em;vertical-align:-0.1944em;",[86,3504,419],{"className":3505},[1003,1007],[86,3507,3509,3513],{"className":3508},[1003],[86,3510,3486],{"className":3511,"style":3512},[1003,1007],"margin-right:0.0715em;",[86,3514,3516],{"className":3515},[1012],[86,3517,3519],{"className":3518},[1016],[86,3520,3522],{"className":3521},[1020],[86,3523,3526],{"className":3524,"style":3525},[1024],"height:0.8913em;",[86,3527,3528,3531],{"style":3258},[86,3529],{"className":3530,"style":1032},[1031],[86,3532,3534],{"className":3533},[1036,1037,1038,1039],[86,3535,3489],{"className":3536,"style":3537},[1003,1007,1039],"margin-right:0.1389em;",[12,3539,3273],{},[30,3541,3542,3545,3548],{},[33,3543,3544],{},"Q = Query (el token actual)",[33,3546,3547],{},"K = Keys (todos los tokens del contexto)",[33,3549,3550,3579],{},[86,3551,3553,3566],{"className":3552},[955],[86,3554,3556],{"className":3555},[959],[961,3557,3558],{"xmlns":963},[965,3559,3560,3564],{},[968,3561,3562],{},[974,3563,3489],{},[982,3565,3489],{"encoding":984},[86,3567,3569],{"className":3568,"ariaHidden":990},[989],[86,3570,3572,3576],{"className":3571},[994],[86,3573],{"className":3574,"style":3575},[998],"height:0.6833em;",[86,3577,3489],{"className":3578,"style":3537},[1003,1007]," = Transpuesta",[12,3581,3582],{},"El resultado es una matriz de atención que indica qué tan relevante es cada token del contexto para predecir el siguiente token.",[12,3584,3585],{},"Así el modelo puede entender relaciones como:",[164,3587,3590],{"className":3588,"code":3589,"language":3141},[3139],"\"El perro persiguió al gato porque estaba asustado\"\n",[145,3591,3589],{"__ignoreMap":169},[12,3593,3594],{},"Y decidir si \"asustado\" se refiere al perro o al gato usando contexto completo, no únicamente la palabra anterior.",[12,3596,3597],{},"Asi que, aunque los LLMs son muchísimo más complejos, el objetivo final sigue siendo sorprendentemente parecido al ejemplo inicial:",[16,3599,3600],{},[12,3601,3602],{},"Predecir el siguiente token",{"title":169,"searchDepth":205,"depth":205,"links":3604},[3605],{"id":2293,"depth":192,"text":2294,"children":3606},[3607,3608,3609],{"id":2317,"depth":205,"text":2318},{"id":2396,"depth":205,"text":2397},{"id":2467,"depth":205,"text":2468},"2026-05-14","Mientras exploraba los cursos de Anthropic me encontré con un artículo que me llamó la atención: Capabilities and Limitations of AI. Asi que quise hacer un recorrido sobre las bases y lo que es actualmente la inteligencia artificial.","\u002Fblog\u002Fai-capabilities-and-limitations\u002Fshared\u002Fai-capabilities-limitations.webp","2026-06-24",{},20,"\u002Fblog\u002Fblog\u002Fai-capabilities-and-limitations",{"title":2275,"description":3611},{"loc":3619,"priority":2259,"lastmod":3613},"\u002Fes\u002Fblog\u002Fai-capabilities-and-limitations","ai-capabilities-and-limitations","blog\u002Fblog\u002Fai-capabilities-and-limitations","La inteligencia artificial tiene capacidades impressionantes, pero también presenta limitaciones importantes. En este artículo, exploraremos ambas facetas en el contexto del aprendizaje automático.",[3624,3625,3626,3627,2264],"inteligencia artificial","aprendizaje automático","capacidades de la IA","limitaciones de la IA","BvXgKYrtUOLULH3H7FfWVG-b50CbEOwpkz7QMAbTE7M",{"id":3630,"title":3631,"author":7,"body":3632,"date":3661,"description":3662,"extension":2250,"image":3663,"lastmod":3661,"meta":3664,"navigation":208,"order":3665,"path":3666,"seo":3667,"sitemap":3668,"slug":3670,"stem":3671,"summary":3672,"tags":3673,"__hash__":3677},"content_es\u002Fblog\u002Fblog\u002Fstatistical-tests-and-machine-learning.md","Pruebas Estadísticas y Aprendizaje Automático",{"type":9,"value":3633,"toc":3658},[3634,3642,3650,3652,3654],[12,3635,3636,3637],{},"Artículo anterior de esta serie: ",[22,3638,3641],{"href":3639,"rel":3640},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fprobability-and-machine-learning",[26],"Probabilidad y Aprendizaje Automático",[12,3643,3644,3645],{},"Artículo dónde exploramos sobre la estadística: ",[22,3646,3649],{"href":3647,"rel":3648},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fstatistics-and-machine-learning",[26],"Estadística y Aprendizaje Automático",[40,3651],{},[43,3653],{},[46,3655,3657],{"id":3656},"pruebas-estadísticas","Pruebas Estadísticas",{"title":169,"searchDepth":205,"depth":205,"links":3659},[3660],{"id":3656,"depth":192,"text":3657},"2026-05-12","Artículo anterior de esta serie: Probabilidad y Aprendizaje Automático","\u002Fblog\u002Fstatistical-tests-and-machine-learning\u002Fshared\u002Fstatistical-tests-machine-learning.webp",{},10,"\u002Fblog\u002Fblog\u002Fstatistical-tests-and-machine-learning",{"title":3631,"description":3662},{"loc":3669,"priority":2259,"lastmod":3661},"\u002Fes\u002Fblog\u002Fstatistical-tests-and-machine-learning","statistical-tests-and-machine-learning","blog\u002Fblog\u002Fstatistical-tests-and-machine-learning","Las pruebas estadísticas nos permiten evaluar hipótesis y tomar decisiones basadas en datos. En este artículo, exploraremos cómo se utiliza esta herramienta en el contexto del aprendizaje automático.",[3625,3674,3675,2264,3676],"pruebas estadísticas","análisis de datos","data analysis","AJrkhPTBnBhFGqri9m16iUtmoHWP7QhtyGM1pVWi--M",{"id":3679,"title":3641,"author":7,"body":3680,"date":12720,"description":3684,"extension":2250,"image":12721,"lastmod":3661,"meta":12722,"navigation":208,"order":315,"path":12723,"seo":12724,"sitemap":12725,"slug":12727,"stem":12728,"summary":12729,"tags":12730,"__hash__":12732},"content_es\u002Fblog\u002Fblog\u002Fprobability-and-machine-learning.md",{"type":9,"value":3681,"toc":12691},[3682,3685,3690,3692,3694,3698,3709,3714,3721,3976,3979,4029,4033,4044,4058,4064,4067,4205,4208,4598,4602,4615,4619,4641,4644,4723,4726,4765,4768,4771,4774,4778,4781,4932,4935,5104,5170,5174,5181,5287,5290,5433,5436,5440,5443,5519,5521,5541,5546,5555,5562,5565,5803,5805,6812,6815,7215,7218,7221,7603,7606,7617,7620,7697,7700,7703,7727,7730,7733,7736,7745,7749,7752,7764,7771,7775,7778,7782,7785,7790,7796,7801,7807,7811,7814,7834,7838,7841,7847,7850,8334,8336,9146,9361,9364,9644,9647,9650,9652,9656,9664,9668,9671,9780,9787,10496,10505,10508,10514,10518,10521,10881,10947,11069,11080,11089,11092,11101,11105,11108,11546,11738,11741,11778,11781,11816,11819,11823,11910,11919,11923,11932,12121,12124,12133,12665,12671,12680,12683,12685,12688],[12,3683,3684],{},"Luego de explorar la estadística y su relación con el aprendizaje automático, es hora de adentrarnos en otro concepto fundamental: la probabilidad.",[12,3686,3636,3687],{},[22,3688,3649],{"href":3647,"rel":3689},[26],[40,3691],{},[43,3693],{},[46,3695,3697],{"id":3696},"qué-es-la-probabilidad","¿Qué es la probabilidad?",[12,3699,3700,3701,3704,3705,3708],{},"La probabilidad es una medida numérica de la ",[122,3702,3703],{},"posibilidad"," de que ocurra un ",[122,3706,3707],{},"evento",". Se expresa como un número entre 0 y 1, donde 0 indica que el evento es imposible, 0.5 indica que el evento es equiprobable, y 1 indica que el evento es seguro. La probabilidad se utiliza para modelar la incertidumbre y tomar decisiones informadas en situaciones donde no se tiene certeza absoluta.",[16,3710,3711],{},[12,3712,3713],{},"Equiprobable: Se refiere a la situación en la que todos los resultados posibles de un experimento tienen la misma probabilidad de ocurrir. Por ejemplo, al lanzar una moneda justa, las posibilidades de obtener cara o cruz son equiprobables, ya que cada resultado tiene una probabilidad de 0.5.",[12,3715,3716,3717,3720],{},"Matemáticamente, la probabilidad de un evento A se denota como ",[145,3718,3719],{},"P(A)"," y se calcula utilizando la fórmula:",[86,3722,3724],{"className":3723},[3173],[86,3725,3727,3785],{"className":3726},[955],[86,3728,3730],{"className":3729},[959],[961,3731,3732],{"xmlns":963,"display":3182},[965,3733,3734,3782],{},[968,3735,3736,3739,3741,3744,3746,3748],{},[974,3737,3738],{},"P",[3191,3740,243],{"stretchy":3295},[974,3742,3743],{},"A",[3191,3745,867],{"stretchy":3295},[3191,3747,258],{},[3749,3750,3751,3769],"mfrac",{},[968,3752,3753,3757,3766],{},[3754,3755,3756],"mtext",{},"N",[3758,3759,3760,3763],"mover",{"accent":990},[3754,3761,3762],{},"u",[3191,3764,3765],{},"ˊ",[3754,3767,3768],{},"mero de resultados favorables",[968,3770,3771,3773,3779],{},[3754,3772,3756],{},[3758,3774,3775,3777],{"accent":990},[3754,3776,3762],{},[3191,3778,3765],{},[3754,3780,3781],{},"mero total de resultados posibles",[982,3783,3784],{"encoding":984},"P(A) = \\frac{\\text{Número de resultados favorables}}{\\text{Número total de resultados posibles}}",[86,3786,3788,3816],{"className":3787,"ariaHidden":990},[989],[86,3789,3791,3795,3798,3801,3804,3807,3810,3813],{"className":3790},[994],[86,3792],{"className":3793,"style":3794},[998],"height:1em;vertical-align:-0.25em;",[86,3796,3738],{"className":3797,"style":3537},[1003,1007],[86,3799,243],{"className":3800},[3320],[86,3802,3743],{"className":3803},[1003,1007],[86,3805,867],{"className":3806},[3356],[86,3808],{"className":3809,"style":3222},[3221],[86,3811,258],{"className":3812},[3226],[86,3814],{"className":3815,"style":3222},[3221],[86,3817,3819,3823],{"className":3818},[994],[86,3820],{"className":3821,"style":3822},[998],"height:2.2519em;vertical-align:-0.8804em;",[86,3824,3826,3830,3973],{"className":3825},[1003],[86,3827],{"className":3828},[3320,3829],"nulldelimiter",[86,3831,3833],{"className":3832},[3749],[86,3834,3837,3964],{"className":3835},[1016,3836],"vlist-t2",[86,3838,3840,3959],{"className":3839},[1020],[86,3841,3844,3899,3910],{"className":3842,"style":3843},[1024],"height:1.3714em;",[86,3845,3847,3851],{"style":3846},"top:-2.314em;",[86,3848],{"className":3849,"style":3850},[1031],"height:3em;",[86,3852,3854],{"className":3853},[1003],[86,3855,3857,3860,3896],{"className":3856},[1003,3141],[86,3858,3756],{"className":3859},[1003],[86,3861,3864],{"className":3862},[1003,3863],"accent",[86,3865,3867],{"className":3866},[1016],[86,3868,3870],{"className":3869},[1020],[86,3871,3874,3883],{"className":3872,"style":3873},[1024],"height:0.6944em;",[86,3875,3877,3880],{"style":3876},"top:-3em;",[86,3878],{"className":3879,"style":3850},[1031],[86,3881,3762],{"className":3882},[1003],[86,3884,3885,3888],{"style":3876},[86,3886],{"className":3887,"style":3850},[1031],[86,3889,3893],{"className":3890,"style":3892},[3891],"accent-body","left:-0.25em;",[86,3894,3765],{"className":3895},[1003],[86,3897,3781],{"className":3898},[1003],[86,3900,3902,3905],{"style":3901},"top:-3.23em;",[86,3903],{"className":3904,"style":3850},[1031],[86,3906],{"className":3907,"style":3909},[3908],"frac-line","border-bottom-width:0.04em;",[86,3911,3913,3916],{"style":3912},"top:-3.677em;",[86,3914],{"className":3915,"style":3850},[1031],[86,3917,3919],{"className":3918},[1003],[86,3920,3922,3925,3956],{"className":3921},[1003,3141],[86,3923,3756],{"className":3924},[1003],[86,3926,3928],{"className":3927},[1003,3863],[86,3929,3931],{"className":3930},[1016],[86,3932,3934],{"className":3933},[1020],[86,3935,3937,3945],{"className":3936,"style":3873},[1024],[86,3938,3939,3942],{"style":3876},[86,3940],{"className":3941,"style":3850},[1031],[86,3943,3762],{"className":3944},[1003],[86,3946,3947,3950],{"style":3876},[86,3948],{"className":3949,"style":3850},[1031],[86,3951,3953],{"className":3952,"style":3892},[3891],[86,3954,3765],{"className":3955},[1003],[86,3957,3768],{"className":3958},[1003],[86,3960,3963],{"className":3961},[3962],"vlist-s","​",[86,3965,3967],{"className":3966},[1020],[86,3968,3971],{"className":3969,"style":3970},[1024],"height:0.8804em;",[86,3972],{},[86,3974],{"className":3975},[3356,3829],[12,3977,3978],{},"Hagámos una tabla simple de eventos y sus probabilidades para ilustrar este concepto:",[461,3980,3981,3994],{},[464,3982,3983],{},[467,3984,3985,3988,3991],{},[470,3986,3987],{},"Evento",[470,3989,3990],{},"Probabilidad",[470,3992,3993],{},"Explicación",[480,3995,3996,4007,4018],{},[467,3997,3998,4001,4004],{},[485,3999,4000],{},"Lanzar un dado y obtener un 6",[485,4002,4003],{},"1\u002F6 = 0.1667",[485,4005,4006],{},"Hay 6 resultados posibles (1, 2, 3, 4, 5, 6) y solo uno de ellos es favorable (obtener un 6).",[467,4008,4009,4012,4015],{},[485,4010,4011],{},"Lanzar una moneda y obtener cara",[485,4013,4014],{},"1\u002F2 = 0.5",[485,4016,4017],{},"Hay 2 resultados posibles (cara o cruz) y solo uno de ellos es favorable (obtener cara).",[467,4019,4020,4023,4026],{},[485,4021,4022],{},"Lanzar un dado y obtener un número par",[485,4024,4025],{},"3\u002F6 = 0.5",[485,4027,4028],{},"Hay 6 resultados posibles (1, 2, 3, 4, 5, 6) y tres de ellos son favorables (2, 4, 6).",[323,4030,4032],{"id":4031},"espacio-muestral","Espacio muestral",[12,4034,4035,4036,4039,4040,4043],{},"El espacio muestral es el conjunto de todos los resultados posibles de un experimento. Por ejemplo, al lanzar un dado, el espacio muestral es ",[145,4037,4038],{},"{1, 2, 3, 4, 5, 6}",". Al lanzar una moneda, el espacio muestral es ",[145,4041,4042],{},"{cara, cruz}",".\nSe puede clasificar en 2 tipos:",[30,4045,4046,4052],{},[33,4047,4048,4051],{},[122,4049,4050],{},"Espacio muestral discreto",": Contiene un número finito o contable de resultados. Por ejemplo, al lanzar un dado, el espacio muestral es discreto porque solo hay 6 resultados posibles.",[33,4053,4054,4057],{},[122,4055,4056],{},"Espacio muestral continuo",": Contiene un número infinito de resultados posibles. Por ejemplo, al medir la altura de una persona, el espacio muestral es continuo porque puede tomar cualquier valor dentro de un rango.",[12,4059,4060,4061,61],{},"¿Y si tenemos más de un experimento? Por ejemplo, al lanzar dos dados, el espacio muestral se compone de todas las combinaciones posibles de los resultados de ambos dados, lo que da lugar a 36 resultados posibles ",[145,4062,4063],{},"(1,1), (1,2), ..., (6,6)",[12,4065,4066],{},"Para un solo dado, el espacio muestral es:",[86,4068,4070],{"className":4069},[3173],[86,4071,4073,4121],{"className":4072},[955],[86,4074,4076],{"className":4075},[959],[961,4077,4078],{"xmlns":963,"display":3182},[965,4079,4080,4118],{},[968,4081,4082,4085,4087,4090,4092,4094,4096,4098,4101,4103,4106,4108,4110,4112,4115],{},[974,4083,4084],{},"S",[3191,4086,258],{},[3191,4088,4089],{"stretchy":3295},"{",[978,4091,802],{},[3191,4093,291],{"separator":990},[978,4095,980],{},[3191,4097,291],{"separator":990},[978,4099,4100],{},"3",[3191,4102,291],{"separator":990},[978,4104,4105],{},"4",[3191,4107,291],{"separator":990},[978,4109,1108],{},[3191,4111,291],{"separator":990},[978,4113,4114],{},"6",[3191,4116,4117],{"stretchy":3295},"}",[982,4119,4120],{"encoding":984},"S = \\{1, 2, 3, 4, 5, 6\\}",[86,4122,4124,4143],{"className":4123,"ariaHidden":990},[989],[86,4125,4127,4130,4134,4137,4140],{"className":4126},[994],[86,4128],{"className":4129,"style":3575},[998],[86,4131,4084],{"className":4132,"style":4133},[1003,1007],"margin-right:0.0576em;",[86,4135],{"className":4136,"style":3222},[3221],[86,4138,258],{"className":4139},[3226],[86,4141],{"className":4142,"style":3222},[3221],[86,4144,4146,4149,4152,4155,4159,4163,4166,4169,4172,4175,4178,4181,4184,4187,4190,4193,4196,4199,4202],{"className":4145},[994],[86,4147],{"className":4148,"style":3794},[998],[86,4150,4089],{"className":4151},[3320],[86,4153,802],{"className":4154},[1003],[86,4156,291],{"className":4157},[4158],"mpunct",[86,4160],{"className":4161,"style":4162},[3221],"margin-right:0.1667em;",[86,4164,980],{"className":4165},[1003],[86,4167,291],{"className":4168},[4158],[86,4170],{"className":4171,"style":4162},[3221],[86,4173,4100],{"className":4174},[1003],[86,4176,291],{"className":4177},[4158],[86,4179],{"className":4180,"style":4162},[3221],[86,4182,4105],{"className":4183},[1003],[86,4185,291],{"className":4186},[4158],[86,4188],{"className":4189,"style":4162},[3221],[86,4191,1108],{"className":4192},[1003],[86,4194,291],{"className":4195},[4158],[86,4197],{"className":4198,"style":4162},[3221],[86,4200,4114],{"className":4201},[1003],[86,4203,4117],{"className":4204},[3356],[12,4206,4207],{},"Para dos dados, el espacio muestral es:",[86,4209,4211],{"className":4210},[3173],[86,4212,4214,4349],{"className":4213},[955],[86,4215,4217],{"className":4216},[959],[961,4218,4219],{"xmlns":963,"display":3182},[965,4220,4221,4346],{},[968,4222,4223,4225,4227,4229,4231,4233,4235,4237,4239,4241,4243,4245,4247,4249,4251,4253,4255,4257,4259,4261,4263,4265,4267,4269,4271,4273,4275,4277,4279,4281,4283,4285,4287,4289,4291,4293,4295,4297,4299,4301,4303,4305,4307,4309,4311,4313,4315,4317,4319,4321,4323,4325,4328,4330,4332,4334,4336,4338,4340,4342,4344],{},[974,4224,4084],{},[3191,4226,258],{},[3191,4228,4089],{"stretchy":3295},[3191,4230,243],{"stretchy":3295},[978,4232,802],{},[3191,4234,291],{"separator":990},[978,4236,802],{},[3191,4238,867],{"stretchy":3295},[3191,4240,291],{"separator":990},[3191,4242,243],{"stretchy":3295},[978,4244,802],{},[3191,4246,291],{"separator":990},[978,4248,980],{},[3191,4250,867],{"stretchy":3295},[3191,4252,291],{"separator":990},[3191,4254,243],{"stretchy":3295},[978,4256,802],{},[3191,4258,291],{"separator":990},[978,4260,4100],{},[3191,4262,867],{"stretchy":3295},[3191,4264,291],{"separator":990},[3191,4266,243],{"stretchy":3295},[978,4268,802],{},[3191,4270,291],{"separator":990},[978,4272,4105],{},[3191,4274,867],{"stretchy":3295},[3191,4276,291],{"separator":990},[3191,4278,243],{"stretchy":3295},[978,4280,802],{},[3191,4282,291],{"separator":990},[978,4284,1108],{},[3191,4286,867],{"stretchy":3295},[3191,4288,291],{"separator":990},[3191,4290,243],{"stretchy":3295},[978,4292,802],{},[3191,4294,291],{"separator":990},[978,4296,4114],{},[3191,4298,867],{"stretchy":3295},[3191,4300,291],{"separator":990},[3191,4302,243],{"stretchy":3295},[978,4304,980],{},[3191,4306,291],{"separator":990},[978,4308,802],{},[3191,4310,867],{"stretchy":3295},[3191,4312,291],{"separator":990},[3191,4314,243],{"stretchy":3295},[978,4316,980],{},[3191,4318,291],{"separator":990},[978,4320,980],{},[3191,4322,867],{"stretchy":3295},[3191,4324,291],{"separator":990},[974,4326,61],{"mathvariant":4327},"normal",[974,4329,61],{"mathvariant":4327},[974,4331,61],{"mathvariant":4327},[3191,4333,291],{"separator":990},[3191,4335,243],{"stretchy":3295},[978,4337,4114],{},[3191,4339,291],{"separator":990},[978,4341,4114],{},[3191,4343,867],{"stretchy":3295},[3191,4345,4117],{"stretchy":3295},[982,4347,4348],{"encoding":984},"S = \\{(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2), ..., (6,6)\\}",[86,4350,4352,4370],{"className":4351,"ariaHidden":990},[989],[86,4353,4355,4358,4361,4364,4367],{"className":4354},[994],[86,4356],{"className":4357,"style":3575},[998],[86,4359,4084],{"className":4360,"style":4133},[1003,1007],[86,4362],{"className":4363,"style":3222},[3221],[86,4365,258],{"className":4366},[3226],[86,4368],{"className":4369,"style":3222},[3221],[86,4371,4373,4376,4380,4383,4386,4389,4392,4395,4398,4401,4404,4407,4410,4413,4416,4419,4422,4425,4428,4431,4434,4437,4440,4443,4446,4449,4452,4455,4458,4461,4464,4467,4470,4473,4476,4479,4482,4485,4488,4491,4494,4497,4500,4503,4506,4509,4512,4515,4518,4521,4524,4527,4530,4533,4536,4539,4542,4545,4548,4551,4554,4557,4560,4563,4566,4569,4573,4576,4579,4582,4585,4588,4591,4594],{"className":4372},[994],[86,4374],{"className":4375,"style":3794},[998],[86,4377,4379],{"className":4378},[3320],"{(",[86,4381,802],{"className":4382},[1003],[86,4384,291],{"className":4385},[4158],[86,4387],{"className":4388,"style":4162},[3221],[86,4390,802],{"className":4391},[1003],[86,4393,867],{"className":4394},[3356],[86,4396,291],{"className":4397},[4158],[86,4399],{"className":4400,"style":4162},[3221],[86,4402,243],{"className":4403},[3320],[86,4405,802],{"className":4406},[1003],[86,4408,291],{"className":4409},[4158],[86,4411],{"className":4412,"style":4162},[3221],[86,4414,980],{"className":4415},[1003],[86,4417,867],{"className":4418},[3356],[86,4420,291],{"className":4421},[4158],[86,4423],{"className":4424,"style":4162},[3221],[86,4426,243],{"className":4427},[3320],[86,4429,802],{"className":4430},[1003],[86,4432,291],{"className":4433},[4158],[86,4435],{"className":4436,"style":4162},[3221],[86,4438,4100],{"className":4439},[1003],[86,4441,867],{"className":4442},[3356],[86,4444,291],{"className":4445},[4158],[86,4447],{"className":4448,"style":4162},[3221],[86,4450,243],{"className":4451},[3320],[86,4453,802],{"className":4454},[1003],[86,4456,291],{"className":4457},[4158],[86,4459],{"className":4460,"style":4162},[3221],[86,4462,4105],{"className":4463},[1003],[86,4465,867],{"className":4466},[3356],[86,4468,291],{"className":4469},[4158],[86,4471],{"className":4472,"style":4162},[3221],[86,4474,243],{"className":4475},[3320],[86,4477,802],{"className":4478},[1003],[86,4480,291],{"className":4481},[4158],[86,4483],{"className":4484,"style":4162},[3221],[86,4486,1108],{"className":4487},[1003],[86,4489,867],{"className":4490},[3356],[86,4492,291],{"className":4493},[4158],[86,4495],{"className":4496,"style":4162},[3221],[86,4498,243],{"className":4499},[3320],[86,4501,802],{"className":4502},[1003],[86,4504,291],{"className":4505},[4158],[86,4507],{"className":4508,"style":4162},[3221],[86,4510,4114],{"className":4511},[1003],[86,4513,867],{"className":4514},[3356],[86,4516,291],{"className":4517},[4158],[86,4519],{"className":4520,"style":4162},[3221],[86,4522,243],{"className":4523},[3320],[86,4525,980],{"className":4526},[1003],[86,4528,291],{"className":4529},[4158],[86,4531],{"className":4532,"style":4162},[3221],[86,4534,802],{"className":4535},[1003],[86,4537,867],{"className":4538},[3356],[86,4540,291],{"className":4541},[4158],[86,4543],{"className":4544,"style":4162},[3221],[86,4546,243],{"className":4547},[3320],[86,4549,980],{"className":4550},[1003],[86,4552,291],{"className":4553},[4158],[86,4555],{"className":4556,"style":4162},[3221],[86,4558,980],{"className":4559},[1003],[86,4561,867],{"className":4562},[3356],[86,4564,291],{"className":4565},[4158],[86,4567],{"className":4568,"style":4162},[3221],[86,4570,4572],{"className":4571},[1003],"...",[86,4574,291],{"className":4575},[4158],[86,4577],{"className":4578,"style":4162},[3221],[86,4580,243],{"className":4581},[3320],[86,4583,4114],{"className":4584},[1003],[86,4586,291],{"className":4587},[4158],[86,4589],{"className":4590,"style":4162},[3221],[86,4592,4114],{"className":4593},[1003],[86,4595,4597],{"className":4596},[3356],")}",[1612,4599,4601],{"id":4600},"eventos","Eventos",[12,4603,4604,4605,4607,4608,4611,4612,61],{},"Un evento es simplemente un subconjunto del espacio muestral. Al lanzar un dado, el evento \"obtener un número par\" es un subconjunto del espacio muestral ",[145,4606,4038],{}," y lo podemos escribir como ",[145,4609,4610],{},"A = {2, 4, 6}",". La probabilidad de este evento se calcula como ",[145,4613,4614],{},"P(A) = 3\u002F6 = 0.5",[323,4616,4618],{"id":4617},"variables-aleatorias","Variables aleatorias",[12,4620,4621,4622,4625,4626,4628,4629,4632,4633,4636,4637,4640],{},"Una variable aleatoria es una función que asigna un valor numérico a cada resultado posible de un experimento. Por ejemplo, al lanzar un dado, podemos definir una variable aleatoria ",[145,4623,4624],{},"X"," que representa el número que obtenemos, en este caso, ",[145,4627,4624],{}," puede tomar los valores 1, 2, 3, 4, 5 o 6. Pero también podriamos definir una variable aleatoria ",[145,4630,4631],{},"Y"," que representa si el número es par o impar, donde ",[145,4634,4635],{},"Y = 1"," si el número es par y ",[145,4638,4639],{},"Y = 0"," si el número es impar.",[12,4642,4643],{},"Formalmente una variable aleatoria se denota como:",[86,4645,4647],{"className":4646},[3173],[86,4648,4650,4673],{"className":4649},[955],[86,4651,4653],{"className":4652},[959],[961,4654,4655],{"xmlns":963,"display":3182},[965,4656,4657,4670],{},[968,4658,4659,4661,4663,4665,4668],{},[974,4660,4624],{},[3191,4662,162],{},[974,4664,4084],{},[3191,4666,4667],{},"→",[974,4669,976],{"mathvariant":3198},[982,4671,4672],{"encoding":984},"X: S \\rightarrow \\mathbb{R}",[86,4674,4676,4695,4713],{"className":4675,"ariaHidden":990},[989],[86,4677,4679,4682,4686,4689,4692],{"className":4678},[994],[86,4680],{"className":4681,"style":3575},[998],[86,4683,4624],{"className":4684,"style":4685},[1003,1007],"margin-right:0.0785em;",[86,4687],{"className":4688,"style":3222},[3221],[86,4690,162],{"className":4691},[3226],[86,4693],{"className":4694,"style":3222},[3221],[86,4696,4698,4701,4704,4707,4710],{"className":4697},[994],[86,4699],{"className":4700,"style":3575},[998],[86,4702,4084],{"className":4703,"style":4133},[1003,1007],[86,4705],{"className":4706,"style":3222},[3221],[86,4708,4667],{"className":4709},[3226],[86,4711],{"className":4712,"style":3222},[3221],[86,4714,4716,4720],{"className":4715},[994],[86,4717],{"className":4718,"style":4719},[998],"height:0.6889em;",[86,4721,976],{"className":4722},[1003,3243],[12,4724,4725],{},"Dónde:",[30,4727,4728,4733],{},[33,4729,4730,4732],{},[145,4731,4084],{}," es el espacio muestral.",[33,4734,4735,4764],{},[86,4736,4738,4752],{"className":4737},[955],[86,4739,4741],{"className":4740},[959],[961,4742,4743],{"xmlns":963},[965,4744,4745,4749],{},[968,4746,4747],{},[974,4748,976],{"mathvariant":3198},[982,4750,4751],{"encoding":984},"\\mathbb{R}",[86,4753,4755],{"className":4754,"ariaHidden":990},[989],[86,4756,4758,4761],{"className":4757},[994],[86,4759],{"className":4760,"style":4719},[998],[86,4762,976],{"className":4763},[1003,3243]," es el conjunto de los números reales.",[12,4766,4767],{},"La variable comparte la misma propiedad que el espacio muestral, en cuánto a que puede ser discreta o continua dependiendo del tipo de resultados que pueda tomar.",[12,4769,4770],{},"El espacio muestral describe todos los resultados posibles de un experimento, mientras que una variable aleatoria asigna un valor numérico a cada uno de esos resultados.",[12,4772,4773],{},"Esta traducción de resultados a números es fundamental para el aprendizaje automático, ya que nos permite trabajar con datos de manera cuantitativa y aplicar técnicas estadísticas y algorítmicas para hacer predicciones y tomar decisiones informadas.",[323,4775,4777],{"id":4776},"eventos-dependientes","Eventos dependientes",[12,4779,4780],{},"Dos eventos A y B son dependientes si la ocurrencia de uno afecta la probabilidad de ocurrencia del otro. Matemáticamente, esto se expresa como:",[86,4782,4784],{"className":4783},[3173],[86,4785,4787,4824],{"className":4786},[955],[86,4788,4790],{"className":4789},[959],[961,4791,4792],{"xmlns":963,"display":3182},[965,4793,4794,4821],{},[968,4795,4796,4798,4800,4802,4805,4808,4810,4813,4815,4817,4819],{},[974,4797,3738],{},[3191,4799,243],{"stretchy":3295},[974,4801,3743],{},[3191,4803,4804],{},"∣",[974,4806,4807],{},"B",[3191,4809,867],{"stretchy":3295},[3191,4811,4812],{"mathvariant":4327},"≠",[974,4814,3738],{},[3191,4816,243],{"stretchy":3295},[974,4818,3743],{},[3191,4820,867],{"stretchy":3295},[982,4822,4823],{"encoding":984},"P(A \\mid B) \\neq P(A)",[86,4825,4827,4851,4914],{"className":4826,"ariaHidden":990},[989],[86,4828,4830,4833,4836,4839,4842,4845,4848],{"className":4829},[994],[86,4831],{"className":4832,"style":3794},[998],[86,4834,3738],{"className":4835,"style":3537},[1003,1007],[86,4837,243],{"className":4838},[3320],[86,4840,3743],{"className":4841},[1003,1007],[86,4843],{"className":4844,"style":3222},[3221],[86,4846,4804],{"className":4847},[3226],[86,4849],{"className":4850,"style":3222},[3221],[86,4852,4854,4857,4861,4864,4867,4911],{"className":4853},[994],[86,4855],{"className":4856,"style":3794},[998],[86,4858,4807],{"className":4859,"style":4860},[1003,1007],"margin-right:0.0502em;",[86,4862,867],{"className":4863},[3356],[86,4865],{"className":4866,"style":3222},[3221],[86,4868,4870,4904,4908],{"className":4869},[3226],[86,4871,4873],{"className":4872},[3226],[86,4874,4877],{"className":4875},[1003,4876],"vbox",[86,4878,4881],{"className":4879},[4880],"thinbox",[86,4882,4885,4889,4900],{"className":4883},[4884],"rlap",[86,4886],{"className":4887,"style":4888},[998],"height:0.8889em;vertical-align:-0.1944em;",[86,4890,4893],{"className":4891},[4892],"inner",[86,4894,4896],{"className":4895},[1003],[86,4897,4899],{"className":4898},[3226],"",[86,4901],{"className":4902},[4903],"fix",[86,4905],{"className":4906},[3221,4907],"nobreak",[86,4909,258],{"className":4910},[3226],[86,4912],{"className":4913,"style":3222},[3221],[86,4915,4917,4920,4923,4926,4929],{"className":4916},[994],[86,4918],{"className":4919,"style":3794},[998],[86,4921,3738],{"className":4922,"style":3537},[1003,1007],[86,4924,243],{"className":4925},[3320],[86,4927,3743],{"className":4928},[1003,1007],[86,4930,867],{"className":4931},[3356],[12,4933,4934],{},"Para calcular la probabilidad de eventos dependientes, se utiliza la fórmula de la probabilidad condicional:",[86,4936,4938],{"className":4937},[3173],[86,4939,4941,4991],{"className":4940},[955],[86,4942,4944],{"className":4943},[959],[961,4945,4946],{"xmlns":963,"display":3182},[965,4947,4948,4988],{},[968,4949,4950,4952,4954,4956,4959,4961,4963,4965,4967,4969,4971,4973,4976,4978,4980,4982,4984,4986],{},[974,4951,3738],{},[3191,4953,243],{"stretchy":3295},[974,4955,3743],{},[3191,4957,4958],{},"∩",[974,4960,4807],{},[3191,4962,867],{"stretchy":3295},[3191,4964,258],{},[974,4966,3738],{},[3191,4968,243],{"stretchy":3295},[974,4970,3743],{},[3191,4972,867],{"stretchy":3295},[3191,4974,4975],{},"⋅",[974,4977,3738],{},[3191,4979,243],{"stretchy":3295},[974,4981,4807],{},[3191,4983,4804],{},[974,4985,3743],{},[3191,4987,867],{"stretchy":3295},[982,4989,4990],{"encoding":984},"P(A \\cap B) = P(A) \\cdot P(B \\mid A)",[86,4992,4994,5020,5041,5068,5092],{"className":4993,"ariaHidden":990},[989],[86,4995,4997,5000,5003,5006,5009,5013,5017],{"className":4996},[994],[86,4998],{"className":4999,"style":3794},[998],[86,5001,3738],{"className":5002,"style":3537},[1003,1007],[86,5004,243],{"className":5005},[3320],[86,5007,3743],{"className":5008},[1003,1007],[86,5010],{"className":5011,"style":5012},[3221],"margin-right:0.2222em;",[86,5014,4958],{"className":5015},[5016],"mbin",[86,5018],{"className":5019,"style":5012},[3221],[86,5021,5023,5026,5029,5032,5035,5038],{"className":5022},[994],[86,5024],{"className":5025,"style":3794},[998],[86,5027,4807],{"className":5028,"style":4860},[1003,1007],[86,5030,867],{"className":5031},[3356],[86,5033],{"className":5034,"style":3222},[3221],[86,5036,258],{"className":5037},[3226],[86,5039],{"className":5040,"style":3222},[3221],[86,5042,5044,5047,5050,5053,5056,5059,5062,5065],{"className":5043},[994],[86,5045],{"className":5046,"style":3794},[998],[86,5048,3738],{"className":5049,"style":3537},[1003,1007],[86,5051,243],{"className":5052},[3320],[86,5054,3743],{"className":5055},[1003,1007],[86,5057,867],{"className":5058},[3356],[86,5060],{"className":5061,"style":5012},[3221],[86,5063,4975],{"className":5064},[5016],[86,5066],{"className":5067,"style":5012},[3221],[86,5069,5071,5074,5077,5080,5083,5086,5089],{"className":5070},[994],[86,5072],{"className":5073,"style":3794},[998],[86,5075,3738],{"className":5076,"style":3537},[1003,1007],[86,5078,243],{"className":5079},[3320],[86,5081,4807],{"className":5082,"style":4860},[1003,1007],[86,5084],{"className":5085,"style":3222},[3221],[86,5087,4804],{"className":5088},[3226],[86,5090],{"className":5091,"style":3222},[3221],[86,5093,5095,5098,5101],{"className":5094},[994],[86,5096],{"className":5097,"style":3794},[998],[86,5099,3743],{"className":5100},[1003,1007],[86,5102,867],{"className":5103},[3356],[16,5105,5106],{},[12,5107,5108,5109,5139,5140,5169],{},"El símbolo ",[86,5110,5112,5126],{"className":5111},[955],[86,5113,5115],{"className":5114},[959],[961,5116,5117],{"xmlns":963},[965,5118,5119,5123],{},[968,5120,5121],{},[3191,5122,4958],{},[982,5124,5125],{"encoding":984},"\\cap",[86,5127,5129],{"className":5128,"ariaHidden":990},[989],[86,5130,5132,5136],{"className":5131},[994],[86,5133],{"className":5134,"style":5135},[998],"height:0.5556em;",[86,5137,4958],{"className":5138},[1003]," representa la intersección de dos eventos, es decir, la ocurrencia simultánea de ambos eventos A y B.\nEl símbolo ",[86,5141,5143,5157],{"className":5142},[955],[86,5144,5146],{"className":5145},[959],[961,5147,5148],{"xmlns":963},[965,5149,5150,5154],{},[968,5151,5152],{},[3191,5153,4804],{},[982,5155,5156],{"encoding":984},"\\mid",[86,5158,5160],{"className":5159,"ariaHidden":990},[989],[86,5161,5163,5166],{"className":5162},[994],[86,5164],{"className":5165,"style":3794},[998],[86,5167,4804],{"className":5168},[3226]," representa la condición de que el evento A ha ocurrido.",[323,5171,5173],{"id":5172},"eventos-independientes","Eventos independientes",[12,5175,5176,5177,5180],{},"Dos eventos A y B son independientes si la ocurrencia de uno ",[145,5178,5179],{},"NO"," afecta la probabilidad de ocurrencia del otro:",[86,5182,5184],{"className":5183},[3173],[86,5185,5187,5221],{"className":5186},[955],[86,5188,5190],{"className":5189},[959],[961,5191,5192],{"xmlns":963,"display":3182},[965,5193,5194,5218],{},[968,5195,5196,5198,5200,5202,5204,5206,5208,5210,5212,5214,5216],{},[974,5197,3738],{},[3191,5199,243],{"stretchy":3295},[974,5201,3743],{},[3191,5203,4804],{},[974,5205,4807],{},[3191,5207,867],{"stretchy":3295},[3191,5209,258],{},[974,5211,3738],{},[3191,5213,243],{"stretchy":3295},[974,5215,3743],{},[3191,5217,867],{"stretchy":3295},[982,5219,5220],{"encoding":984},"P(A \\mid B) = P(A)",[86,5222,5224,5248,5269],{"className":5223,"ariaHidden":990},[989],[86,5225,5227,5230,5233,5236,5239,5242,5245],{"className":5226},[994],[86,5228],{"className":5229,"style":3794},[998],[86,5231,3738],{"className":5232,"style":3537},[1003,1007],[86,5234,243],{"className":5235},[3320],[86,5237,3743],{"className":5238},[1003,1007],[86,5240],{"className":5241,"style":3222},[3221],[86,5243,4804],{"className":5244},[3226],[86,5246],{"className":5247,"style":3222},[3221],[86,5249,5251,5254,5257,5260,5263,5266],{"className":5250},[994],[86,5252],{"className":5253,"style":3794},[998],[86,5255,4807],{"className":5256,"style":4860},[1003,1007],[86,5258,867],{"className":5259},[3356],[86,5261],{"className":5262,"style":3222},[3221],[86,5264,258],{"className":5265},[3226],[86,5267],{"className":5268,"style":3222},[3221],[86,5270,5272,5275,5278,5281,5284],{"className":5271},[994],[86,5273],{"className":5274,"style":3794},[998],[86,5276,3738],{"className":5277,"style":3537},[1003,1007],[86,5279,243],{"className":5280},[3320],[86,5282,3743],{"className":5283},[1003,1007],[86,5285,867],{"className":5286},[3356],[12,5288,5289],{},"Y para verificar si dos eventos son independientes, se puede usar la siguiente fórmula:",[86,5291,5293],{"className":5292},[3173],[86,5294,5296,5340],{"className":5295},[955],[86,5297,5299],{"className":5298},[959],[961,5300,5301],{"xmlns":963,"display":3182},[965,5302,5303,5337],{},[968,5304,5305,5307,5309,5311,5313,5315,5317,5319,5321,5323,5325,5327,5329,5331,5333,5335],{},[974,5306,3738],{},[3191,5308,243],{"stretchy":3295},[974,5310,3743],{},[3191,5312,4958],{},[974,5314,4807],{},[3191,5316,867],{"stretchy":3295},[3191,5318,258],{},[974,5320,3738],{},[3191,5322,243],{"stretchy":3295},[974,5324,3743],{},[3191,5326,867],{"stretchy":3295},[3191,5328,4975],{},[974,5330,3738],{},[3191,5332,243],{"stretchy":3295},[974,5334,4807],{},[3191,5336,867],{"stretchy":3295},[982,5338,5339],{"encoding":984},"P(A \\cap B) = P(A) \\cdot P(B)",[86,5341,5343,5367,5388,5415],{"className":5342,"ariaHidden":990},[989],[86,5344,5346,5349,5352,5355,5358,5361,5364],{"className":5345},[994],[86,5347],{"className":5348,"style":3794},[998],[86,5350,3738],{"className":5351,"style":3537},[1003,1007],[86,5353,243],{"className":5354},[3320],[86,5356,3743],{"className":5357},[1003,1007],[86,5359],{"className":5360,"style":5012},[3221],[86,5362,4958],{"className":5363},[5016],[86,5365],{"className":5366,"style":5012},[3221],[86,5368,5370,5373,5376,5379,5382,5385],{"className":5369},[994],[86,5371],{"className":5372,"style":3794},[998],[86,5374,4807],{"className":5375,"style":4860},[1003,1007],[86,5377,867],{"className":5378},[3356],[86,5380],{"className":5381,"style":3222},[3221],[86,5383,258],{"className":5384},[3226],[86,5386],{"className":5387,"style":3222},[3221],[86,5389,5391,5394,5397,5400,5403,5406,5409,5412],{"className":5390},[994],[86,5392],{"className":5393,"style":3794},[998],[86,5395,3738],{"className":5396,"style":3537},[1003,1007],[86,5398,243],{"className":5399},[3320],[86,5401,3743],{"className":5402},[1003,1007],[86,5404,867],{"className":5405},[3356],[86,5407],{"className":5408,"style":5012},[3221],[86,5410,4975],{"className":5411},[5016],[86,5413],{"className":5414,"style":5012},[3221],[86,5416,5418,5421,5424,5427,5430],{"className":5417},[994],[86,5419],{"className":5420,"style":3794},[998],[86,5422,3738],{"className":5423,"style":3537},[1003,1007],[86,5425,243],{"className":5426},[3320],[86,5428,4807],{"className":5429,"style":4860},[1003,1007],[86,5431,867],{"className":5432},[3356],[12,5434,5435],{},"En el contexto del aprendizaje automático, la independencia de eventos es un concepto importante, ya que muchos algoritmos asumen que las características de los datos son independientes entre sí para simplificar el modelo y reducir la complejidad computacional.",[323,5437,5439],{"id":5438},"naive-bayes","Naive Bayes",[12,5441,5442],{},"En artículos anteriores de esta serie, hemos visto ya su aplicación en problemas de clasificación. Cuando un modelo predice una clase, en realidad está estimando la probabilidad de que esa clase sea la correcta dado los datos de entrada:",[86,5444,5446],{"className":5445},[3173],[86,5447,5449,5474],{"className":5448},[955],[86,5450,5452],{"className":5451},[959],[961,5453,5454],{"xmlns":963,"display":3182},[965,5455,5456,5471],{},[968,5457,5458,5460,5462,5465,5467,5469],{},[974,5459,3738],{},[3191,5461,243],{"stretchy":3295},[3754,5463,5464],{},"y",[3191,5466,4804],{},[3754,5468,3189],{},[3191,5470,867],{"stretchy":3295},[982,5472,5473],{"encoding":984},"P(\\text{y} \\mid \\text{x})",[86,5475,5477,5504],{"className":5476,"ariaHidden":990},[989],[86,5478,5480,5483,5486,5489,5495,5498,5501],{"className":5479},[994],[86,5481],{"className":5482,"style":3794},[998],[86,5484,3738],{"className":5485,"style":3537},[1003,1007],[86,5487,243],{"className":5488},[3320],[86,5490,5492],{"className":5491},[1003,3141],[86,5493,5464],{"className":5494},[1003],[86,5496],{"className":5497,"style":3222},[3221],[86,5499,4804],{"className":5500},[3226],[86,5502],{"className":5503,"style":3222},[3221],[86,5505,5507,5510,5516],{"className":5506},[994],[86,5508],{"className":5509,"style":3794},[998],[86,5511,5513],{"className":5512},[1003,3141],[86,5514,3189],{"className":5515},[1003],[86,5517,867],{"className":5518},[3356],[12,5520,3135],{},[30,5522,5523,5529],{},[33,5524,5525,5526,61],{},"En un problema de clasificación binaria, el modelo podría predecir que la probabilidad de que una imagen contenga un gato es del 80%, lo que se expresa como ",[145,5527,5528],{},"P(gato | imagen) = 0.8",[33,5530,5531,5532,93,5535,392,5538,61],{},"En un problema de clasificación multiclase, el modelo podría predecir que la probabilidad de que una imagen contenga un gato es del 60%, un perro del 30% y un pájaro del 10%, lo que se expresa como ",[145,5533,5534],{},"P(gato | imagen) = 0.6",[145,5536,5537],{},"P(perro | imagen) = 0.3",[145,5539,5540],{},"P(pájaro | imagen) = 0.1",[12,5542,5543,5544,162],{},"Pero también hay otra aplicación bastante importante, y es el de ",[122,5545,5439],{},[12,5547,5548,5550,5551,5554],{},[122,5549,5439],{}," es un algoritmo de clasificación basado en el ",[122,5552,5553],{},"Teorema de Bayes"," y en una suposición \"ingenua\" (naive):",[12,5556,5557],{},[122,5558,5559],{},[901,5560,5561],{},"Asume que las variables predictoras son independientes entre sí dado la clase",[12,5563,5564],{},"Parte del Teorema de Bayes:",[86,5566,5568],{"className":5567},[3173],[86,5569,5571,5633],{"className":5570},[955],[86,5572,5574],{"className":5573},[959],[961,5575,5576],{"xmlns":963,"display":3182},[965,5577,5578,5630],{},[968,5579,5580,5582,5584,5586,5588,5590,5592,5594],{},[974,5581,3738],{},[3191,5583,243],{"stretchy":3295},[974,5585,1514],{},[3191,5587,4804],{},[974,5589,4624],{},[3191,5591,867],{"stretchy":3295},[3191,5593,258],{},[3749,5595,5596,5620],{},[968,5597,5598,5600,5602,5604,5606,5608,5610,5612,5614,5616,5618],{},[974,5599,3738],{},[3191,5601,243],{"stretchy":3295},[974,5603,4624],{},[3191,5605,4804],{},[974,5607,1514],{},[3191,5609,867],{"stretchy":3295},[3191,5611,4975],{},[974,5613,3738],{},[3191,5615,243],{"stretchy":3295},[974,5617,1514],{},[3191,5619,867],{"stretchy":3295},[968,5621,5622,5624,5626,5628],{},[974,5623,3738],{},[3191,5625,243],{"stretchy":3295},[974,5627,4624],{},[3191,5629,867],{"stretchy":3295},[982,5631,5632],{"encoding":984},"P(C \\mid X) = \\frac{P(X \\mid C) \\cdot P(C)}{P(X)}",[86,5634,5636,5660,5681],{"className":5635,"ariaHidden":990},[989],[86,5637,5639,5642,5645,5648,5651,5654,5657],{"className":5638},[994],[86,5640],{"className":5641,"style":3794},[998],[86,5643,3738],{"className":5644,"style":3537},[1003,1007],[86,5646,243],{"className":5647},[3320],[86,5649,1514],{"className":5650,"style":3512},[1003,1007],[86,5652],{"className":5653,"style":3222},[3221],[86,5655,4804],{"className":5656},[3226],[86,5658],{"className":5659,"style":3222},[3221],[86,5661,5663,5666,5669,5672,5675,5678],{"className":5662},[994],[86,5664],{"className":5665,"style":3794},[998],[86,5667,4624],{"className":5668,"style":4685},[1003,1007],[86,5670,867],{"className":5671},[3356],[86,5673],{"className":5674,"style":3222},[3221],[86,5676,258],{"className":5677},[3226],[86,5679],{"className":5680,"style":3222},[3221],[86,5682,5684,5688],{"className":5683},[994],[86,5685],{"className":5686,"style":5687},[998],"height:2.363em;vertical-align:-0.936em;",[86,5689,5691,5694,5800],{"className":5690},[1003],[86,5692],{"className":5693},[3320,3829],[86,5695,5697],{"className":5696},[3749],[86,5698,5700,5791],{"className":5699},[1016,3836],[86,5701,5703,5788],{"className":5702},[1020],[86,5704,5707,5727,5735],{"className":5705,"style":5706},[1024],"height:1.427em;",[86,5708,5709,5712],{"style":3846},[86,5710],{"className":5711,"style":3850},[1031],[86,5713,5715,5718,5721,5724],{"className":5714},[1003],[86,5716,3738],{"className":5717,"style":3537},[1003,1007],[86,5719,243],{"className":5720},[3320],[86,5722,4624],{"className":5723,"style":4685},[1003,1007],[86,5725,867],{"className":5726},[3356],[86,5728,5729,5732],{"style":3901},[86,5730],{"className":5731,"style":3850},[1031],[86,5733],{"className":5734,"style":3909},[3908],[86,5736,5737,5740],{"style":3912},[86,5738],{"className":5739,"style":3850},[1031],[86,5741,5743,5746,5749,5752,5755,5758,5761,5764,5767,5770,5773,5776,5779,5782,5785],{"className":5742},[1003],[86,5744,3738],{"className":5745,"style":3537},[1003,1007],[86,5747,243],{"className":5748},[3320],[86,5750,4624],{"className":5751,"style":4685},[1003,1007],[86,5753],{"className":5754,"style":3222},[3221],[86,5756,4804],{"className":5757},[3226],[86,5759],{"className":5760,"style":3222},[3221],[86,5762,1514],{"className":5763,"style":3512},[1003,1007],[86,5765,867],{"className":5766},[3356],[86,5768],{"className":5769,"style":5012},[3221],[86,5771,4975],{"className":5772},[5016],[86,5774],{"className":5775,"style":5012},[3221],[86,5777,3738],{"className":5778,"style":3537},[1003,1007],[86,5780,243],{"className":5781},[3320],[86,5783,1514],{"className":5784,"style":3512},[1003,1007],[86,5786,867],{"className":5787},[3356],[86,5789,3963],{"className":5790},[3962],[86,5792,5794],{"className":5793},[1020],[86,5795,5798],{"className":5796,"style":5797},[1024],"height:0.936em;",[86,5799],{},[86,5801],{"className":5802},[3356,3829],[12,5804,3273],{},[30,5806,5807,5838,5869,6089,6288,6457],{},[33,5808,5809,5837],{},[86,5810,5812,5825],{"className":5811},[955],[86,5813,5815],{"className":5814},[959],[961,5816,5817],{"xmlns":963},[965,5818,5819,5823],{},[968,5820,5821],{},[974,5822,1514],{},[982,5824,1514],{"encoding":984},[86,5826,5828],{"className":5827,"ariaHidden":990},[989],[86,5829,5831,5834],{"className":5830},[994],[86,5832],{"className":5833,"style":3575},[998],[86,5835,1514],{"className":5836,"style":3512},[1003,1007],": clase (ej. spam \u002F no spam)",[33,5839,5840,5868],{},[86,5841,5843,5856],{"className":5842},[955],[86,5844,5846],{"className":5845},[959],[961,5847,5848],{"xmlns":963},[965,5849,5850,5854],{},[968,5851,5852],{},[974,5853,4624],{},[982,5855,4624],{"encoding":984},[86,5857,5859],{"className":5858,"ariaHidden":990},[989],[86,5860,5862,5865],{"className":5861},[994],[86,5863],{"className":5864,"style":3575},[998],[86,5866,4624],{"className":5867,"style":4685},[1003,1007],": conjunto de características",[33,5870,5871,5915,5916,392,5998,61],{},[86,5872,5874,5894],{"className":5873},[955],[86,5875,5877],{"className":5876},[959],[961,5878,5879],{"xmlns":963},[965,5880,5881,5891],{},[968,5882,5883,5885,5887,5889],{},[974,5884,3738],{},[3191,5886,243],{"stretchy":3295},[974,5888,1514],{},[3191,5890,867],{"stretchy":3295},[982,5892,5893],{"encoding":984},"P(C)",[86,5895,5897],{"className":5896,"ariaHidden":990},[989],[86,5898,5900,5903,5906,5909,5912],{"className":5899},[994],[86,5901],{"className":5902,"style":3794},[998],[86,5904,3738],{"className":5905,"style":3537},[1003,1007],[86,5907,243],{"className":5908},[3320],[86,5910,1514],{"className":5911,"style":3512},[1003,1007],[86,5913,867],{"className":5914},[3356],": probabilidad previa (prior), es la probabilidad de la clase antes de observar las características, prior porque representa lo que sabemos antes de ver los datos. Por ejemplo, si el 40% de los correos son spam, entonces ",[86,5917,5919,5951],{"className":5918},[955],[86,5920,5922],{"className":5921},[959],[961,5923,5924],{"xmlns":963},[965,5925,5926,5948],{},[968,5927,5928,5930,5932,5934,5936,5938,5941,5943,5945],{},[974,5929,3738],{},[3191,5931,243],{"stretchy":3295},[974,5933,4084],{},[974,5935,12],{},[974,5937,22],{},[974,5939,5940],{},"m",[3191,5942,867],{"stretchy":3295},[3191,5944,258],{},[978,5946,5947],{},"0.4",[982,5949,5950],{"encoding":984},"P(Spam) = 0.4",[86,5952,5954,5988],{"className":5953,"ariaHidden":990},[989],[86,5955,5957,5960,5963,5966,5969,5972,5976,5979,5982,5985],{"className":5956},[994],[86,5958],{"className":5959,"style":3794},[998],[86,5961,3738],{"className":5962,"style":3537},[1003,1007],[86,5964,243],{"className":5965},[3320],[86,5967,4084],{"className":5968,"style":4133},[1003,1007],[86,5970,12],{"className":5971},[1003,1007],[86,5973,5975],{"className":5974},[1003,1007],"am",[86,5977,867],{"className":5978},[3356],[86,5980],{"className":5981,"style":3222},[3221],[86,5983,258],{"className":5984},[3226],[86,5986],{"className":5987,"style":3222},[3221],[86,5989,5991,5995],{"className":5990},[994],[86,5992],{"className":5993,"style":5994},[998],"height:0.6444em;",[86,5996,5947],{"className":5997},[1003],[86,5999,6001,6037],{"className":6000},[955],[86,6002,6004],{"className":6003},[959],[961,6005,6006],{"xmlns":963},[965,6007,6008,6034],{},[968,6009,6010,6012,6014,6016,6019,6021,6023,6025,6027,6029,6031],{},[974,6011,3738],{},[3191,6013,243],{"stretchy":3295},[974,6015,3756],{},[974,6017,6018],{},"o",[974,6020,4084],{},[974,6022,12],{},[974,6024,22],{},[974,6026,5940],{},[3191,6028,867],{"stretchy":3295},[3191,6030,258],{},[978,6032,6033],{},"0.6",[982,6035,6036],{"encoding":984},"P(NoSpam) = 0.6",[86,6038,6040,6080],{"className":6039,"ariaHidden":990},[989],[86,6041,6043,6046,6049,6052,6056,6059,6062,6065,6068,6071,6074,6077],{"className":6042},[994],[86,6044],{"className":6045,"style":3794},[998],[86,6047,3738],{"className":6048,"style":3537},[1003,1007],[86,6050,243],{"className":6051},[3320],[86,6053,3756],{"className":6054,"style":6055},[1003,1007],"margin-right:0.109em;",[86,6057,6018],{"className":6058},[1003,1007],[86,6060,4084],{"className":6061,"style":4133},[1003,1007],[86,6063,12],{"className":6064},[1003,1007],[86,6066,5975],{"className":6067},[1003,1007],[86,6069,867],{"className":6070},[3356],[86,6072],{"className":6073,"style":3222},[3221],[86,6075,258],{"className":6076},[3226],[86,6078],{"className":6079,"style":3222},[3221],[86,6081,6083,6086],{"className":6082},[994],[86,6084],{"className":6085,"style":5994},[998],[86,6087,6033],{"className":6088},[1003],[33,6090,6091,6157,6158,61],{},[86,6092,6094,6118],{"className":6093},[955],[86,6095,6097],{"className":6096},[959],[961,6098,6099],{"xmlns":963},[965,6100,6101,6115],{},[968,6102,6103,6105,6107,6109,6111,6113],{},[974,6104,3738],{},[3191,6106,243],{"stretchy":3295},[974,6108,4624],{},[3191,6110,4804],{},[974,6112,1514],{},[3191,6114,867],{"stretchy":3295},[982,6116,6117],{"encoding":984},"P(X \\mid C)",[86,6119,6121,6145],{"className":6120,"ariaHidden":990},[989],[86,6122,6124,6127,6130,6133,6136,6139,6142],{"className":6123},[994],[86,6125],{"className":6126,"style":3794},[998],[86,6128,3738],{"className":6129,"style":3537},[1003,1007],[86,6131,243],{"className":6132},[3320],[86,6134,4624],{"className":6135,"style":4685},[1003,1007],[86,6137],{"className":6138,"style":3222},[3221],[86,6140,4804],{"className":6141},[3226],[86,6143],{"className":6144,"style":3222},[3221],[86,6146,6148,6151,6154],{"className":6147},[994],[86,6149],{"className":6150,"style":3794},[998],[86,6152,1514],{"className":6153,"style":3512},[1003,1007],[86,6155,867],{"className":6156},[3356],": verosimilitud (likelihood), es decir, la probabilidad de observar las características dado la clase. Por ejemplo, la probabilidad de que un correo contenga la palabra \"oferta\" dado que es spam podría ser ",[86,6159,6161,6210],{"className":6160},[955],[86,6162,6164],{"className":6163},[959],[961,6165,6166],{"xmlns":963},[965,6167,6168,6207],{},[968,6169,6170,6172,6174,6176,6179,6182,6185,6188,6190,6192,6194,6196,6198,6200,6202,6204],{},[974,6171,3738],{},[3191,6173,243],{"stretchy":3295},[974,6175,6018],{},[974,6177,6178],{},"f",[974,6180,6181],{},"e",[974,6183,6184],{},"r",[974,6186,6187],{},"t",[974,6189,22],{},[3191,6191,4804],{},[974,6193,4084],{},[974,6195,12],{},[974,6197,22],{},[974,6199,5940],{},[3191,6201,867],{"stretchy":3295},[3191,6203,258],{},[978,6205,6206],{},"0.7",[982,6208,6209],{"encoding":984},"P(oferta \\mid Spam) = 0.7",[86,6211,6213,6252,6279],{"className":6212,"ariaHidden":990},[989],[86,6214,6216,6219,6222,6225,6228,6232,6237,6240,6243,6246,6249],{"className":6215},[994],[86,6217],{"className":6218,"style":3794},[998],[86,6220,3738],{"className":6221,"style":3537},[1003,1007],[86,6223,243],{"className":6224},[3320],[86,6226,6018],{"className":6227},[1003,1007],[86,6229,6178],{"className":6230,"style":6231},[1003,1007],"margin-right:0.1076em;",[86,6233,6236],{"className":6234,"style":6235},[1003,1007],"margin-right:0.0278em;","er",[86,6238,6187],{"className":6239},[1003,1007],[86,6241,22],{"className":6242},[1003,1007],[86,6244],{"className":6245,"style":3222},[3221],[86,6247,4804],{"className":6248},[3226],[86,6250],{"className":6251,"style":3222},[3221],[86,6253,6255,6258,6261,6264,6267,6270,6273,6276],{"className":6254},[994],[86,6256],{"className":6257,"style":3794},[998],[86,6259,4084],{"className":6260,"style":4133},[1003,1007],[86,6262,12],{"className":6263},[1003,1007],[86,6265,5975],{"className":6266},[1003,1007],[86,6268,867],{"className":6269},[3356],[86,6271],{"className":6272,"style":3222},[3221],[86,6274,258],{"className":6275},[3226],[86,6277],{"className":6278,"style":3222},[3221],[86,6280,6282,6285],{"className":6281},[994],[86,6283],{"className":6284,"style":5994},[998],[86,6286,6206],{"className":6287},[1003],[33,6289,6290,6356,6357,61],{},[86,6291,6293,6317],{"className":6292},[955],[86,6294,6296],{"className":6295},[959],[961,6297,6298],{"xmlns":963},[965,6299,6300,6314],{},[968,6301,6302,6304,6306,6308,6310,6312],{},[974,6303,3738],{},[3191,6305,243],{"stretchy":3295},[974,6307,1514],{},[3191,6309,4804],{},[974,6311,4624],{},[3191,6313,867],{"stretchy":3295},[982,6315,6316],{"encoding":984},"P(C \\mid X)",[86,6318,6320,6344],{"className":6319,"ariaHidden":990},[989],[86,6321,6323,6326,6329,6332,6335,6338,6341],{"className":6322},[994],[86,6324],{"className":6325,"style":3794},[998],[86,6327,3738],{"className":6328,"style":3537},[1003,1007],[86,6330,243],{"className":6331},[3320],[86,6333,1514],{"className":6334,"style":3512},[1003,1007],[86,6336],{"className":6337,"style":3222},[3221],[86,6339,4804],{"className":6340},[3226],[86,6342],{"className":6343,"style":3222},[3221],[86,6345,6347,6350,6353],{"className":6346},[994],[86,6348],{"className":6349,"style":3794},[998],[86,6351,4624],{"className":6352,"style":4685},[1003,1007],[86,6354,867],{"className":6355},[3356],": probabilidad posterior, es decir, la probabilidad actualizada de la clase después de observar las características. Por ejemplo, la probabilidad de que un correo sea spam dado que contiene la palabra \"oferta\" podría ser ",[86,6358,6360,6400],{"className":6359},[955],[86,6361,6363],{"className":6362},[959],[961,6364,6365],{"xmlns":963},[965,6366,6367,6397],{},[968,6368,6369,6371,6373,6375,6377,6379,6381,6383,6385,6387,6389,6391,6393,6395],{},[974,6370,3738],{},[3191,6372,243],{"stretchy":3295},[974,6374,4084],{},[974,6376,12],{},[974,6378,22],{},[974,6380,5940],{},[3191,6382,4804],{},[974,6384,6018],{},[974,6386,6178],{},[974,6388,6181],{},[974,6390,6184],{},[974,6392,6187],{},[974,6394,22],{},[3191,6396,867],{"stretchy":3295},[982,6398,6399],{"encoding":984},"P(Spam \\mid oferta)",[86,6401,6403,6433],{"className":6402,"ariaHidden":990},[989],[86,6404,6406,6409,6412,6415,6418,6421,6424,6427,6430],{"className":6405},[994],[86,6407],{"className":6408,"style":3794},[998],[86,6410,3738],{"className":6411,"style":3537},[1003,1007],[86,6413,243],{"className":6414},[3320],[86,6416,4084],{"className":6417,"style":4133},[1003,1007],[86,6419,12],{"className":6420},[1003,1007],[86,6422,5975],{"className":6423},[1003,1007],[86,6425],{"className":6426,"style":3222},[3221],[86,6428,4804],{"className":6429},[3226],[86,6431],{"className":6432,"style":3222},[3221],[86,6434,6436,6439,6442,6445,6448,6451,6454],{"className":6435},[994],[86,6437],{"className":6438,"style":3794},[998],[86,6440,6018],{"className":6441},[1003,1007],[86,6443,6178],{"className":6444,"style":6231},[1003,1007],[86,6446,6236],{"className":6447,"style":6235},[1003,1007],[86,6449,6187],{"className":6450},[1003,1007],[86,6452,22],{"className":6453},[1003,1007],[86,6455,867],{"className":6456},[3356],[33,6458,6459,6503,6504],{},[86,6460,6462,6482],{"className":6461},[955],[86,6463,6465],{"className":6464},[959],[961,6466,6467],{"xmlns":963},[965,6468,6469,6479],{},[968,6470,6471,6473,6475,6477],{},[974,6472,3738],{},[3191,6474,243],{"stretchy":3295},[974,6476,4624],{},[3191,6478,867],{"stretchy":3295},[982,6480,6481],{"encoding":984},"P(X)",[86,6483,6485],{"className":6484,"ariaHidden":990},[989],[86,6486,6488,6491,6494,6497,6500],{"className":6487},[994],[86,6489],{"className":6490,"style":3794},[998],[86,6492,3738],{"className":6493,"style":3537},[1003,1007],[86,6495,243],{"className":6496},[3320],[86,6498,4624],{"className":6499,"style":4685},[1003,1007],[86,6501,867],{"className":6502},[3356],": probabilidad total de observar la evidencia (normalización). Su función es normalizar el resultado para que la probabilidad final sea un valor entre 0 y 1. Se calcula sumando las probabilidades de observar las características para todas las clases posibles:\n",[86,6505,6507],{"className":6506},[3173],[86,6508,6510,6611],{"className":6509},[955],[86,6511,6513],{"className":6512},[959],[961,6514,6515],{"xmlns":963,"display":3182},[965,6516,6517,6608],{},[968,6518,6519,6521,6523,6525,6527,6529,6531,6533,6535,6537,6539,6541,6543,6545,6547,6549,6551,6553,6555,6557,6559,6561,6563,6566,6568,6570,6572,6574,6576,6578,6580,6582,6584,6586,6588,6590,6592,6594,6596,6598,6600,6602,6604,6606],{},[974,6520,3738],{},[3191,6522,243],{"stretchy":3295},[974,6524,4624],{},[3191,6526,867],{"stretchy":3295},[3191,6528,258],{},[974,6530,3738],{},[3191,6532,243],{"stretchy":3295},[974,6534,4624],{},[3191,6536,4804],{},[974,6538,4084],{},[974,6540,12],{},[974,6542,22],{},[974,6544,5940],{},[3191,6546,867],{"stretchy":3295},[3191,6548,4975],{},[974,6550,3738],{},[3191,6552,243],{"stretchy":3295},[974,6554,4084],{},[974,6556,12],{},[974,6558,22],{},[974,6560,5940],{},[3191,6562,867],{"stretchy":3295},[3191,6564,6565],{},"+",[974,6567,3738],{},[3191,6569,243],{"stretchy":3295},[974,6571,4624],{},[3191,6573,4804],{},[974,6575,3756],{},[974,6577,6018],{},[974,6579,4084],{},[974,6581,12],{},[974,6583,22],{},[974,6585,5940],{},[3191,6587,867],{"stretchy":3295},[3191,6589,4975],{},[974,6591,3738],{},[3191,6593,243],{"stretchy":3295},[974,6595,3756],{},[974,6597,6018],{},[974,6599,4084],{},[974,6601,12],{},[974,6603,22],{},[974,6605,5940],{},[3191,6607,867],{"stretchy":3295},[982,6609,6610],{"encoding":984},"P(X) = P(X \\mid Spam) \\cdot P(Spam) + P(X \\mid NoSpam) \\cdot P(NoSpam)",[86,6612,6614,6641,6665,6692,6725,6749,6782],{"className":6613,"ariaHidden":990},[989],[86,6615,6617,6620,6623,6626,6629,6632,6635,6638],{"className":6616},[994],[86,6618],{"className":6619,"style":3794},[998],[86,6621,3738],{"className":6622,"style":3537},[1003,1007],[86,6624,243],{"className":6625},[3320],[86,6627,4624],{"className":6628,"style":4685},[1003,1007],[86,6630,867],{"className":6631},[3356],[86,6633],{"className":6634,"style":3222},[3221],[86,6636,258],{"className":6637},[3226],[86,6639],{"className":6640,"style":3222},[3221],[86,6642,6644,6647,6650,6653,6656,6659,6662],{"className":6643},[994],[86,6645],{"className":6646,"style":3794},[998],[86,6648,3738],{"className":6649,"style":3537},[1003,1007],[86,6651,243],{"className":6652},[3320],[86,6654,4624],{"className":6655,"style":4685},[1003,1007],[86,6657],{"className":6658,"style":3222},[3221],[86,6660,4804],{"className":6661},[3226],[86,6663],{"className":6664,"style":3222},[3221],[86,6666,6668,6671,6674,6677,6680,6683,6686,6689],{"className":6667},[994],[86,6669],{"className":6670,"style":3794},[998],[86,6672,4084],{"className":6673,"style":4133},[1003,1007],[86,6675,12],{"className":6676},[1003,1007],[86,6678,5975],{"className":6679},[1003,1007],[86,6681,867],{"className":6682},[3356],[86,6684],{"className":6685,"style":5012},[3221],[86,6687,4975],{"className":6688},[5016],[86,6690],{"className":6691,"style":5012},[3221],[86,6693,6695,6698,6701,6704,6707,6710,6713,6716,6719,6722],{"className":6694},[994],[86,6696],{"className":6697,"style":3794},[998],[86,6699,3738],{"className":6700,"style":3537},[1003,1007],[86,6702,243],{"className":6703},[3320],[86,6705,4084],{"className":6706,"style":4133},[1003,1007],[86,6708,12],{"className":6709},[1003,1007],[86,6711,5975],{"className":6712},[1003,1007],[86,6714,867],{"className":6715},[3356],[86,6717],{"className":6718,"style":5012},[3221],[86,6720,6565],{"className":6721},[5016],[86,6723],{"className":6724,"style":5012},[3221],[86,6726,6728,6731,6734,6737,6740,6743,6746],{"className":6727},[994],[86,6729],{"className":6730,"style":3794},[998],[86,6732,3738],{"className":6733,"style":3537},[1003,1007],[86,6735,243],{"className":6736},[3320],[86,6738,4624],{"className":6739,"style":4685},[1003,1007],[86,6741],{"className":6742,"style":3222},[3221],[86,6744,4804],{"className":6745},[3226],[86,6747],{"className":6748,"style":3222},[3221],[86,6750,6752,6755,6758,6761,6764,6767,6770,6773,6776,6779],{"className":6751},[994],[86,6753],{"className":6754,"style":3794},[998],[86,6756,3756],{"className":6757,"style":6055},[1003,1007],[86,6759,6018],{"className":6760},[1003,1007],[86,6762,4084],{"className":6763,"style":4133},[1003,1007],[86,6765,12],{"className":6766},[1003,1007],[86,6768,5975],{"className":6769},[1003,1007],[86,6771,867],{"className":6772},[3356],[86,6774],{"className":6775,"style":5012},[3221],[86,6777,4975],{"className":6778},[5016],[86,6780],{"className":6781,"style":5012},[3221],[86,6783,6785,6788,6791,6794,6797,6800,6803,6806,6809],{"className":6784},[994],[86,6786],{"className":6787,"style":3794},[998],[86,6789,3738],{"className":6790,"style":3537},[1003,1007],[86,6792,243],{"className":6793},[3320],[86,6795,3756],{"className":6796,"style":6055},[1003,1007],[86,6798,6018],{"className":6799},[1003,1007],[86,6801,4084],{"className":6802,"style":4133},[1003,1007],[86,6804,12],{"className":6805},[1003,1007],[86,6807,5975],{"className":6808},[1003,1007],[86,6810,867],{"className":6811},[3356],[12,6813,6814],{},"La parte \"naive\" consiste en asumir que:",[86,6816,6818],{"className":6817},[3173],[86,6819,6821,6906],{"className":6820},[955],[86,6822,6824],{"className":6823},[959],[961,6825,6826],{"xmlns":963,"display":3182},[965,6827,6828,6903],{},[968,6829,6830,6832,6834,6836,6838,6840,6842,6844,6846,6848,6855,6857,6859,6861,6863,6865,6867,6873,6875,6877,6879,6881,6884,6886,6888,6890,6897,6899,6901],{},[974,6831,3738],{},[3191,6833,243],{"stretchy":3295},[974,6835,4624],{},[3191,6837,4804],{},[974,6839,1514],{},[3191,6841,867],{"stretchy":3295},[3191,6843,258],{},[974,6845,3738],{},[3191,6847,243],{"stretchy":3295},[6849,6850,6851,6853],"msub",{},[974,6852,3189],{},[978,6854,802],{},[3191,6856,4804],{},[974,6858,1514],{},[3191,6860,867],{"stretchy":3295},[3191,6862,4975],{},[974,6864,3738],{},[3191,6866,243],{"stretchy":3295},[6849,6868,6869,6871],{},[974,6870,3189],{},[978,6872,980],{},[3191,6874,4804],{},[974,6876,1514],{},[3191,6878,867],{"stretchy":3295},[3191,6880,4975],{},[3191,6882,6883],{},"…",[3191,6885,4975],{},[974,6887,3738],{},[3191,6889,243],{"stretchy":3295},[6849,6891,6892,6894],{},[974,6893,3189],{},[974,6895,6896],{},"n",[3191,6898,4804],{},[974,6900,1514],{},[3191,6902,867],{"stretchy":3295},[982,6904,6905],{"encoding":984},"P(X \\mid C) = P(x_1 \\mid C) \\cdot P(x_2 \\mid C) \\cdot \\ldots \\cdot P(x_n \\mid C)",[86,6907,6909,6933,6954,7018,7039,7100,7121,7141,7203],{"className":6908,"ariaHidden":990},[989],[86,6910,6912,6915,6918,6921,6924,6927,6930],{"className":6911},[994],[86,6913],{"className":6914,"style":3794},[998],[86,6916,3738],{"className":6917,"style":3537},[1003,1007],[86,6919,243],{"className":6920},[3320],[86,6922,4624],{"className":6923,"style":4685},[1003,1007],[86,6925],{"className":6926,"style":3222},[3221],[86,6928,4804],{"className":6929},[3226],[86,6931],{"className":6932,"style":3222},[3221],[86,6934,6936,6939,6942,6945,6948,6951],{"className":6935},[994],[86,6937],{"className":6938,"style":3794},[998],[86,6940,1514],{"className":6941,"style":3512},[1003,1007],[86,6943,867],{"className":6944},[3356],[86,6946],{"className":6947,"style":3222},[3221],[86,6949,258],{"className":6950},[3226],[86,6952],{"className":6953,"style":3222},[3221],[86,6955,6957,6960,6963,6966,7009,7012,7015],{"className":6956},[994],[86,6958],{"className":6959,"style":3794},[998],[86,6961,3738],{"className":6962,"style":3537},[1003,1007],[86,6964,243],{"className":6965},[3320],[86,6967,6969,6972],{"className":6968},[1003],[86,6970,3189],{"className":6971},[1003,1007],[86,6973,6975],{"className":6974},[1012],[86,6976,6978,7000],{"className":6977},[1016,3836],[86,6979,6981,6997],{"className":6980},[1020],[86,6982,6985],{"className":6983,"style":6984},[1024],"height:0.3011em;",[86,6986,6988,6991],{"style":6987},"top:-2.55em;margin-left:0em;margin-right:0.05em;",[86,6989],{"className":6990,"style":1032},[1031],[86,6992,6994],{"className":6993},[1036,1037,1038,1039],[86,6995,802],{"className":6996},[1003,1039],[86,6998,3963],{"className":6999},[3962],[86,7001,7003],{"className":7002},[1020],[86,7004,7007],{"className":7005,"style":7006},[1024],"height:0.15em;",[86,7008],{},[86,7010],{"className":7011,"style":3222},[3221],[86,7013,4804],{"className":7014},[3226],[86,7016],{"className":7017,"style":3222},[3221],[86,7019,7021,7024,7027,7030,7033,7036],{"className":7020},[994],[86,7022],{"className":7023,"style":3794},[998],[86,7025,1514],{"className":7026,"style":3512},[1003,1007],[86,7028,867],{"className":7029},[3356],[86,7031],{"className":7032,"style":5012},[3221],[86,7034,4975],{"className":7035},[5016],[86,7037],{"className":7038,"style":5012},[3221],[86,7040,7042,7045,7048,7051,7091,7094,7097],{"className":7041},[994],[86,7043],{"className":7044,"style":3794},[998],[86,7046,3738],{"className":7047,"style":3537},[1003,1007],[86,7049,243],{"className":7050},[3320],[86,7052,7054,7057],{"className":7053},[1003],[86,7055,3189],{"className":7056},[1003,1007],[86,7058,7060],{"className":7059},[1012],[86,7061,7063,7083],{"className":7062},[1016,3836],[86,7064,7066,7080],{"className":7065},[1020],[86,7067,7069],{"className":7068,"style":6984},[1024],[86,7070,7071,7074],{"style":6987},[86,7072],{"className":7073,"style":1032},[1031],[86,7075,7077],{"className":7076},[1036,1037,1038,1039],[86,7078,980],{"className":7079},[1003,1039],[86,7081,3963],{"className":7082},[3962],[86,7084,7086],{"className":7085},[1020],[86,7087,7089],{"className":7088,"style":7006},[1024],[86,7090],{},[86,7092],{"className":7093,"style":3222},[3221],[86,7095,4804],{"className":7096},[3226],[86,7098],{"className":7099,"style":3222},[3221],[86,7101,7103,7106,7109,7112,7115,7118],{"className":7102},[994],[86,7104],{"className":7105,"style":3794},[998],[86,7107,1514],{"className":7108,"style":3512},[1003,1007],[86,7110,867],{"className":7111},[3356],[86,7113],{"className":7114,"style":5012},[3221],[86,7116,4975],{"className":7117},[5016],[86,7119],{"className":7120,"style":5012},[3221],[86,7122,7124,7128,7132,7135,7138],{"className":7123},[994],[86,7125],{"className":7126,"style":7127},[998],"height:0.4445em;",[86,7129,6883],{"className":7130},[7131],"minner",[86,7133],{"className":7134,"style":5012},[3221],[86,7136,4975],{"className":7137},[5016],[86,7139],{"className":7140,"style":5012},[3221],[86,7142,7144,7147,7150,7153,7194,7197,7200],{"className":7143},[994],[86,7145],{"className":7146,"style":3794},[998],[86,7148,3738],{"className":7149,"style":3537},[1003,1007],[86,7151,243],{"className":7152},[3320],[86,7154,7156,7159],{"className":7155},[1003],[86,7157,3189],{"className":7158},[1003,1007],[86,7160,7162],{"className":7161},[1012],[86,7163,7165,7186],{"className":7164},[1016,3836],[86,7166,7168,7183],{"className":7167},[1020],[86,7169,7172],{"className":7170,"style":7171},[1024],"height:0.1514em;",[86,7173,7174,7177],{"style":6987},[86,7175],{"className":7176,"style":1032},[1031],[86,7178,7180],{"className":7179},[1036,1037,1038,1039],[86,7181,6896],{"className":7182},[1003,1007,1039],[86,7184,3963],{"className":7185},[3962],[86,7187,7189],{"className":7188},[1020],[86,7190,7192],{"className":7191,"style":7006},[1024],[86,7193],{},[86,7195],{"className":7196,"style":3222},[3221],[86,7198,4804],{"className":7199},[3226],[86,7201],{"className":7202,"style":3222},[3221],[86,7204,7206,7209,7212],{"className":7205},[994],[86,7207],{"className":7208,"style":3794},[998],[86,7210,1514],{"className":7211,"style":3512},[1003,1007],[86,7213,867],{"className":7214},[3356],[12,7216,7217],{},"Es decir, cada variable contribuye de manera independiente a la probabilidad final.",[12,7219,7220],{},"El modelo predice la clase con mayor probabilidad posterior:",[86,7222,7224],{"className":7223},[3173],[86,7225,7227,7311],{"className":7226},[955],[86,7228,7230],{"className":7229},[959],[961,7231,7232],{"xmlns":963,"display":3182},[965,7233,7234,7308],{},[968,7235,7236,7243,7245,7248,7251,7253,7265,7267,7269,7271,7273,7275,7292,7294,7296,7302,7304,7306],{},[3758,7237,7238,7240],{"accent":990},[974,7239,1514],{},[3191,7241,7242],{},"^",[3191,7244,258],{},[974,7246,7247],{},"arg",[3191,7249,7250],{},"⁡",[3191,7252,4975],{},[7254,7255,7256,7263],"munder",{},[968,7257,7258,7261],{},[974,7259,7260],{},"max",[3191,7262,7250],{},[974,7264,1514],{},[3191,7266,4975],{},[974,7268,3738],{},[3191,7270,243],{"stretchy":3295},[974,7272,1514],{},[3191,7274,867],{"stretchy":3295},[7276,7277,7278,7281,7290],"munderover",{},[3191,7279,7280],{},"∏",[968,7282,7283,7286,7288],{},[974,7284,7285],{},"i",[3191,7287,258],{},[978,7289,802],{},[974,7291,6896],{},[974,7293,3738],{},[3191,7295,243],{"stretchy":3295},[6849,7297,7298,7300],{},[974,7299,3189],{},[974,7301,7285],{},[3191,7303,4804],{},[974,7305,1514],{},[3191,7307,867],{"stretchy":3295},[982,7309,7310],{"encoding":984},"\\hat{C} = \\arg \\cdot \\max_C \\cdot P(C) \\prod_{i=1}^{n} P(x_i \\mid C)",[86,7312,7314,7363,7591],{"className":7313,"ariaHidden":990},[989],[86,7315,7317,7321,7354,7357,7360],{"className":7316},[994],[86,7318],{"className":7319,"style":7320},[998],"height:0.9468em;",[86,7322,7324],{"className":7323},[1003,3863],[86,7325,7327],{"className":7326},[1016],[86,7328,7330],{"className":7329},[1020],[86,7331,7333,7341],{"className":7332,"style":7320},[1024],[86,7334,7335,7338],{"style":3876},[86,7336],{"className":7337,"style":3850},[1031],[86,7339,1514],{"className":7340,"style":3512},[1003,1007],[86,7342,7344,7347],{"style":7343},"top:-3.2523em;",[86,7345],{"className":7346,"style":3850},[1031],[86,7348,7351],{"className":7349,"style":7350},[3891],"left:-0.1667em;",[86,7352,7242],{"className":7353},[1003],[86,7355],{"className":7356,"style":3222},[3221],[86,7358,258],{"className":7359},[3226],[86,7361],{"className":7362,"style":3222},[3221],[86,7364,7366,7370,7379,7382,7385,7388,7436,7439,7442,7445,7448,7451,7454,7457,7532,7535,7538,7541,7582,7585,7588],{"className":7365},[994],[86,7367],{"className":7368,"style":7369},[998],"height:2.9291em;vertical-align:-1.2777em;",[86,7371,7374,7375],{"className":7372},[7373],"mop","ar",[86,7376,7378],{"style":7377},"margin-right:0.0139em;","g",[86,7380],{"className":7381,"style":4162},[3221],[86,7383,4975],{"className":7384},[1003],[86,7386],{"className":7387,"style":4162},[3221],[86,7389,7392],{"className":7390},[7373,7391],"op-limits",[86,7393,7395,7427],{"className":7394},[1016,3836],[86,7396,7398,7424],{"className":7397},[1020],[86,7399,7402,7414],{"className":7400,"style":7401},[1024],"height:0.4306em;",[86,7403,7405,7408],{"style":7404},"top:-2.3557em;margin-left:0em;",[86,7406],{"className":7407,"style":3850},[1031],[86,7409,7411],{"className":7410},[1036,1037,1038,1039],[86,7412,1514],{"className":7413,"style":3512},[1003,1007,1039],[86,7415,7416,7419],{"style":3876},[86,7417],{"className":7418,"style":3850},[1031],[86,7420,7421],{},[86,7422,7260],{"className":7423},[7373],[86,7425,3963],{"className":7426},[3962],[86,7428,7430],{"className":7429},[1020],[86,7431,7434],{"className":7432,"style":7433},[1024],"height:0.7443em;",[86,7435],{},[86,7437],{"className":7438,"style":4162},[3221],[86,7440,4975],{"className":7441},[1003],[86,7443,3738],{"className":7444,"style":3537},[1003,1007],[86,7446,243],{"className":7447},[3320],[86,7449,1514],{"className":7450,"style":3512},[1003,1007],[86,7452,867],{"className":7453},[3356],[86,7455],{"className":7456,"style":4162},[3221],[86,7458,7460],{"className":7459},[7373,7391],[86,7461,7463,7523],{"className":7462},[1016,3836],[86,7464,7466,7520],{"className":7465},[1020],[86,7467,7470,7492,7505],{"className":7468,"style":7469},[1024],"height:1.6514em;",[86,7471,7473,7477],{"style":7472},"top:-1.8723em;margin-left:0em;",[86,7474],{"className":7475,"style":7476},[1031],"height:3.05em;",[86,7478,7480],{"className":7479},[1036,1037,1038,1039],[86,7481,7483,7486,7489],{"className":7482},[1003,1039],[86,7484,7285],{"className":7485},[1003,1007,1039],[86,7487,258],{"className":7488},[3226,1039],[86,7490,802],{"className":7491},[1003,1039],[86,7493,7495,7498],{"style":7494},"top:-3.05em;",[86,7496],{"className":7497,"style":7476},[1031],[86,7499,7500],{},[86,7501,7280],{"className":7502},[7373,7503,7504],"op-symbol","large-op",[86,7506,7508,7511],{"style":7507},"top:-4.3em;margin-left:0em;",[86,7509],{"className":7510,"style":7476},[1031],[86,7512,7514],{"className":7513},[1036,1037,1038,1039],[86,7515,7517],{"className":7516},[1003,1039],[86,7518,6896],{"className":7519},[1003,1007,1039],[86,7521,3963],{"className":7522},[3962],[86,7524,7526],{"className":7525},[1020],[86,7527,7530],{"className":7528,"style":7529},[1024],"height:1.2777em;",[86,7531],{},[86,7533],{"className":7534,"style":4162},[3221],[86,7536,3738],{"className":7537,"style":3537},[1003,1007],[86,7539,243],{"className":7540},[3320],[86,7542,7544,7547],{"className":7543},[1003],[86,7545,3189],{"className":7546},[1003,1007],[86,7548,7550],{"className":7549},[1012],[86,7551,7553,7574],{"className":7552},[1016,3836],[86,7554,7556,7571],{"className":7555},[1020],[86,7557,7560],{"className":7558,"style":7559},[1024],"height:0.3117em;",[86,7561,7562,7565],{"style":6987},[86,7563],{"className":7564,"style":1032},[1031],[86,7566,7568],{"className":7567},[1036,1037,1038,1039],[86,7569,7285],{"className":7570},[1003,1007,1039],[86,7572,3963],{"className":7573},[3962],[86,7575,7577],{"className":7576},[1020],[86,7578,7580],{"className":7579,"style":7006},[1024],[86,7581],{},[86,7583],{"className":7584,"style":3222},[3221],[86,7586,4804],{"className":7587},[3226],[86,7589],{"className":7590,"style":3222},[3221],[86,7592,7594,7597,7600],{"className":7593},[994],[86,7595],{"className":7596,"style":3794},[998],[86,7598,1514],{"className":7599,"style":3512},[1003,1007],[86,7601,867],{"className":7602},[3356],[12,7604,7605],{},"Imaginemos que buscamos clasificar un correo como spam, tendríamos características como:",[30,7607,7608,7611,7614],{},[33,7609,7610],{},"Contiene la palabra \"oferta\"",[33,7612,7613],{},"Contiene muchos signos de exclamación",[33,7615,7616],{},"Tiene enlaces externos",[12,7618,7619],{},"Naive Bayes calcula:",[86,7621,7623],{"className":7622},[3173],[86,7624,7626,7652],{"className":7625},[955],[86,7627,7629],{"className":7628},[959],[961,7630,7631],{"xmlns":963,"display":3182},[965,7632,7633,7649],{},[968,7634,7635,7637,7639,7642,7644,7647],{},[974,7636,3738],{},[3191,7638,243],{"stretchy":3295},[3754,7640,7641],{},"Spam",[3191,7643,4804],{},[3754,7645,7646],{},"caracteristicas",[3191,7648,867],{"stretchy":3295},[982,7650,7651],{"encoding":984},"P(\\text{Spam} \\mid \\text{caracteristicas})",[86,7653,7655,7682],{"className":7654,"ariaHidden":990},[989],[86,7656,7658,7661,7664,7667,7673,7676,7679],{"className":7657},[994],[86,7659],{"className":7660,"style":3794},[998],[86,7662,3738],{"className":7663,"style":3537},[1003,1007],[86,7665,243],{"className":7666},[3320],[86,7668,7670],{"className":7669},[1003,3141],[86,7671,7641],{"className":7672},[1003],[86,7674],{"className":7675,"style":3222},[3221],[86,7677,4804],{"className":7678},[3226],[86,7680],{"className":7681,"style":3222},[3221],[86,7683,7685,7688,7694],{"className":7684},[994],[86,7686],{"className":7687,"style":3794},[998],[86,7689,7691],{"className":7690},[1003,3141],[86,7692,7646],{"className":7693},[1003],[86,7695,867],{"className":7696},[3356],[12,7698,7699],{},"Multiplicando las probabilidades individuales de cada característica dado que es spam.",[12,7701,7702],{},"Existen variantes según el tipo de datos:",[117,7704,7705,7711,7721],{},[33,7706,7707,7710],{},[122,7708,7709],{},"Gaussian Naive Bayes",": Se usa cuando las variables son continuas y se asume distribución normal, como en el caso de: edades, -",[33,7712,7713,7716,7717,7720],{},[122,7714,7715],{},"Multinomial Naive Bayes",": Muy usado en ",[122,7718,7719],{},"procesamiento de texto",", se basa en conteos de frecuencia de palabras.",[33,7722,7723,7726],{},[122,7724,7725],{},"Bernoulli Naive Bayes",": Trabaja con variables binarias (presencia o ausencia). Ideal para tareas de clasificación de texto donde solo importa si una palabra está presente o no.",[12,7728,7729],{},"Posee varias ventajas y desventajas que lo hacen adecuado para ciertos tipos de problemas y no para otros.",[12,7731,7732],{},"Entre sus ventajas está su simplicidad, que es muy rápido y puede funcionar bien con pocos datos, especialmente en tareas de procesamiento de lenguaje natural (NLP) como clasificación de texto o detección de spam.",[12,7734,7735],{},"En cambio, sus desventajas incluyen la suposición fuerte de independencia entre características (en la realidad las variables suelen estar correlacionadas), el problema de probabilidad cero (cuando una característica no aparece en el entrenamiento para una clase, aunque puede arreglarse con Laplace smoothing) y la incapacidad para capturar relaciones complejas entre variables.",[16,7737,7738],{},[12,7739,7740,7741,7744],{},"¿Por qué funciona si la independencia es irreal? Porque en clasificación, muchas veces ",[122,7742,7743],{},"no necesitamos que las probabilidades sean perfectas",", solo necesitamos que la clase correcta tenga la probabilidad más alta. Naive Bayes suele acertar en la comparación relativa, aunque el valor exacto no sea completamente preciso.",[1612,7746,7748],{"id":7747},"ejercicio-práctico","Ejercicio práctico",[12,7750,7751],{},"Haremos un ejercicio con un dataset de correos electrónicos para clasificar si son spam o no spam usando Naive Bayes. Para esto, usaremos el dataset \"SMS Spam Collection\" que contiene mensajes de texto etiquetados como \"ham\" (no spam) o \"spam\".",[16,7753,7754],{},[12,7755,7756,7757,61],{},"Puedes ver el código y seguir el ejercicio en esta ",[22,7758,7763],{"rel":7759,"href":7762,"target":27},[7760,7761],"noopener","noreferrer","https:\u002F\u002Fcolab.research.google.com\u002Fdrive\u002F1cPc735Pqffpx2NwGM8wkMPr36arkIari?usp=sharing","notebook de Google Colab",[12,7765,7766,7767],{},"Dataset: ",[22,7768,7769],{"href":7769,"rel":7770},"https:\u002F\u002Farchive.ics.uci.edu\u002Fml\u002Fdatasets\u002FSMS+Spam+Collection",[26],[46,7772,7774],{"id":7773},"árboles-de-probabilidad","Árboles de probabilidad",[12,7776,7777],{},"Los árboles de probabilidad son una herramienta visual que se utiliza para representar y calcular probabilidades de eventos compuestos. Se construyen a partir de un nodo raíz que representa el evento inicial, y a partir de ahí se ramifican en nodos hijos que representan eventos posteriores o condiciones adicionales. Cada rama del árbol representa una posible secuencia de eventos, y se asigna una probabilidad a cada rama.",[323,7779,7781],{"id":7780},"como-se-contruyen","Como se contruyen",[12,7783,7784],{},"Veámos cómo construir un árbol de probabilidad paso a paso, usando como ejemplo el lanzamiento de una moneda dos veces:",[117,7786,7787],{},[33,7788,7789],{},"El primer paso es identificar el evento inicial: Se dibuja el nodo raíz y sus posibles resultados. Por ejemplo, al lanzar una moneda, el nodo raíz representaría el lanzamiento y las ramas representarían los resultados posibles (cara o cruz).",[46,7791,7792],{"id":169},[7793,7794],"mermaid-diagram",{"content":7795},"graph TD\n   A[Lanzar una moneda] --> | 0.5 | B(Cara)\n   A --> | 0.5 | C(Cruz)",[117,7797,7798],{"start":192},[33,7799,7800],{},"Agregamos el segundo evento condicionado al primer evento: Si queremos lanzar la moneda dos veces, agregamos un segundo nivel al árbol. Cada rama del primer nivel se ramifica en dos nuevas ramas que representan los resultados del segundo lanzamiento.",[46,7802,7804],{"id":7803},"_1",[7793,7805],{"content":7806},"graph TD\n   A[Lanzar una moneda] --> | 0.5 | B(Cara)\n   A --> | 0.5 | C(Cruz)\n   B --> | 0.5 | D(Cara)\n   B --> | 0.5 | E(Cruz)\n   C --> | 0.5 | F(Cara)\n   C --> | 0.5 | G(Cruz)",[323,7808,7810],{"id":7809},"operaciones","Operaciones",[12,7812,7813],{},"Pero, ¿cómo se calculan las probabilidades de eventos compuestos usando el árbol? Aquí es donde entran en juego las reglas de probabilidad:",[30,7815,7816,7825],{},[33,7817,7818,7821,7822,61],{},[122,7819,7820],{},"Regla del producto (intersección)",": Para obtener la probabilidad de una secuencia especifica de eventos, se multiplican las probabilidades a lo largo de la rama correspondiente. Por ejemplo, la probabilidad de obtener cara en el primer lanzamiento y cruz en el segundo lanzamiento se calcula como ",[145,7823,7824],{},"P(Cara, Cruz) = P(Cara) * P(Cruz | Cara) = 0.5 * 0.5 = 0.25",[33,7826,7827,7830,7831,61],{},[122,7828,7829],{},"Regla de la suma (unión)",": Si un evento puede ocurrir de varias maneras, se suman las probabilidades de cada rama que conduce a ese evento. Por ejemplo, la probabilidad de obtener exactamente una cara en dos lanzamientos se calcula sumando las probabilidades de las ramas que representan esa situación: ",[145,7832,7833],{},"P(1 Cara) = P(Cara, Cruz) + P(Cruz, Cara) = 0.25 + 0.25 = 0.5",[46,7835,7837],{"id":7836},"ejemplo-de-aplicación","Ejemplo de aplicación",[12,7839,7840],{},"Hagámos un ejemplos mas interesante, supongamos que tenemos un test para detectar una enfermedad que es 99% preciso (es decir, tiene una tasa de falsos positivos del 1% y una tasa de falsos negativos del 1%). La prevalencia de la enfermedad en la población es del 0.1%. Queremos calcular la probabilidad de que una persona tenga la enfermedad dado que el test ha dado positivo.\nPara resolver este problema, podemos construir un árbol de probabilidad:",[46,7842,7844],{"id":7843},"_2",[7793,7845],{"content":7846},"graph TD\n   A[Estado de la persona] --> |0.001| B(Enfermo)\n   A --> |0.999| C(No enfermo)\n   B --> |0.99| D(Test positivo)\n   B --> |0.01| E(Test negativo)\n   C --> |0.01| F(Test positivo)\n   C --> |0.99| G(Test negativo)",[12,7848,7849],{},"En este árbol, el nodo raíz representa el estado de la persona, y las ramas representan las probabilidades de cada resultado dado la condición de estar enfermo o no estar enfermo. Para calcular la probabilidad de que una persona tenga la enfermedad dado que el test ha dado positivo, utilizamos la regla del producto y la regla de la suma:",[86,7851,7853],{"className":7852},[3173],[86,7854,7856,8030],{"className":7855},[955],[86,7857,7859],{"className":7858},[959],[961,7860,7861],{"xmlns":963,"display":3182},[965,7862,7863,8027],{},[968,7864,7865,7867,7869,7872,7874,7876,7878,7880,7882,7884,7886,7888,7890,7893,7895,7898,7900,7902,7904,7906,7908,7910,7913,7915,7917,7919],{},[974,7866,3738],{},[3191,7868,243],{"stretchy":3295},[974,7870,7871],{},"E",[974,7873,6896],{},[974,7875,6178],{},[974,7877,6181],{},[974,7879,6184],{},[974,7881,5940],{},[974,7883,6018],{},[3191,7885,4804],{},[974,7887,3489],{},[974,7889,6181],{},[974,7891,7892],{},"s",[974,7894,6187],{},[3754,7896,7897],{}," ",[974,7899,12],{},[974,7901,6018],{},[974,7903,7892],{},[974,7905,7285],{},[974,7907,6187],{},[974,7909,7285],{},[974,7911,7912],{},"v",[974,7914,6018],{},[3191,7916,867],{"stretchy":3295},[3191,7918,258],{},[3749,7920,7921,7993],{},[968,7922,7923,7925,7927,7929,7931,7933,7935,7937,7939,7941,7943,7945,7947,7949,7951,7953,7955,7957,7959,7961,7963,7965,7967,7969,7971,7973,7975,7977,7979,7981,7983,7985,7987,7989,7991],{},[974,7924,3738],{},[3191,7926,243],{"stretchy":3295},[974,7928,3489],{},[974,7930,6181],{},[974,7932,7892],{},[974,7934,6187],{},[3754,7936,7897],{},[974,7938,12],{},[974,7940,6018],{},[974,7942,7892],{},[974,7944,7285],{},[974,7946,6187],{},[974,7948,7285],{},[974,7950,7912],{},[974,7952,6018],{},[3191,7954,4804],{},[974,7956,7871],{},[974,7958,6896],{},[974,7960,6178],{},[974,7962,6181],{},[974,7964,6184],{},[974,7966,5940],{},[974,7968,6018],{},[3191,7970,867],{"stretchy":3295},[3191,7972,4975],{},[974,7974,3738],{},[3191,7976,243],{"stretchy":3295},[974,7978,7871],{},[974,7980,6896],{},[974,7982,6178],{},[974,7984,6181],{},[974,7986,6184],{},[974,7988,5940],{},[974,7990,6018],{},[3191,7992,867],{"stretchy":3295},[968,7994,7995,7997,7999,8001,8003,8005,8007,8009,8011,8013,8015,8017,8019,8021,8023,8025],{},[974,7996,3738],{},[3191,7998,243],{"stretchy":3295},[974,8000,3489],{},[974,8002,6181],{},[974,8004,7892],{},[974,8006,6187],{},[3754,8008,7897],{},[974,8010,12],{},[974,8012,6018],{},[974,8014,7892],{},[974,8016,7285],{},[974,8018,6187],{},[974,8020,7285],{},[974,8022,7912],{},[974,8024,6018],{},[3191,8026,867],{"stretchy":3295},[982,8028,8029],{"encoding":984},"P(Enfermo \\mid Test \\, positivo) = \\frac{P(Test \\, positivo \\mid Enfermo) \\cdot P(Enfermo)}{P(Test \\, positivo)}",[86,8031,8033,8072,8125],{"className":8032,"ariaHidden":990},[989],[86,8034,8036,8039,8042,8045,8048,8051,8054,8057,8060,8063,8066,8069],{"className":8035},[994],[86,8037],{"className":8038,"style":3794},[998],[86,8040,3738],{"className":8041,"style":3537},[1003,1007],[86,8043,243],{"className":8044},[3320],[86,8046,7871],{"className":8047,"style":4133},[1003,1007],[86,8049,6896],{"className":8050},[1003,1007],[86,8052,6178],{"className":8053,"style":6231},[1003,1007],[86,8055,6236],{"className":8056,"style":6235},[1003,1007],[86,8058,5940],{"className":8059},[1003,1007],[86,8061,6018],{"className":8062},[1003,1007],[86,8064],{"className":8065,"style":3222},[3221],[86,8067,4804],{"className":8068},[3226],[86,8070],{"className":8071,"style":3222},[3221],[86,8073,8075,8078,8081,8084,8087,8090,8093,8097,8100,8103,8106,8110,8113,8116,8119,8122],{"className":8074},[994],[86,8076],{"className":8077,"style":3794},[998],[86,8079,3489],{"className":8080,"style":3537},[1003,1007],[86,8082,2532],{"className":8083},[1003,1007],[86,8085,6187],{"className":8086},[1003,1007],[86,8088],{"className":8089,"style":4162},[3221],[86,8091,12],{"className":8092},[1003,1007],[86,8094,8096],{"className":8095},[1003,1007],"os",[86,8098,7285],{"className":8099},[1003,1007],[86,8101,6187],{"className":8102},[1003,1007],[86,8104,7285],{"className":8105},[1003,1007],[86,8107,7912],{"className":8108,"style":8109},[1003,1007],"margin-right:0.0359em;",[86,8111,6018],{"className":8112},[1003,1007],[86,8114,867],{"className":8115},[3356],[86,8117],{"className":8118,"style":3222},[3221],[86,8120,258],{"className":8121},[3226],[86,8123],{"className":8124,"style":3222},[3221],[86,8126,8128,8131],{"className":8127},[994],[86,8129],{"className":8130,"style":5687},[998],[86,8132,8134,8137,8331],{"className":8133},[1003],[86,8135],{"className":8136},[3320,3829],[86,8138,8140],{"className":8139},[3749],[86,8141,8143,8323],{"className":8142},[1016,3836],[86,8144,8146,8320],{"className":8145},[1020],[86,8147,8149,8199,8207],{"className":8148,"style":5706},[1024],[86,8150,8151,8154],{"style":3846},[86,8152],{"className":8153,"style":3850},[1031],[86,8155,8157,8160,8163,8166,8169,8172,8175,8178,8181,8184,8187,8190,8193,8196],{"className":8156},[1003],[86,8158,3738],{"className":8159,"style":3537},[1003,1007],[86,8161,243],{"className":8162},[3320],[86,8164,3489],{"className":8165,"style":3537},[1003,1007],[86,8167,2532],{"className":8168},[1003,1007],[86,8170,6187],{"className":8171},[1003,1007],[86,8173],{"className":8174,"style":4162},[3221],[86,8176,12],{"className":8177},[1003,1007],[86,8179,8096],{"className":8180},[1003,1007],[86,8182,7285],{"className":8183},[1003,1007],[86,8185,6187],{"className":8186},[1003,1007],[86,8188,7285],{"className":8189},[1003,1007],[86,8191,7912],{"className":8192,"style":8109},[1003,1007],[86,8194,6018],{"className":8195},[1003,1007],[86,8197,867],{"className":8198},[3356],[86,8200,8201,8204],{"style":3901},[86,8202],{"className":8203,"style":3850},[1031],[86,8205],{"className":8206,"style":3909},[3908],[86,8208,8209,8212],{"style":3912},[86,8210],{"className":8211,"style":3850},[1031],[86,8213,8215,8218,8221,8224,8227,8230,8233,8236,8239,8242,8245,8248,8251,8254,8257,8260,8263,8266,8269,8272,8275,8278,8281,8284,8287,8290,8293,8296,8299,8302,8305,8308,8311,8314,8317],{"className":8214},[1003],[86,8216,3738],{"className":8217,"style":3537},[1003,1007],[86,8219,243],{"className":8220},[3320],[86,8222,3489],{"className":8223,"style":3537},[1003,1007],[86,8225,2532],{"className":8226},[1003,1007],[86,8228,6187],{"className":8229},[1003,1007],[86,8231],{"className":8232,"style":4162},[3221],[86,8234,12],{"className":8235},[1003,1007],[86,8237,8096],{"className":8238},[1003,1007],[86,8240,7285],{"className":8241},[1003,1007],[86,8243,6187],{"className":8244},[1003,1007],[86,8246,7285],{"className":8247},[1003,1007],[86,8249,7912],{"className":8250,"style":8109},[1003,1007],[86,8252,6018],{"className":8253},[1003,1007],[86,8255],{"className":8256,"style":3222},[3221],[86,8258,4804],{"className":8259},[3226],[86,8261],{"className":8262,"style":3222},[3221],[86,8264,7871],{"className":8265,"style":4133},[1003,1007],[86,8267,6896],{"className":8268},[1003,1007],[86,8270,6178],{"className":8271,"style":6231},[1003,1007],[86,8273,6236],{"className":8274,"style":6235},[1003,1007],[86,8276,5940],{"className":8277},[1003,1007],[86,8279,6018],{"className":8280},[1003,1007],[86,8282,867],{"className":8283},[3356],[86,8285],{"className":8286,"style":5012},[3221],[86,8288,4975],{"className":8289},[5016],[86,8291],{"className":8292,"style":5012},[3221],[86,8294,3738],{"className":8295,"style":3537},[1003,1007],[86,8297,243],{"className":8298},[3320],[86,8300,7871],{"className":8301,"style":4133},[1003,1007],[86,8303,6896],{"className":8304},[1003,1007],[86,8306,6178],{"className":8307,"style":6231},[1003,1007],[86,8309,6236],{"className":8310,"style":6235},[1003,1007],[86,8312,5940],{"className":8313},[1003,1007],[86,8315,6018],{"className":8316},[1003,1007],[86,8318,867],{"className":8319},[3356],[86,8321,3963],{"className":8322},[3962],[86,8324,8326],{"className":8325},[1020],[86,8327,8329],{"className":8328,"style":5797},[1024],[86,8330],{},[86,8332],{"className":8333},[3356,3829],[12,8335,3273],{},[30,8337,8338,8511,8608],{},[33,8339,8340,8510],{},[86,8341,8343,8408],{"className":8342},[955],[86,8344,8346],{"className":8345},[959],[961,8347,8348],{"xmlns":963},[965,8349,8350,8405],{},[968,8351,8352,8354,8356,8358,8360,8362,8364,8366,8368,8370,8372,8374,8376,8378,8380,8382,8384,8386,8388,8390,8392,8394,8396,8398,8400,8402],{},[974,8353,3738],{},[3191,8355,243],{"stretchy":3295},[974,8357,3489],{},[974,8359,6181],{},[974,8361,7892],{},[974,8363,6187],{},[3754,8365,7897],{},[974,8367,12],{},[974,8369,6018],{},[974,8371,7892],{},[974,8373,7285],{},[974,8375,6187],{},[974,8377,7285],{},[974,8379,7912],{},[974,8381,6018],{},[3191,8383,4804],{},[974,8385,7871],{},[974,8387,6896],{},[974,8389,6178],{},[974,8391,6181],{},[974,8393,6184],{},[974,8395,5940],{},[974,8397,6018],{},[3191,8399,867],{"stretchy":3295},[3191,8401,258],{},[978,8403,8404],{},"0.99",[982,8406,8407],{"encoding":984},"P(Test \\, positivo \\mid Enfermo) = 0.99",[86,8409,8411,8465,8501],{"className":8410,"ariaHidden":990},[989],[86,8412,8414,8417,8420,8423,8426,8429,8432,8435,8438,8441,8444,8447,8450,8453,8456,8459,8462],{"className":8413},[994],[86,8415],{"className":8416,"style":3794},[998],[86,8418,3738],{"className":8419,"style":3537},[1003,1007],[86,8421,243],{"className":8422},[3320],[86,8424,3489],{"className":8425,"style":3537},[1003,1007],[86,8427,2532],{"className":8428},[1003,1007],[86,8430,6187],{"className":8431},[1003,1007],[86,8433],{"className":8434,"style":4162},[3221],[86,8436,12],{"className":8437},[1003,1007],[86,8439,8096],{"className":8440},[1003,1007],[86,8442,7285],{"className":8443},[1003,1007],[86,8445,6187],{"className":8446},[1003,1007],[86,8448,7285],{"className":8449},[1003,1007],[86,8451,7912],{"className":8452,"style":8109},[1003,1007],[86,8454,6018],{"className":8455},[1003,1007],[86,8457],{"className":8458,"style":3222},[3221],[86,8460,4804],{"className":8461},[3226],[86,8463],{"className":8464,"style":3222},[3221],[86,8466,8468,8471,8474,8477,8480,8483,8486,8489,8492,8495,8498],{"className":8467},[994],[86,8469],{"className":8470,"style":3794},[998],[86,8472,7871],{"className":8473,"style":4133},[1003,1007],[86,8475,6896],{"className":8476},[1003,1007],[86,8478,6178],{"className":8479,"style":6231},[1003,1007],[86,8481,6236],{"className":8482,"style":6235},[1003,1007],[86,8484,5940],{"className":8485},[1003,1007],[86,8487,6018],{"className":8488},[1003,1007],[86,8490,867],{"className":8491},[3356],[86,8493],{"className":8494,"style":3222},[3221],[86,8496,258],{"className":8497},[3226],[86,8499],{"className":8500,"style":3222},[3221],[86,8502,8504,8507],{"className":8503},[994],[86,8505],{"className":8506,"style":5994},[998],[86,8508,8404],{"className":8509},[1003]," (tasa de verdaderos positivos)",[33,8512,8513,8607],{},[86,8514,8516,8553],{"className":8515},[955],[86,8517,8519],{"className":8518},[959],[961,8520,8521],{"xmlns":963},[965,8522,8523,8550],{},[968,8524,8525,8527,8529,8531,8533,8535,8537,8539,8541,8543,8545,8547],{},[974,8526,3738],{},[3191,8528,243],{"stretchy":3295},[974,8530,7871],{},[974,8532,6896],{},[974,8534,6178],{},[974,8536,6181],{},[974,8538,6184],{},[974,8540,5940],{},[974,8542,6018],{},[3191,8544,867],{"stretchy":3295},[3191,8546,258],{},[978,8548,8549],{},"0.001",[982,8551,8552],{"encoding":984},"P(Enfermo) = 0.001",[86,8554,8556,8598],{"className":8555,"ariaHidden":990},[989],[86,8557,8559,8562,8565,8568,8571,8574,8577,8580,8583,8586,8589,8592,8595],{"className":8558},[994],[86,8560],{"className":8561,"style":3794},[998],[86,8563,3738],{"className":8564,"style":3537},[1003,1007],[86,8566,243],{"className":8567},[3320],[86,8569,7871],{"className":8570,"style":4133},[1003,1007],[86,8572,6896],{"className":8573},[1003,1007],[86,8575,6178],{"className":8576,"style":6231},[1003,1007],[86,8578,6236],{"className":8579,"style":6235},[1003,1007],[86,8581,5940],{"className":8582},[1003,1007],[86,8584,6018],{"className":8585},[1003,1007],[86,8587,867],{"className":8588},[3356],[86,8590],{"className":8591,"style":3222},[3221],[86,8593,258],{"className":8594},[3226],[86,8596],{"className":8597,"style":3222},[3221],[86,8599,8601,8604],{"className":8600},[994],[86,8602],{"className":8603,"style":5994},[998],[86,8605,8549],{"className":8606},[1003]," (prevalencia de la enfermedad)",[33,8609,8610],{},[86,8611,8613,8813],{"className":8612},[955],[86,8614,8616],{"className":8615},[959],[961,8617,8618],{"xmlns":963},[965,8619,8620,8810],{},[968,8621,8622,8624,8626,8628,8630,8632,8634,8636,8638,8640,8642,8644,8646,8648,8650,8652,8654,8656,8658,8660,8662,8664,8666,8668,8670,8672,8674,8676,8678,8680,8682,8684,8686,8688,8690,8692,8694,8696,8698,8700,8702,8704,8706,8708,8710,8712,8714,8716,8718,8720,8722,8724,8726,8728,8730,8732,8734,8736,8738,8740,8742,8744,8746,8748,8750,8752,8754,8756,8758,8760,8762,8764,8766,8768,8770,8772,8774,8776,8778,8780,8782,8784,8786,8788,8790,8792,8794,8796,8798,8800,8802,8804,8806,8808],{},[974,8623,3738],{},[3191,8625,243],{"stretchy":3295},[974,8627,3489],{},[974,8629,6181],{},[974,8631,7892],{},[974,8633,6187],{},[3754,8635,7897],{},[974,8637,12],{},[974,8639,6018],{},[974,8641,7892],{},[974,8643,7285],{},[974,8645,6187],{},[974,8647,7285],{},[974,8649,7912],{},[974,8651,6018],{},[3191,8653,867],{"stretchy":3295},[3191,8655,258],{},[974,8657,3738],{},[3191,8659,243],{"stretchy":3295},[974,8661,3489],{},[974,8663,6181],{},[974,8665,7892],{},[974,8667,6187],{},[3754,8669,7897],{},[974,8671,12],{},[974,8673,6018],{},[974,8675,7892],{},[974,8677,7285],{},[974,8679,6187],{},[974,8681,7285],{},[974,8683,7912],{},[974,8685,6018],{},[3191,8687,4804],{},[974,8689,7871],{},[974,8691,6896],{},[974,8693,6178],{},[974,8695,6181],{},[974,8697,6184],{},[974,8699,5940],{},[974,8701,6018],{},[3191,8703,867],{"stretchy":3295},[3191,8705,4975],{},[974,8707,3738],{},[3191,8709,243],{"stretchy":3295},[974,8711,7871],{},[974,8713,6896],{},[974,8715,6178],{},[974,8717,6181],{},[974,8719,6184],{},[974,8721,5940],{},[974,8723,6018],{},[3191,8725,867],{"stretchy":3295},[3191,8727,6565],{},[974,8729,3738],{},[3191,8731,243],{"stretchy":3295},[974,8733,3489],{},[974,8735,6181],{},[974,8737,7892],{},[974,8739,6187],{},[3754,8741,7897],{},[974,8743,12],{},[974,8745,6018],{},[974,8747,7892],{},[974,8749,7285],{},[974,8751,6187],{},[974,8753,7285],{},[974,8755,7912],{},[974,8757,6018],{},[3191,8759,4804],{},[974,8761,3756],{},[974,8763,6018],{},[3754,8765,7897],{},[974,8767,6181],{},[974,8769,6896],{},[974,8771,6178],{},[974,8773,6181],{},[974,8775,6184],{},[974,8777,5940],{},[974,8779,6018],{},[3191,8781,867],{"stretchy":3295},[3191,8783,4975],{},[974,8785,3738],{},[3191,8787,243],{"stretchy":3295},[974,8789,3756],{},[974,8791,6018],{},[3754,8793,7897],{},[974,8795,6181],{},[974,8797,6896],{},[974,8799,6178],{},[974,8801,6181],{},[974,8803,6184],{},[974,8805,5940],{},[974,8807,6018],{},[3191,8809,867],{"stretchy":3295},[982,8811,8812],{"encoding":984},"P(Test \\, positivo) = P(Test \\, positivo \\mid Enfermo) \\cdot P(Enfermo) + P(Test \\, positivo \\mid No \\, enfermo) \\cdot P(No \\, enfermo)",[86,8814,8816,8873,8927,8963,9005,9059,9104],{"className":8815,"ariaHidden":990},[989],[86,8817,8819,8822,8825,8828,8831,8834,8837,8840,8843,8846,8849,8852,8855,8858,8861,8864,8867,8870],{"className":8818},[994],[86,8820],{"className":8821,"style":3794},[998],[86,8823,3738],{"className":8824,"style":3537},[1003,1007],[86,8826,243],{"className":8827},[3320],[86,8829,3489],{"className":8830,"style":3537},[1003,1007],[86,8832,2532],{"className":8833},[1003,1007],[86,8835,6187],{"className":8836},[1003,1007],[86,8838],{"className":8839,"style":4162},[3221],[86,8841,12],{"className":8842},[1003,1007],[86,8844,8096],{"className":8845},[1003,1007],[86,8847,7285],{"className":8848},[1003,1007],[86,8850,6187],{"className":8851},[1003,1007],[86,8853,7285],{"className":8854},[1003,1007],[86,8856,7912],{"className":8857,"style":8109},[1003,1007],[86,8859,6018],{"className":8860},[1003,1007],[86,8862,867],{"className":8863},[3356],[86,8865],{"className":8866,"style":3222},[3221],[86,8868,258],{"className":8869},[3226],[86,8871],{"className":8872,"style":3222},[3221],[86,8874,8876,8879,8882,8885,8888,8891,8894,8897,8900,8903,8906,8909,8912,8915,8918,8921,8924],{"className":8875},[994],[86,8877],{"className":8878,"style":3794},[998],[86,8880,3738],{"className":8881,"style":3537},[1003,1007],[86,8883,243],{"className":8884},[3320],[86,8886,3489],{"className":8887,"style":3537},[1003,1007],[86,8889,2532],{"className":8890},[1003,1007],[86,8892,6187],{"className":8893},[1003,1007],[86,8895],{"className":8896,"style":4162},[3221],[86,8898,12],{"className":8899},[1003,1007],[86,8901,8096],{"className":8902},[1003,1007],[86,8904,7285],{"className":8905},[1003,1007],[86,8907,6187],{"className":8908},[1003,1007],[86,8910,7285],{"className":8911},[1003,1007],[86,8913,7912],{"className":8914,"style":8109},[1003,1007],[86,8916,6018],{"className":8917},[1003,1007],[86,8919],{"className":8920,"style":3222},[3221],[86,8922,4804],{"className":8923},[3226],[86,8925],{"className":8926,"style":3222},[3221],[86,8928,8930,8933,8936,8939,8942,8945,8948,8951,8954,8957,8960],{"className":8929},[994],[86,8931],{"className":8932,"style":3794},[998],[86,8934,7871],{"className":8935,"style":4133},[1003,1007],[86,8937,6896],{"className":8938},[1003,1007],[86,8940,6178],{"className":8941,"style":6231},[1003,1007],[86,8943,6236],{"className":8944,"style":6235},[1003,1007],[86,8946,5940],{"className":8947},[1003,1007],[86,8949,6018],{"className":8950},[1003,1007],[86,8952,867],{"className":8953},[3356],[86,8955],{"className":8956,"style":5012},[3221],[86,8958,4975],{"className":8959},[5016],[86,8961],{"className":8962,"style":5012},[3221],[86,8964,8966,8969,8972,8975,8978,8981,8984,8987,8990,8993,8996,8999,9002],{"className":8965},[994],[86,8967],{"className":8968,"style":3794},[998],[86,8970,3738],{"className":8971,"style":3537},[1003,1007],[86,8973,243],{"className":8974},[3320],[86,8976,7871],{"className":8977,"style":4133},[1003,1007],[86,8979,6896],{"className":8980},[1003,1007],[86,8982,6178],{"className":8983,"style":6231},[1003,1007],[86,8985,6236],{"className":8986,"style":6235},[1003,1007],[86,8988,5940],{"className":8989},[1003,1007],[86,8991,6018],{"className":8992},[1003,1007],[86,8994,867],{"className":8995},[3356],[86,8997],{"className":8998,"style":5012},[3221],[86,9000,6565],{"className":9001},[5016],[86,9003],{"className":9004,"style":5012},[3221],[86,9006,9008,9011,9014,9017,9020,9023,9026,9029,9032,9035,9038,9041,9044,9047,9050,9053,9056],{"className":9007},[994],[86,9009],{"className":9010,"style":3794},[998],[86,9012,3738],{"className":9013,"style":3537},[1003,1007],[86,9015,243],{"className":9016},[3320],[86,9018,3489],{"className":9019,"style":3537},[1003,1007],[86,9021,2532],{"className":9022},[1003,1007],[86,9024,6187],{"className":9025},[1003,1007],[86,9027],{"className":9028,"style":4162},[3221],[86,9030,12],{"className":9031},[1003,1007],[86,9033,8096],{"className":9034},[1003,1007],[86,9036,7285],{"className":9037},[1003,1007],[86,9039,6187],{"className":9040},[1003,1007],[86,9042,7285],{"className":9043},[1003,1007],[86,9045,7912],{"className":9046,"style":8109},[1003,1007],[86,9048,6018],{"className":9049},[1003,1007],[86,9051],{"className":9052,"style":3222},[3221],[86,9054,4804],{"className":9055},[3226],[86,9057],{"className":9058,"style":3222},[3221],[86,9060,9062,9065,9068,9071,9074,9077,9080,9083,9086,9089,9092,9095,9098,9101],{"className":9061},[994],[86,9063],{"className":9064,"style":3794},[998],[86,9066,3756],{"className":9067,"style":6055},[1003,1007],[86,9069,6018],{"className":9070},[1003,1007],[86,9072],{"className":9073,"style":4162},[3221],[86,9075,6181],{"className":9076},[1003,1007],[86,9078,6896],{"className":9079},[1003,1007],[86,9081,6178],{"className":9082,"style":6231},[1003,1007],[86,9084,6236],{"className":9085,"style":6235},[1003,1007],[86,9087,5940],{"className":9088},[1003,1007],[86,9090,6018],{"className":9091},[1003,1007],[86,9093,867],{"className":9094},[3356],[86,9096],{"className":9097,"style":5012},[3221],[86,9099,4975],{"className":9100},[5016],[86,9102],{"className":9103,"style":5012},[3221],[86,9105,9107,9110,9113,9116,9119,9122,9125,9128,9131,9134,9137,9140,9143],{"className":9106},[994],[86,9108],{"className":9109,"style":3794},[998],[86,9111,3738],{"className":9112,"style":3537},[1003,1007],[86,9114,243],{"className":9115},[3320],[86,9117,3756],{"className":9118,"style":6055},[1003,1007],[86,9120,6018],{"className":9121},[1003,1007],[86,9123],{"className":9124,"style":4162},[3221],[86,9126,6181],{"className":9127},[1003,1007],[86,9129,6896],{"className":9130},[1003,1007],[86,9132,6178],{"className":9133,"style":6231},[1003,1007],[86,9135,6236],{"className":9136,"style":6235},[1003,1007],[86,9138,5940],{"className":9139},[1003,1007],[86,9141,6018],{"className":9142},[1003,1007],[86,9144,867],{"className":9145},[3356],[86,9147,9149],{"className":9148},[3173],[86,9150,9152,9219],{"className":9151},[955],[86,9153,9155],{"className":9154},[959],[961,9156,9157],{"xmlns":963,"display":3182},[965,9158,9159,9216],{},[968,9160,9161,9163,9165,9167,9169,9171,9173,9175,9177,9179,9181,9183,9185,9187,9189,9191,9193,9195,9197,9199,9201,9203,9206,9208,9211,9213],{},[974,9162,3738],{},[3191,9164,243],{"stretchy":3295},[974,9166,3489],{},[974,9168,6181],{},[974,9170,7892],{},[974,9172,6187],{},[3754,9174,7897],{},[974,9176,12],{},[974,9178,6018],{},[974,9180,7892],{},[974,9182,7285],{},[974,9184,6187],{},[974,9186,7285],{},[974,9188,7912],{},[974,9190,6018],{},[3191,9192,867],{"stretchy":3295},[3191,9194,258],{},[978,9196,8404],{},[3191,9198,4975],{},[978,9200,8549],{},[3191,9202,6565],{},[978,9204,9205],{},"0.01",[3191,9207,4975],{},[978,9209,9210],{},"0.999",[3191,9212,258],{},[978,9214,9215],{},"0.01098",[982,9217,9218],{"encoding":984},"P(Test \\, positivo) = 0.99 \\cdot 0.001 + 0.01 \\cdot 0.999 = 0.01098",[86,9220,9222,9279,9297,9316,9334,9352],{"className":9221,"ariaHidden":990},[989],[86,9223,9225,9228,9231,9234,9237,9240,9243,9246,9249,9252,9255,9258,9261,9264,9267,9270,9273,9276],{"className":9224},[994],[86,9226],{"className":9227,"style":3794},[998],[86,9229,3738],{"className":9230,"style":3537},[1003,1007],[86,9232,243],{"className":9233},[3320],[86,9235,3489],{"className":9236,"style":3537},[1003,1007],[86,9238,2532],{"className":9239},[1003,1007],[86,9241,6187],{"className":9242},[1003,1007],[86,9244],{"className":9245,"style":4162},[3221],[86,9247,12],{"className":9248},[1003,1007],[86,9250,8096],{"className":9251},[1003,1007],[86,9253,7285],{"className":9254},[1003,1007],[86,9256,6187],{"className":9257},[1003,1007],[86,9259,7285],{"className":9260},[1003,1007],[86,9262,7912],{"className":9263,"style":8109},[1003,1007],[86,9265,6018],{"className":9266},[1003,1007],[86,9268,867],{"className":9269},[3356],[86,9271],{"className":9272,"style":3222},[3221],[86,9274,258],{"className":9275},[3226],[86,9277],{"className":9278,"style":3222},[3221],[86,9280,9282,9285,9288,9291,9294],{"className":9281},[994],[86,9283],{"className":9284,"style":5994},[998],[86,9286,8404],{"className":9287},[1003],[86,9289],{"className":9290,"style":5012},[3221],[86,9292,4975],{"className":9293},[5016],[86,9295],{"className":9296,"style":5012},[3221],[86,9298,9300,9304,9307,9310,9313],{"className":9299},[994],[86,9301],{"className":9302,"style":9303},[998],"height:0.7278em;vertical-align:-0.0833em;",[86,9305,8549],{"className":9306},[1003],[86,9308],{"className":9309,"style":5012},[3221],[86,9311,6565],{"className":9312},[5016],[86,9314],{"className":9315,"style":5012},[3221],[86,9317,9319,9322,9325,9328,9331],{"className":9318},[994],[86,9320],{"className":9321,"style":5994},[998],[86,9323,9205],{"className":9324},[1003],[86,9326],{"className":9327,"style":5012},[3221],[86,9329,4975],{"className":9330},[5016],[86,9332],{"className":9333,"style":5012},[3221],[86,9335,9337,9340,9343,9346,9349],{"className":9336},[994],[86,9338],{"className":9339,"style":5994},[998],[86,9341,9210],{"className":9342},[1003],[86,9344],{"className":9345,"style":3222},[3221],[86,9347,258],{"className":9348},[3226],[86,9350],{"className":9351,"style":3222},[3221],[86,9353,9355,9358],{"className":9354},[994],[86,9356],{"className":9357,"style":5994},[998],[86,9359,9215],{"className":9360},[1003],[12,9362,9363],{},"Entonces:",[86,9365,9367],{"className":9366},[3173],[86,9368,9370,9450],{"className":9369},[955],[86,9371,9373],{"className":9372},[959],[961,9374,9375],{"xmlns":963,"display":3182},[965,9376,9377,9447],{},[968,9378,9379,9381,9383,9385,9387,9389,9391,9393,9395,9397,9399,9401,9403,9405,9407,9409,9411,9413,9415,9417,9419,9421,9423,9425,9427,9429,9441,9444],{},[974,9380,3738],{},[3191,9382,243],{"stretchy":3295},[974,9384,7871],{},[974,9386,6896],{},[974,9388,6178],{},[974,9390,6181],{},[974,9392,6184],{},[974,9394,5940],{},[974,9396,6018],{},[3191,9398,4804],{},[974,9400,3489],{},[974,9402,6181],{},[974,9404,7892],{},[974,9406,6187],{},[3754,9408,7897],{},[974,9410,12],{},[974,9412,6018],{},[974,9414,7892],{},[974,9416,7285],{},[974,9418,6187],{},[974,9420,7285],{},[974,9422,7912],{},[974,9424,6018],{},[3191,9426,867],{"stretchy":3295},[3191,9428,258],{},[3749,9430,9431,9439],{},[968,9432,9433,9435,9437],{},[978,9434,8404],{},[3191,9436,4975],{},[978,9438,8549],{},[978,9440,9215],{},[3191,9442,9443],{},"≈",[978,9445,9446],{},"0.09016",[982,9448,9449],{"encoding":984},"P(Enfermo \\mid Test \\, positivo) = \\frac{0.99 \\cdot 0.001}{0.01098} \\approx 0.09016",[86,9451,9453,9492,9543,9635],{"className":9452,"ariaHidden":990},[989],[86,9454,9456,9459,9462,9465,9468,9471,9474,9477,9480,9483,9486,9489],{"className":9455},[994],[86,9457],{"className":9458,"style":3794},[998],[86,9460,3738],{"className":9461,"style":3537},[1003,1007],[86,9463,243],{"className":9464},[3320],[86,9466,7871],{"className":9467,"style":4133},[1003,1007],[86,9469,6896],{"className":9470},[1003,1007],[86,9472,6178],{"className":9473,"style":6231},[1003,1007],[86,9475,6236],{"className":9476,"style":6235},[1003,1007],[86,9478,5940],{"className":9479},[1003,1007],[86,9481,6018],{"className":9482},[1003,1007],[86,9484],{"className":9485,"style":3222},[3221],[86,9487,4804],{"className":9488},[3226],[86,9490],{"className":9491,"style":3222},[3221],[86,9493,9495,9498,9501,9504,9507,9510,9513,9516,9519,9522,9525,9528,9531,9534,9537,9540],{"className":9494},[994],[86,9496],{"className":9497,"style":3794},[998],[86,9499,3489],{"className":9500,"style":3537},[1003,1007],[86,9502,2532],{"className":9503},[1003,1007],[86,9505,6187],{"className":9506},[1003,1007],[86,9508],{"className":9509,"style":4162},[3221],[86,9511,12],{"className":9512},[1003,1007],[86,9514,8096],{"className":9515},[1003,1007],[86,9517,7285],{"className":9518},[1003,1007],[86,9520,6187],{"className":9521},[1003,1007],[86,9523,7285],{"className":9524},[1003,1007],[86,9526,7912],{"className":9527,"style":8109},[1003,1007],[86,9529,6018],{"className":9530},[1003,1007],[86,9532,867],{"className":9533},[3356],[86,9535],{"className":9536,"style":3222},[3221],[86,9538,258],{"className":9539},[3226],[86,9541],{"className":9542,"style":3222},[3221],[86,9544,9546,9550,9626,9629,9632],{"className":9545},[994],[86,9547],{"className":9548,"style":9549},[998],"height:2.0074em;vertical-align:-0.686em;",[86,9551,9553,9556,9623],{"className":9552},[1003],[86,9554],{"className":9555},[3320,3829],[86,9557,9559],{"className":9558},[3749],[86,9560,9562,9614],{"className":9561},[1016,3836],[86,9563,9565,9611],{"className":9564},[1020],[86,9566,9569,9580,9588],{"className":9567,"style":9568},[1024],"height:1.3214em;",[86,9570,9571,9574],{"style":3846},[86,9572],{"className":9573,"style":3850},[1031],[86,9575,9577],{"className":9576},[1003],[86,9578,9215],{"className":9579},[1003],[86,9581,9582,9585],{"style":3901},[86,9583],{"className":9584,"style":3850},[1031],[86,9586],{"className":9587,"style":3909},[3908],[86,9589,9590,9593],{"style":3912},[86,9591],{"className":9592,"style":3850},[1031],[86,9594,9596,9599,9602,9605,9608],{"className":9595},[1003],[86,9597,8404],{"className":9598},[1003],[86,9600],{"className":9601,"style":5012},[3221],[86,9603,4975],{"className":9604},[5016],[86,9606],{"className":9607,"style":5012},[3221],[86,9609,8549],{"className":9610},[1003],[86,9612,3963],{"className":9613},[3962],[86,9615,9617],{"className":9616},[1020],[86,9618,9621],{"className":9619,"style":9620},[1024],"height:0.686em;",[86,9622],{},[86,9624],{"className":9625},[3356,3829],[86,9627],{"className":9628,"style":3222},[3221],[86,9630,9443],{"className":9631},[3226],[86,9633],{"className":9634,"style":3222},[3221],[86,9636,9638,9641],{"className":9637},[994],[86,9639],{"className":9640,"style":5994},[998],[86,9642,9446],{"className":9643},[1003],[12,9645,9646],{},"Esto significa que, a pesar de que el test es muy preciso, la probabilidad de que una persona tenga la enfermedad dado que el test ha dado positivo es solo del 9.016%. Esto se debe a la baja prevalencia de la enfermedad en la población, lo que hace que los falsos positivos tengan un impacto significativo en la probabilidad final.",[12,9648,9649],{},"Si lo vemos con números, de cada 100,000 personas, 100 tendrán la enfermedad (0.1% de prevalencia). De esos 100, 99 darán positivo (tasa de verdaderos positivos del 99%), pero de las 99,900 personas que no tienen la enfermedad, 999 darán positivo (tasa de falsos positivos del 1%). Por lo tanto, hay un total de 1,098 personas que dan positivo, pero solo 99 de ellas realmente tienen la enfermedad, lo que resulta en una probabilidad de aproximadamente el 9.016% de que una persona tenga la enfermedad dado un resultado positivo en el test, ¿mucho más inuitivo, no? :)",[43,9651],{},[46,9653,9655],{"id":9654},"naive-bayes-en-práctica","Naive Bayes en práctica",[12,9657,9658,9659,9663],{},"En el notebook ",[22,9660,9662],{"rel":9661,"href":7762,"target":27},[7760,7761],"Naive Bayes y el Dataset de Spam"," analizamos cada una de las variantes mencionadas anteriormente, explicaremos de manera resumen cada una de ellas aquí.",[323,9665,9667],{"id":9666},"gaussiannb","GaussianNB",[12,9669,9670],{},"El dataset Iris se adapta perfectamente a GaussianNB: cuatro mediciones continuas de flores con distribuciones aproximadamente gaussianas por clase. Primero, analizamos las distribuciones condicionales a la clase:",[164,9672,9674],{"className":166,"code":9673,"language":168,"meta":169,"style":169},"for cls in range(3):\n    sns.kdeplot(X_train[y_train == cls, feat_idx],\n                label=iris.target_names[cls], ax=ax, fill=True, alpha=0.3)\n",[145,9675,9676,9696,9728],{"__ignoreMap":169},[86,9677,9678,9681,9684,9687,9690,9692,9694],{"class":174,"line":175},[86,9679,9680],{"class":178},"for",[86,9682,9683],{"class":215}," cls",[86,9685,9686],{"class":178}," in",[86,9688,9689],{"class":812}," range",[86,9691,243],{"class":219},[86,9693,4100],{"class":223},[86,9695,249],{"class":219},[86,9697,9698,9701,9703,9706,9708,9711,9713,9716,9719,9721,9723,9726],{"class":174,"line":192},[86,9699,9700],{"class":182},"    sns",[86,9702,61],{"class":219},[86,9704,9705],{"class":182},"kdeplot",[86,9707,243],{"class":219},[86,9709,9710],{"class":182},"X_train",[86,9712,572],{"class":219},[86,9714,9715],{"class":182},"y_train ",[86,9717,9718],{"class":235},"==",[86,9720,9683],{"class":215},[86,9722,291],{"class":219},[86,9724,9725],{"class":182}," feat_idx",[86,9727,1147],{"class":219},[86,9729,9730,9733,9735,9738,9740,9743,9745,9748,9751,9754,9756,9759,9761,9764,9766,9768,9770,9773,9775,9778],{"class":174,"line":205},[86,9731,9732],{"class":304},"                label",[86,9734,258],{"class":219},[86,9736,9737],{"class":182},"iris",[86,9739,61],{"class":219},[86,9741,9742],{"class":182},"target_names",[86,9744,572],{"class":219},[86,9746,9747],{"class":215},"cls",[86,9749,9750],{"class":219},"],",[86,9752,9753],{"class":304}," ax",[86,9755,258],{"class":219},[86,9757,9758],{"class":182},"ax",[86,9760,291],{"class":219},[86,9762,9763],{"class":304}," fill",[86,9765,258],{"class":219},[86,9767,310],{"class":178},[86,9769,291],{"class":219},[86,9771,9772],{"class":304}," alpha",[86,9774,258],{"class":219},[86,9776,9777],{"class":223},"0.3",[86,9779,273],{"class":219},[12,9781,9782,9783,9786],{},"Los gráficos KDE confirman una forma de campana para cada especie, exactamente lo que GaussianNB presupone. Tras el ajuste a la longitud y el ancho de los pétalos, los límites de decisión son ",[122,9784,9785],{},"curvos"," (cuadráticos), no rectos. Esto sucede porque GaussianNB asigna a cada clase su propia gaussiana con media y varianza independientes:",[86,9788,9790],{"className":9789},[3173],[86,9791,9793,9921],{"className":9792},[955],[86,9794,9796],{"className":9795},[959],[961,9797,9798],{"xmlns":963,"display":3182},[965,9799,9800,9918],{},[968,9801,9802,9804,9806,9812,9814,9816,9818,9820,9850,9853,9855,9858],{},[974,9803,3738],{},[3191,9805,243],{"stretchy":3295},[6849,9807,9808,9810],{},[974,9809,3189],{},[974,9811,7285],{},[3191,9813,4804],{},[974,9815,1514],{},[3191,9817,867],{"stretchy":3295},[3191,9819,258],{},[3749,9821,9822,9824],{},[978,9823,802],{},[9825,9826,9827],"msqrt",{},[968,9828,9829,9831,9834],{},[978,9830,980],{},[974,9832,9833],{},"π",[9835,9836,9837,9840,9848],"msubsup",{},[974,9838,9839],{},"σ",[968,9841,9842,9844,9846],{},[974,9843,1514],{},[3191,9845,291],{"separator":990},[974,9847,7285],{},[978,9849,980],{},[974,9851,9852],{},"exp",[3191,9854,7250],{},[3754,9856,9857],{}," ⁣",[968,9859,9860,9862,9865,9916],{},[3191,9861,243],{"fence":990},[3191,9863,9864],{},"−",[3749,9866,9867,9898],{},[968,9868,9869,9871,9877,9879,9892],{},[3191,9870,243],{"stretchy":3295},[6849,9872,9873,9875],{},[974,9874,3189],{},[974,9876,7285],{},[3191,9878,9864],{},[6849,9880,9881,9884],{},[974,9882,9883],{},"μ",[968,9885,9886,9888,9890],{},[974,9887,1514],{},[3191,9889,291],{"separator":990},[974,9891,7285],{},[971,9893,9894,9896],{},[3191,9895,867],{"stretchy":3295},[978,9897,980],{},[968,9899,9900,9902],{},[978,9901,980],{},[9835,9903,9904,9906,9914],{},[974,9905,9839],{},[968,9907,9908,9910,9912],{},[974,9909,1514],{},[3191,9911,291],{"separator":990},[974,9913,7285],{},[978,9915,980],{},[3191,9917,867],{"fence":990},[982,9919,9920],{"encoding":984},"P(x_i \\mid C) = \\frac{1}{\\sqrt{2\\pi\\sigma_{C,i}^2}} \\exp\\!\\left(-\\frac{(x_i - \\mu_{C,i})^2}{2\\sigma_{C,i}^2}\\right)",[86,9922,9924,9985,10006],{"className":9923,"ariaHidden":990},[989],[86,9925,9927,9930,9933,9936,9976,9979,9982],{"className":9926},[994],[86,9928],{"className":9929,"style":3794},[998],[86,9931,3738],{"className":9932,"style":3537},[1003,1007],[86,9934,243],{"className":9935},[3320],[86,9937,9939,9942],{"className":9938},[1003],[86,9940,3189],{"className":9941},[1003,1007],[86,9943,9945],{"className":9944},[1012],[86,9946,9948,9968],{"className":9947},[1016,3836],[86,9949,9951,9965],{"className":9950},[1020],[86,9952,9954],{"className":9953,"style":7559},[1024],[86,9955,9956,9959],{"style":6987},[86,9957],{"className":9958,"style":1032},[1031],[86,9960,9962],{"className":9961},[1036,1037,1038,1039],[86,9963,7285],{"className":9964},[1003,1007,1039],[86,9966,3963],{"className":9967},[3962],[86,9969,9971],{"className":9970},[1020],[86,9972,9974],{"className":9973,"style":7006},[1024],[86,9975],{},[86,9977],{"className":9978,"style":3222},[3221],[86,9980,4804],{"className":9981},[3226],[86,9983],{"className":9984,"style":3222},[3221],[86,9986,9988,9991,9994,9997,10000,10003],{"className":9987},[994],[86,9989],{"className":9990,"style":3794},[998],[86,9992,1514],{"className":9993,"style":3512},[1003,1007],[86,9995,867],{"className":9996},[3356],[86,9998],{"className":9999,"style":3222},[3221],[86,10001,258],{"className":10002},[3226],[86,10004],{"className":10005,"style":3222},[3221],[86,10007,10009,10013,10208,10211,10214,10218,10221],{"className":10008},[994],[86,10010],{"className":10011,"style":10012},[998],"height:3.48em;vertical-align:-1.73em;",[86,10014,10016,10019,10205],{"className":10015},[1003],[86,10017],{"className":10018},[3320,3829],[86,10020,10022],{"className":10021},[3749],[86,10023,10025,10196],{"className":10024},[1016,3836],[86,10026,10028,10193],{"className":10027},[1020],[86,10029,10031,10172,10181],{"className":10030,"style":9568},[1024],[86,10032,10034,10038],{"style":10033},"top:-2.11em;",[86,10035],{"className":10036,"style":10037},[1031],"height:3.1681em;",[86,10039,10041],{"className":10040},[1003],[86,10042,10045],{"className":10043},[1003,10044],"sqrt",[86,10046,10048,10163],{"className":10047},[1016,3836],[86,10049,10051,10160],{"className":10050},[1020],[86,10052,10055,10138],{"className":10053,"style":10054},[1024],"height:1.1681em;",[86,10056,10060,10064],{"className":10057,"style":10059},[10058],"svg-align","top:-3.8em;",[86,10061],{"className":10062,"style":10063},[1031],"height:3.8em;",[86,10065,10068,10071,10074],{"className":10066,"style":10067},[1003],"padding-left:1em;",[86,10069,980],{"className":10070},[1003],[86,10072,9833],{"className":10073,"style":8109},[1003,1007],[86,10075,10077,10080],{"className":10076},[1003],[86,10078,9839],{"className":10079,"style":8109},[1003,1007],[86,10081,10083],{"className":10082},[1012],[86,10084,10086,10129],{"className":10085},[1016,3836],[86,10087,10089,10126],{"className":10088},[1020],[86,10090,10093,10114],{"className":10091,"style":10092},[1024],"height:0.7959em;",[86,10094,10096,10099],{"style":10095},"top:-2.4065em;margin-left:-0.0359em;margin-right:0.05em;",[86,10097],{"className":10098,"style":1032},[1031],[86,10100,10102],{"className":10101},[1036,1037,1038,1039],[86,10103,10105,10108,10111],{"className":10104},[1003,1039],[86,10106,1514],{"className":10107,"style":3512},[1003,1007,1039],[86,10109,291],{"className":10110},[4158,1039],[86,10112,7285],{"className":10113},[1003,1007,1039],[86,10115,10117,10120],{"style":10116},"top:-3.0448em;margin-right:0.05em;",[86,10118],{"className":10119,"style":1032},[1031],[86,10121,10123],{"className":10122},[1036,1037,1038,1039],[86,10124,980],{"className":10125},[1003,1039],[86,10127,3963],{"className":10128},[3962],[86,10130,10132],{"className":10131},[1020],[86,10133,10136],{"className":10134,"style":10135},[1024],"height:0.4296em;",[86,10137],{},[86,10139,10141,10144],{"style":10140},"top:-3.1281em;",[86,10142],{"className":10143,"style":10063},[1031],[86,10145,10149],{"className":10146,"style":10148},[10147],"hide-tail","min-width:1.02em;height:1.88em;",[10150,10151,10157],"svg",{"xmlns":10152,"width":10153,"height":10154,"viewBox":10155,"preserveAspectRatio":10156},"http:\u002F\u002Fwww.w3.org\u002F2000\u002Fsvg","400em","1.88em","0 0 400000 1944","xMinYMin slice",[246,10158],{"d":10159},"M983 90\nl0 -0\nc4,-6.7,10,-10,18,-10 H400000v40\nH1013.1s-83.4,268,-264.1,840c-180.7,572,-277,876.3,-289,913c-4.7,4.7,-12.7,7,-24,7\ns-12,0,-12,0c-1.3,-3.3,-3.7,-11.7,-7,-25c-35.3,-125.3,-106.7,-373.3,-214,-744\nc-10,12,-21,25,-33,39s-32,39,-32,39c-6,-5.3,-15,-14,-27,-26s25,-30,25,-30\nc26.7,-32.7,52,-63,76,-91s52,-60,52,-60s208,722,208,722\nc56,-175.3,126.3,-397.3,211,-666c84.7,-268.7,153.8,-488.2,207.5,-658.5\nc53.7,-170.3,84.5,-266.8,92.5,-289.5z\nM1001 80h400000v40h-400000z",[86,10161,3963],{"className":10162},[3962],[86,10164,10166],{"className":10165},[1020],[86,10167,10170],{"className":10168,"style":10169},[1024],"height:0.6719em;",[86,10171],{},[86,10173,10175,10178],{"style":10174},"top:-3.3981em;",[86,10176],{"className":10177,"style":10037},[1031],[86,10179],{"className":10180,"style":3909},[3908],[86,10182,10184,10187],{"style":10183},"top:-3.8451em;",[86,10185],{"className":10186,"style":10037},[1031],[86,10188,10190],{"className":10189},[1003],[86,10191,802],{"className":10192},[1003],[86,10194,3963],{"className":10195},[3962],[86,10197,10199],{"className":10198},[1020],[86,10200,10203],{"className":10201,"style":10202},[1024],"height:1.73em;",[86,10204],{},[86,10206],{"className":10207},[3356,3829],[86,10209],{"className":10210,"style":4162},[3221],[86,10212,9852],{"className":10213},[7373],[86,10215],{"className":10216,"style":10217},[3221],"margin-right:-0.1667em;",[86,10219],{"className":10220,"style":4162},[3221],[86,10222,10224,10234,10237,10490],{"className":10223},[7131],[86,10225,10229],{"className":10226,"style":10228},[3320,10227],"delimcenter","top:0em;",[86,10230,243],{"className":10231},[10232,10233],"delimsizing","size4",[86,10235,9864],{"className":10236},[1003],[86,10238,10240,10243,10487],{"className":10239},[1003],[86,10241],{"className":10242},[3320,3829],[86,10244,10246],{"className":10245},[3749],[86,10247,10249,10478],{"className":10248},[1016,3836],[86,10250,10252,10475],{"className":10251},[1020],[86,10253,10256,10327,10335],{"className":10254,"style":10255},[1024],"height:1.4911em;",[86,10257,10258,10261],{"style":3846},[86,10259],{"className":10260,"style":3850},[1031],[86,10262,10264,10267],{"className":10263},[1003],[86,10265,980],{"className":10266},[1003],[86,10268,10270,10273],{"className":10269},[1003],[86,10271,9839],{"className":10272,"style":8109},[1003,1007],[86,10274,10276],{"className":10275},[1012],[86,10277,10279,10319],{"className":10278},[1016,3836],[86,10280,10282,10316],{"className":10281},[1020],[86,10283,10285,10305],{"className":10284,"style":10092},[1024],[86,10286,10287,10290],{"style":10095},[86,10288],{"className":10289,"style":1032},[1031],[86,10291,10293],{"className":10292},[1036,1037,1038,1039],[86,10294,10296,10299,10302],{"className":10295},[1003,1039],[86,10297,1514],{"className":10298,"style":3512},[1003,1007,1039],[86,10300,291],{"className":10301},[4158,1039],[86,10303,7285],{"className":10304},[1003,1007,1039],[86,10306,10307,10310],{"style":10116},[86,10308],{"className":10309,"style":1032},[1031],[86,10311,10313],{"className":10312},[1036,1037,1038,1039],[86,10314,980],{"className":10315},[1003,1039],[86,10317,3963],{"className":10318},[3962],[86,10320,10322],{"className":10321},[1020],[86,10323,10325],{"className":10324,"style":10135},[1024],[86,10326],{},[86,10328,10329,10332],{"style":3901},[86,10330],{"className":10331,"style":3850},[1031],[86,10333],{"className":10334,"style":3909},[3908],[86,10336,10337,10340],{"style":3912},[86,10338],{"className":10339,"style":3850},[1031],[86,10341,10343,10346,10386,10389,10392,10395,10446],{"className":10342},[1003],[86,10344,243],{"className":10345},[3320],[86,10347,10349,10352],{"className":10348},[1003],[86,10350,3189],{"className":10351},[1003,1007],[86,10353,10355],{"className":10354},[1012],[86,10356,10358,10378],{"className":10357},[1016,3836],[86,10359,10361,10375],{"className":10360},[1020],[86,10362,10364],{"className":10363,"style":7559},[1024],[86,10365,10366,10369],{"style":6987},[86,10367],{"className":10368,"style":1032},[1031],[86,10370,10372],{"className":10371},[1036,1037,1038,1039],[86,10373,7285],{"className":10374},[1003,1007,1039],[86,10376,3963],{"className":10377},[3962],[86,10379,10381],{"className":10380},[1020],[86,10382,10384],{"className":10383,"style":7006},[1024],[86,10385],{},[86,10387],{"className":10388,"style":5012},[3221],[86,10390,9864],{"className":10391},[5016],[86,10393],{"className":10394,"style":5012},[3221],[86,10396,10398,10401],{"className":10397},[1003],[86,10399,9883],{"className":10400},[1003,1007],[86,10402,10404],{"className":10403},[1012],[86,10405,10407,10437],{"className":10406},[1016,3836],[86,10408,10410,10434],{"className":10409},[1020],[86,10411,10414],{"className":10412,"style":10413},[1024],"height:0.3283em;",[86,10415,10416,10419],{"style":6987},[86,10417],{"className":10418,"style":1032},[1031],[86,10420,10422],{"className":10421},[1036,1037,1038,1039],[86,10423,10425,10428,10431],{"className":10424},[1003,1039],[86,10426,1514],{"className":10427,"style":3512},[1003,1007,1039],[86,10429,291],{"className":10430},[4158,1039],[86,10432,7285],{"className":10433},[1003,1007,1039],[86,10435,3963],{"className":10436},[3962],[86,10438,10440],{"className":10439},[1020],[86,10441,10444],{"className":10442,"style":10443},[1024],"height:0.2861em;",[86,10445],{},[86,10447,10449,10452],{"className":10448},[3356],[86,10450,867],{"className":10451},[3356],[86,10453,10455],{"className":10454},[1012],[86,10456,10458],{"className":10457},[1016],[86,10459,10461],{"className":10460},[1020],[86,10462,10464],{"className":10463,"style":999},[1024],[86,10465,10466,10469],{"style":1027},[86,10467],{"className":10468,"style":1032},[1031],[86,10470,10472],{"className":10471},[1036,1037,1038,1039],[86,10473,980],{"className":10474},[1003,1039],[86,10476,3963],{"className":10477},[3962],[86,10479,10481],{"className":10480},[1020],[86,10482,10485],{"className":10483,"style":10484},[1024],"height:1.1156em;",[86,10486],{},[86,10488],{"className":10489},[3356,3829],[86,10491,10493],{"className":10492,"style":10228},[3356,10227],[86,10494,867],{"className":10495},[10232,10233],[12,10497,10498,10502],{},[1945,10499],{"alt":10500,"src":10501},"Límites de decisión de GaussianNB en características de pétalos de iris","\u002Fblog\u002Fprobability-and-machine-learning\u002Fshared\u002Fnb_gaussian_boundary.webp",[901,10503,10504],{},"Límites de decisión de GaussianNB - Iris (longitud del pétalo vs. anchura del pétalo)",[12,10506,10507],{},"El gráfico de probabilidad posterior para una sola muestra de prueba nos dice con qué confianza el modelo asigna probabilidades. Aunque se incumple el supuesto de independencia (la longitud y el ancho del pétalo tienen una correlación de aproximadamente 0,96), GaussianNB alcanza una precisión de validación 5-fold CV Accuracy de aproximadamente el 96 %.",[164,10509,10512],{"className":10510,"code":10511,"language":3141},[3139],"GaussianNB 5-fold CV Accuracy: 0.953 +\u002F- 0.027\nIndividual fold scores: [0.933 0.967 0.933 0.933 1.   ]\n",[145,10513,10511],{"__ignoreMap":169},[323,10515,10517],{"id":10516},"multinomialnb","MultinomialNB",[12,10519,10520],{},"Para la clasificación de texto, las características son recuentos de palabras: números enteros no negativos que se ajustan a la verosimilitud multinomial:",[86,10522,10524],{"className":10523},[3173],[86,10525,10527,10599],{"className":10526},[955],[86,10528,10530],{"className":10529},[959],[961,10531,10532],{"xmlns":963,"display":3182},[965,10533,10534,10596],{},[968,10535,10536,10538,10540,10546,10548,10550,10552,10554],{},[974,10537,3738],{},[3191,10539,243],{"stretchy":3295},[6849,10541,10542,10544],{},[974,10543,3189],{},[974,10545,7285],{},[3191,10547,4804],{},[974,10549,1514],{},[3191,10551,867],{"stretchy":3295},[3191,10553,258],{},[3749,10555,10556,10575],{},[968,10557,10558,10570,10572],{},[6849,10559,10560,10562],{},[974,10561,3756],{},[968,10563,10564,10566,10568],{},[974,10565,1514],{},[3191,10567,291],{"separator":990},[974,10569,7285],{},[3191,10571,6565],{},[974,10573,10574],{},"α",[968,10576,10577,10583,10585,10587,10589,10591,10594],{},[6849,10578,10579,10581],{},[974,10580,3756],{},[974,10582,1514],{},[3191,10584,6565],{},[974,10586,10574],{},[3191,10588,4975],{},[974,10590,4804],{"mathvariant":4327},[974,10592,10593],{},"V",[974,10595,4804],{"mathvariant":4327},[982,10597,10598],{"encoding":984},"P(x_i \\mid C) = \\frac{N_{C,i} + \\alpha}{N_C + \\alpha \\cdot |V|}",[86,10600,10602,10663,10684],{"className":10601,"ariaHidden":990},[989],[86,10603,10605,10608,10611,10614,10654,10657,10660],{"className":10604},[994],[86,10606],{"className":10607,"style":3794},[998],[86,10609,3738],{"className":10610,"style":3537},[1003,1007],[86,10612,243],{"className":10613},[3320],[86,10615,10617,10620],{"className":10616},[1003],[86,10618,3189],{"className":10619},[1003,1007],[86,10621,10623],{"className":10622},[1012],[86,10624,10626,10646],{"className":10625},[1016,3836],[86,10627,10629,10643],{"className":10628},[1020],[86,10630,10632],{"className":10631,"style":7559},[1024],[86,10633,10634,10637],{"style":6987},[86,10635],{"className":10636,"style":1032},[1031],[86,10638,10640],{"className":10639},[1036,1037,1038,1039],[86,10641,7285],{"className":10642},[1003,1007,1039],[86,10644,3963],{"className":10645},[3962],[86,10647,10649],{"className":10648},[1020],[86,10650,10652],{"className":10651,"style":7006},[1024],[86,10653],{},[86,10655],{"className":10656,"style":3222},[3221],[86,10658,4804],{"className":10659},[3226],[86,10661],{"className":10662,"style":3222},[3221],[86,10664,10666,10669,10672,10675,10678,10681],{"className":10665},[994],[86,10667],{"className":10668,"style":3794},[998],[86,10670,1514],{"className":10671,"style":3512},[1003,1007],[86,10673,867],{"className":10674},[3356],[86,10676],{"className":10677,"style":3222},[3221],[86,10679,258],{"className":10680},[3226],[86,10682],{"className":10683,"style":3222},[3221],[86,10685,10687,10691],{"className":10686},[994],[86,10688],{"className":10689,"style":10690},[998],"height:2.2963em;vertical-align:-0.936em;",[86,10692,10694,10697,10878],{"className":10693},[1003],[86,10695],{"className":10696},[3320,3829],[86,10698,10700],{"className":10699},[3749],[86,10701,10703,10870],{"className":10702},[1016,3836],[86,10704,10706,10867],{"className":10705},[1020],[86,10707,10710,10790,10798],{"className":10708,"style":10709},[1024],"height:1.3603em;",[86,10711,10712,10715],{"style":3846},[86,10713],{"className":10714,"style":3850},[1031],[86,10716,10718,10759,10762,10765,10768,10772,10775,10778,10781,10784,10787],{"className":10717},[1003],[86,10719,10721,10724],{"className":10720},[1003],[86,10722,3756],{"className":10723,"style":6055},[1003,1007],[86,10725,10727],{"className":10726},[1012],[86,10728,10730,10751],{"className":10729},[1016,3836],[86,10731,10733,10748],{"className":10732},[1020],[86,10734,10736],{"className":10735,"style":10413},[1024],[86,10737,10739,10742],{"style":10738},"top:-2.55em;margin-left:-0.109em;margin-right:0.05em;",[86,10740],{"className":10741,"style":1032},[1031],[86,10743,10745],{"className":10744},[1036,1037,1038,1039],[86,10746,1514],{"className":10747,"style":3512},[1003,1007,1039],[86,10749,3963],{"className":10750},[3962],[86,10752,10754],{"className":10753},[1020],[86,10755,10757],{"className":10756,"style":7006},[1024],[86,10758],{},[86,10760],{"className":10761,"style":5012},[3221],[86,10763,6565],{"className":10764},[5016],[86,10766],{"className":10767,"style":5012},[3221],[86,10769,10574],{"className":10770,"style":10771},[1003,1007],"margin-right:0.0037em;",[86,10773],{"className":10774,"style":5012},[3221],[86,10776,4975],{"className":10777},[5016],[86,10779],{"className":10780,"style":5012},[3221],[86,10782,4804],{"className":10783},[1003],[86,10785,10593],{"className":10786,"style":5012},[1003,1007],[86,10788,4804],{"className":10789},[1003],[86,10791,10792,10795],{"style":3901},[86,10793],{"className":10794,"style":3850},[1031],[86,10796],{"className":10797,"style":3909},[3908],[86,10799,10800,10803],{"style":3912},[86,10801],{"className":10802,"style":3850},[1031],[86,10804,10806,10855,10858,10861,10864],{"className":10805},[1003],[86,10807,10809,10812],{"className":10808},[1003],[86,10810,3756],{"className":10811,"style":6055},[1003,1007],[86,10813,10815],{"className":10814},[1012],[86,10816,10818,10847],{"className":10817},[1016,3836],[86,10819,10821,10844],{"className":10820},[1020],[86,10822,10824],{"className":10823,"style":10413},[1024],[86,10825,10826,10829],{"style":10738},[86,10827],{"className":10828,"style":1032},[1031],[86,10830,10832],{"className":10831},[1036,1037,1038,1039],[86,10833,10835,10838,10841],{"className":10834},[1003,1039],[86,10836,1514],{"className":10837,"style":3512},[1003,1007,1039],[86,10839,291],{"className":10840},[4158,1039],[86,10842,7285],{"className":10843},[1003,1007,1039],[86,10845,3963],{"className":10846},[3962],[86,10848,10850],{"className":10849},[1020],[86,10851,10853],{"className":10852,"style":10443},[1024],[86,10854],{},[86,10856],{"className":10857,"style":5012},[3221],[86,10859,6565],{"className":10860},[5016],[86,10862],{"className":10863,"style":5012},[3221],[86,10865,10574],{"className":10866,"style":10771},[1003,1007],[86,10868,3963],{"className":10869},[3962],[86,10871,10873],{"className":10872},[1020],[86,10874,10876],{"className":10875,"style":5797},[1024],[86,10877],{},[86,10879],{"className":10880},[3356,3829],[12,10882,10883,10884,10887,10888,10917,10918,10946],{},"El parámetro de suavizado de Laplace (",[122,10885,10886],{},"Laplace smoothing",") ",[86,10889,10891,10905],{"className":10890},[955],[86,10892,10894],{"className":10893},[959],[961,10895,10896],{"xmlns":963},[965,10897,10898,10902],{},[968,10899,10900],{},[974,10901,10574],{},[982,10903,10904],{"encoding":984},"\\alpha",[86,10906,10908],{"className":10907,"ariaHidden":990},[989],[86,10909,10911,10914],{"className":10910},[994],[86,10912],{"className":10913,"style":7401},[998],[86,10915,10574],{"className":10916,"style":10771},[1003,1007]," evita el problema de la frecuencia cero: si una palabra nunca aparece en los datos de entrenamiento de la clase ",[86,10919,10921,10934],{"className":10920},[955],[86,10922,10924],{"className":10923},[959],[961,10925,10926],{"xmlns":963},[965,10927,10928,10932],{},[968,10929,10930],{},[974,10931,1514],{},[982,10933,1514],{"encoding":984},[86,10935,10937],{"className":10936,"ariaHidden":990},[989],[86,10938,10940,10943],{"className":10939},[994],[86,10941],{"className":10942,"style":3575},[998],[86,10944,1514],{"className":10945,"style":3512},[1003,1007],", de lo contrario, anularía toda la distribución posterior. El notebook demuestra esto en el conjunto de datos de 20 grupos de noticias (4 categorías: béisbol, espacio, política\u002Farmas, gráficos por computadora):",[164,10948,10950],{"className":166,"code":10949,"language":168,"meta":169,"style":169},"vec = CountVectorizer(stop_words='english', max_features=10_000)\nX_train_counts = vec.fit_transform(news_train.data)\n\nmnb = MultinomialNB(alpha=1.0)\nmnb.fit(X_train_counts, news_train.target)\n",[145,10951,10952,10989,11016,11020,11042],{"__ignoreMap":169},[86,10953,10954,10957,10959,10962,10964,10967,10969,10972,10975,10977,10979,10982,10984,10987],{"class":174,"line":175},[86,10955,10956],{"class":182},"vec ",[86,10958,258],{"class":219},[86,10960,10961],{"class":182}," CountVectorizer",[86,10963,243],{"class":219},[86,10965,10966],{"class":304},"stop_words",[86,10968,258],{"class":219},[86,10970,10971],{"class":575},"'",[86,10973,10974],{"class":579},"english",[86,10976,10971],{"class":575},[86,10978,291],{"class":219},[86,10980,10981],{"class":304}," max_features",[86,10983,258],{"class":219},[86,10985,10986],{"class":223},"10_000",[86,10988,273],{"class":219},[86,10990,10991,10994,10996,10999,11001,11004,11006,11009,11011,11014],{"class":174,"line":192},[86,10992,10993],{"class":182},"X_train_counts ",[86,10995,258],{"class":219},[86,10997,10998],{"class":182}," vec",[86,11000,61],{"class":219},[86,11002,11003],{"class":182},"fit_transform",[86,11005,243],{"class":219},[86,11007,11008],{"class":182},"news_train",[86,11010,61],{"class":219},[86,11012,11013],{"class":182},"data",[86,11015,273],{"class":219},[86,11017,11018],{"class":174,"line":205},[86,11019,209],{"emptyLinePlaceholder":208},[86,11021,11022,11025,11027,11030,11032,11035,11037,11040],{"class":174,"line":212},[86,11023,11024],{"class":182},"mnb ",[86,11026,258],{"class":219},[86,11028,11029],{"class":182}," MultinomialNB",[86,11031,243],{"class":219},[86,11033,11034],{"class":304},"alpha",[86,11036,258],{"class":219},[86,11038,11039],{"class":223},"1.0",[86,11041,273],{"class":219},[86,11043,11044,11047,11049,11052,11054,11057,11059,11062,11064,11067],{"class":174,"line":227},[86,11045,11046],{"class":182},"mnb",[86,11048,61],{"class":219},[86,11050,11051],{"class":182},"fit",[86,11053,243],{"class":219},[86,11055,11056],{"class":182},"X_train_counts",[86,11058,291],{"class":219},[86,11060,11061],{"class":182}," news_train",[86,11063,61],{"class":219},[86,11065,11066],{"class":182},"target",[86,11068,273],{"class":219},[12,11070,11071,11072,11075,11076,11079],{},"Al analizar ",[145,11073,11074],{},"feature_log_prob_"," se revelan las palabras más informativas de cada categoría. Las palabras principales para ",[145,11077,11078],{},"sci.space"," incluyen términos específicos del dominio como \"nasa\", \"órbita\" y \"transbordador\": el modelo aprende señales lingüísticas reales, no ruido.",[12,11081,11082,11086],{},[1945,11083],{"alt":11084,"src":11085},"Palabras más informativas por categoría","\u002Fblog\u002Fprobability-and-machine-learning\u002Fshared\u002Fnb_multinomial_top_words.webp",[901,11087,11088],{},"Palabras más informativas por categoría - MultinomialNB en 20 grupos de noticias",[12,11090,11091],{},"Un barrido alfa muestra cómo la intensidad del suavizado afecta la precisión: un suavizado insuficiente (alfa cercano a 0) provoca sobreajuste en palabras poco frecuentes; un suavizado excesivo diluye la señal. El valor óptimo suele estar entre 0,1 y 1,0.",[12,11093,11094,11098],{},[1945,11095],{"alt":11096,"src":11097},"Efecto del Laplace smoothing en la precisión de la validación cruzada","\u002Fblog\u002Fprobability-and-machine-learning\u002Fshared\u002Fnb_multinomial_alpha.webp",[901,11099,11100],{},"Barrido de parámetros de Laplace smoothing: precisión de la validación cruzada de 5 pliegues",[323,11102,11104],{"id":11103},"bernoullinb","BernoulliNB",[12,11106,11107],{},"BernoulliNB trata cada característica como un indicador binario: ¿estaba presente (1) o ausente (0) esta palabra?",[86,11109,11111],{"className":11110},[3173],[86,11112,11114,11201],{"className":11113},[955],[86,11115,11117],{"className":11116},[959],[961,11118,11119],{"xmlns":963,"display":3182},[965,11120,11121,11198],{},[968,11122,11123,11125,11127,11133,11135,11137,11139,11141,11143,11145,11147,11149,11151,11161,11163,11166,11168,11170,11172,11174,11176,11178,11180,11182],{},[974,11124,3738],{},[3191,11126,243],{"stretchy":3295},[6849,11128,11129,11131],{},[974,11130,3189],{},[974,11132,7285],{},[3191,11134,4804],{},[974,11136,1514],{},[3191,11138,867],{"stretchy":3295},[3191,11140,258],{},[974,11142,3738],{},[3191,11144,243],{"stretchy":3295},[974,11146,7285],{},[3191,11148,4804],{},[974,11150,1514],{},[971,11152,11153,11155],{},[3191,11154,867],{"stretchy":3295},[6849,11156,11157,11159],{},[974,11158,3189],{},[974,11160,7285],{},[3191,11162,4975],{},[3191,11164,243],{"fence":990,"stretchy":990,"minsize":11165,"maxsize":11165},"1.2em",[978,11167,802],{},[3191,11169,9864],{},[974,11171,3738],{},[3191,11173,243],{"stretchy":3295},[974,11175,7285],{},[3191,11177,4804],{},[974,11179,1514],{},[3191,11181,867],{"stretchy":3295},[971,11183,11184,11186],{},[3191,11185,867],{"fence":990,"stretchy":990,"minsize":11165,"maxsize":11165},[968,11187,11188,11190,11192],{},[978,11189,802],{},[3191,11191,9864],{},[6849,11193,11194,11196],{},[974,11195,3189],{},[974,11197,7285],{},[982,11199,11200],{"encoding":984},"P(x_i \\mid C) = P(i \\mid C)^{x_i} \\cdot \\bigl(1 - P(i \\mid C)\\bigr)^{1 - x_i}",[86,11202,11204,11265,11286,11310,11404,11429,11453],{"className":11203,"ariaHidden":990},[989],[86,11205,11207,11210,11213,11216,11256,11259,11262],{"className":11206},[994],[86,11208],{"className":11209,"style":3794},[998],[86,11211,3738],{"className":11212,"style":3537},[1003,1007],[86,11214,243],{"className":11215},[3320],[86,11217,11219,11222],{"className":11218},[1003],[86,11220,3189],{"className":11221},[1003,1007],[86,11223,11225],{"className":11224},[1012],[86,11226,11228,11248],{"className":11227},[1016,3836],[86,11229,11231,11245],{"className":11230},[1020],[86,11232,11234],{"className":11233,"style":7559},[1024],[86,11235,11236,11239],{"style":6987},[86,11237],{"className":11238,"style":1032},[1031],[86,11240,11242],{"className":11241},[1036,1037,1038,1039],[86,11243,7285],{"className":11244},[1003,1007,1039],[86,11246,3963],{"className":11247},[3962],[86,11249,11251],{"className":11250},[1020],[86,11252,11254],{"className":11253,"style":7006},[1024],[86,11255],{},[86,11257],{"className":11258,"style":3222},[3221],[86,11260,4804],{"className":11261},[3226],[86,11263],{"className":11264,"style":3222},[3221],[86,11266,11268,11271,11274,11277,11280,11283],{"className":11267},[994],[86,11269],{"className":11270,"style":3794},[998],[86,11272,1514],{"className":11273,"style":3512},[1003,1007],[86,11275,867],{"className":11276},[3356],[86,11278],{"className":11279,"style":3222},[3221],[86,11281,258],{"className":11282},[3226],[86,11284],{"className":11285,"style":3222},[3221],[86,11287,11289,11292,11295,11298,11301,11304,11307],{"className":11288},[994],[86,11290],{"className":11291,"style":3794},[998],[86,11293,3738],{"className":11294,"style":3537},[1003,1007],[86,11296,243],{"className":11297},[3320],[86,11299,7285],{"className":11300},[1003,1007],[86,11302],{"className":11303,"style":3222},[3221],[86,11305,4804],{"className":11306},[3226],[86,11308],{"className":11309,"style":3222},[3221],[86,11311,11313,11316,11319,11395,11398,11401],{"className":11312},[994],[86,11314],{"className":11315,"style":3794},[998],[86,11317,1514],{"className":11318,"style":3512},[1003,1007],[86,11320,11322,11325],{"className":11321},[3356],[86,11323,867],{"className":11324},[3356],[86,11326,11328],{"className":11327},[1012],[86,11329,11331],{"className":11330},[1016],[86,11332,11334],{"className":11333},[1020],[86,11335,11338],{"className":11336,"style":11337},[1024],"height:0.7144em;",[86,11339,11340,11343],{"style":3258},[86,11341],{"className":11342,"style":1032},[1031],[86,11344,11346],{"className":11345},[1036,1037,1038,1039],[86,11347,11349],{"className":11348},[1003,1039],[86,11350,11352,11355],{"className":11351},[1003,1039],[86,11353,3189],{"className":11354},[1003,1007,1039],[86,11356,11358],{"className":11357},[1012],[86,11359,11361,11386],{"className":11360},[1016,3836],[86,11362,11364,11383],{"className":11363},[1020],[86,11365,11368],{"className":11366,"style":11367},[1024],"height:0.3281em;",[86,11369,11371,11375],{"style":11370},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[86,11372],{"className":11373,"style":11374},[1031],"height:2.5em;",[86,11376,11380],{"className":11377},[1036,11378,11379,1039],"reset-size3","size1",[86,11381,7285],{"className":11382},[1003,1007,1039],[86,11384,3963],{"className":11385},[3962],[86,11387,11389],{"className":11388},[1020],[86,11390,11393],{"className":11391,"style":11392},[1024],"height:0.143em;",[86,11394],{},[86,11396],{"className":11397,"style":5012},[3221],[86,11399,4975],{"className":11400},[5016],[86,11402],{"className":11403,"style":5012},[3221],[86,11405,11407,11411,11417,11420,11423,11426],{"className":11406},[994],[86,11408],{"className":11409,"style":11410},[998],"height:1.2em;vertical-align:-0.35em;",[86,11412,11414],{"className":11413},[3320],[86,11415,243],{"className":11416},[10232,11379],[86,11418,802],{"className":11419},[1003],[86,11421],{"className":11422,"style":5012},[3221],[86,11424,9864],{"className":11425},[5016],[86,11427],{"className":11428,"style":5012},[3221],[86,11430,11432,11435,11438,11441,11444,11447,11450],{"className":11431},[994],[86,11433],{"className":11434,"style":3794},[998],[86,11436,3738],{"className":11437,"style":3537},[1003,1007],[86,11439,243],{"className":11440},[3320],[86,11442,7285],{"className":11443},[1003,1007],[86,11445],{"className":11446,"style":3222},[3221],[86,11448,4804],{"className":11449},[3226],[86,11451],{"className":11452,"style":3222},[3221],[86,11454,11456,11460,11463,11466],{"className":11455},[994],[86,11457],{"className":11458,"style":11459},[998],"height:1.404em;vertical-align:-0.35em;",[86,11461,1514],{"className":11462,"style":3512},[1003,1007],[86,11464,867],{"className":11465},[3356],[86,11467,11469,11475],{"className":11468},[3356],[86,11470,11472],{"className":11471},[3356],[86,11473,867],{"className":11474},[10232,11379],[86,11476,11478],{"className":11477},[1012],[86,11479,11481],{"className":11480},[1016],[86,11482,11484],{"className":11483},[1020],[86,11485,11488],{"className":11486,"style":11487},[1024],"height:1.054em;",[86,11489,11491,11494],{"style":11490},"top:-3.3029em;margin-right:0.05em;",[86,11492],{"className":11493,"style":1032},[1031],[86,11495,11497],{"className":11496},[1036,1037,1038,1039],[86,11498,11500,11503,11506],{"className":11499},[1003,1039],[86,11501,802],{"className":11502},[1003,1039],[86,11504,9864],{"className":11505},[5016,1039],[86,11507,11509,11512],{"className":11508},[1003,1039],[86,11510,3189],{"className":11511},[1003,1007,1039],[86,11513,11515],{"className":11514},[1012],[86,11516,11518,11538],{"className":11517},[1016,3836],[86,11519,11521,11535],{"className":11520},[1020],[86,11522,11524],{"className":11523,"style":11367},[1024],[86,11525,11526,11529],{"style":11370},[86,11527],{"className":11528,"style":11374},[1031],[86,11530,11532],{"className":11531},[1036,11378,11379,1039],[86,11533,7285],{"className":11534},[1003,1007,1039],[86,11536,3963],{"className":11537},[3962],[86,11539,11541],{"className":11540},[1020],[86,11542,11544],{"className":11543,"style":11392},[1024],[86,11545],{},[12,11547,11548,11549,11733,11734,11737],{},"La diferencia más importante con respecto a MultinomialNB es en el término ",[86,11550,11552,11598],{"className":11551},[955],[86,11553,11555],{"className":11554},[959],[961,11556,11557],{"xmlns":963},[965,11558,11559,11595],{},[968,11560,11561,11563,11565,11567,11569,11571,11573,11575,11577,11579],{},[3191,11562,243],{"stretchy":3295},[978,11564,802],{},[3191,11566,9864],{},[974,11568,3738],{},[3191,11570,243],{"stretchy":3295},[974,11572,7285],{},[3191,11574,4804],{},[974,11576,1514],{},[3191,11578,867],{"stretchy":3295},[971,11580,11581,11583],{},[3191,11582,867],{"stretchy":3295},[968,11584,11585,11587,11589],{},[978,11586,802],{},[3191,11588,9864],{},[6849,11590,11591,11593],{},[974,11592,3189],{},[974,11594,7285],{},[982,11596,11597],{"encoding":984},"(1 - P(i \\mid C))^{1-x_i}",[86,11599,11601,11622,11646],{"className":11600,"ariaHidden":990},[989],[86,11602,11604,11607,11610,11613,11616,11619],{"className":11603},[994],[86,11605],{"className":11606,"style":3794},[998],[86,11608,243],{"className":11609},[3320],[86,11611,802],{"className":11612},[1003],[86,11614],{"className":11615,"style":5012},[3221],[86,11617,9864],{"className":11618},[5016],[86,11620],{"className":11621,"style":5012},[3221],[86,11623,11625,11628,11631,11634,11637,11640,11643],{"className":11624},[994],[86,11626],{"className":11627,"style":3794},[998],[86,11629,3738],{"className":11630,"style":3537},[1003,1007],[86,11632,243],{"className":11633},[3320],[86,11635,7285],{"className":11636},[1003,1007],[86,11638],{"className":11639,"style":3222},[3221],[86,11641,4804],{"className":11642},[3226],[86,11644],{"className":11645,"style":3222},[3221],[86,11647,11649,11652,11655,11658],{"className":11648},[994],[86,11650],{"className":11651,"style":3316},[998],[86,11653,1514],{"className":11654,"style":3512},[1003,1007],[86,11656,867],{"className":11657},[3356],[86,11659,11661,11664],{"className":11660},[3356],[86,11662,867],{"className":11663},[3356],[86,11665,11667],{"className":11666},[1012],[86,11668,11670],{"className":11669},[1016],[86,11671,11673],{"className":11672},[1020],[86,11674,11676],{"className":11675,"style":999},[1024],[86,11677,11678,11681],{"style":1027},[86,11679],{"className":11680,"style":1032},[1031],[86,11682,11684],{"className":11683},[1036,1037,1038,1039],[86,11685,11687,11690,11693],{"className":11686},[1003,1039],[86,11688,802],{"className":11689},[1003,1039],[86,11691,9864],{"className":11692},[5016,1039],[86,11694,11696,11699],{"className":11695},[1003,1039],[86,11697,3189],{"className":11698},[1003,1007,1039],[86,11700,11702],{"className":11701},[1012],[86,11703,11705,11725],{"className":11704},[1016,3836],[86,11706,11708,11722],{"className":11707},[1020],[86,11709,11711],{"className":11710,"style":11367},[1024],[86,11712,11713,11716],{"style":11370},[86,11714],{"className":11715,"style":11374},[1031],[86,11717,11719],{"className":11718},[1036,11378,11379,1039],[86,11720,7285],{"className":11721},[1003,1007,1039],[86,11723,3963],{"className":11724},[3962],[86,11726,11728],{"className":11727},[1020],[86,11729,11731],{"className":11730,"style":11392},[1024],[86,11732],{},", que ",[122,11735,11736],{},"penaliza la ausencia"," de una palabra. Si \"gol\" está fuertemente asociado con la clase de deportes, pero no aparece en un documento, BernoulliNB lo considera evidencia en contra de la clase de deportes. En el caso de MultinomialNB simplemente ignora las palabras ausentes.",[12,11739,11740],{},"El notebook ilustra esto con un vocabulario sencillo de cinco palabras: un documento que contiene solo \"juego\" (ambiguo) se clasifica de manera diferente según si las palabras de la clase de deportes están presentes o no.",[461,11742,11743,11756],{},[464,11744,11745],{},[467,11746,11747,11750,11753],{},[470,11748,11749],{},"Model",[470,11751,11752],{},"Behavior for absent features",[470,11754,11755],{},"Best for",[480,11757,11758,11768],{},[467,11759,11760,11762,11765],{},[485,11761,10517],{},[485,11763,11764],{},"Ignores absent features",[485,11766,11767],{},"Long documents, articles",[467,11769,11770,11772,11775],{},[485,11771,11104],{},[485,11773,11774],{},"Penalizes absent features",[485,11776,11777],{},"Short texts, tweets, profiles",[12,11779,11780],{},"En el subconjunto de 4 categorías de 20 grupos de noticias:",[461,11782,11783,11795],{},[464,11784,11785],{},[467,11786,11787,11789,11792],{},[470,11788,11749],{},[470,11790,11791],{},"Test Accuracy",[470,11793,11794],{},"CV Accuracy (5-fold)",[480,11796,11797,11807],{},[467,11798,11799,11801,11804],{},[485,11800,10517],{},[485,11802,11803],{},"~0.93",[485,11805,11806],{},"~0.92",[467,11808,11809,11811,11814],{},[485,11810,11104],{},[485,11812,11813],{},"~0.88",[485,11815,11813],{},[12,11817,11818],{},"El método MultinomialNB resulta ventajoso en documentos más largos (las publicaciones en grupos de noticias tienen un promedio de cientos de palabras), pero el método BernoulliNB puede superarlo en textos muy cortos donde la frecuencia no aporta información relevante.",[323,11820,11822],{"id":11821},"comparación-de-los-tres","Comparación de los tres",[461,11824,11825,11841],{},[464,11826,11827],{},[467,11828,11829,11832,11834,11836,11838],{},[470,11830,11831],{},"Propiedad",[470,11833,9667],{},[470,11835,10517],{},[470,11837,11104],{},[470,11839,11840],{},"ComplementNB",[480,11842,11843,11859,11875,11893],{},[467,11844,11845,11848,11851,11854,11857],{},[485,11846,11847],{},"Tipo de característica",[485,11849,11850],{},"Continua",[485,11852,11853],{},"Recuentos no negativos",[485,11855,11856],{},"Binaria (0\u002F1)",[485,11858,11853],{},[467,11860,11861,11863,11866,11869,11872],{},[485,11862,3990],{},[485,11864,11865],{},"PDF Gaussiana",[485,11867,11868],{},"Multinomial",[485,11870,11871],{},"Bernoulli",[485,11873,11874],{},"Multinomial Complementario",[467,11876,11877,11880,11883,11886,11891],{},[485,11878,11879],{},"¿Penaliza la ausencia?",[485,11881,11882],{},"N\u002FA",[485,11884,11885],{},"No",[485,11887,11888],{},[122,11889,11890],{},"Sí",[485,11892,11885],{},[467,11894,11895,11898,11901,11904,11907],{},[485,11896,11897],{},"Ideal para",[485,11899,11900],{},"Biología, sensores",[485,11902,11903],{},"Texto largo",[485,11905,11906],{},"Texto corto, perfiles",[485,11908,11909],{},"Texto desequilibrado",[16,11911,11912],{},[12,11913,11914,11915,11918],{},"La suposición de independencia que vimos en la sección ",[22,11916,5173],{"href":11917},"#eventos-independientes"," es lo que hace que NB sea \"ingenuo\" y precisamente por eso sigue funcionando: en la clasificación, solo necesitamos que la clase correcta ocupe el puesto más alto, no que las probabilidades sean exactas.",[323,11920,11922],{"id":11921},"sms-spam-classifier","SMS Spam Classifier",[12,11924,11925,11926,11931],{},"En el notebook finalizamos con el ",[22,11927,11930],{"href":11928,"rel":11929},"https:\u002F\u002Fwww.kaggle.com\u002Fdatasets\u002Fuciml\u002Fsms-spam-collection-dataset",[26],"SMS Spam Collection",", que contiene 5572 mensajes etiquetados como legítimos o spam. El proceso de preprocesamiento reproduce los pasos teóricos:",[164,11933,11935],{"className":166,"code":11934,"language":168,"meta":169,"style":169},"# 1. Clean - letters only, lowercase\ntext = re.sub('[^a-zA-Z]', ' ', text).lower().split()\n# 2. Remove stopwords\ntext = [w for w in text if w not in stop_words]\n# 3. Lemmatize\ntext = [lemmatizer.lemmatize(w, pos='v') for w in text]\n# 4. TF-IDF vectorization\nX = TfidfVectorizer(max_features=3000).fit_transform(corpus)\n",[145,11936,11937,11942,11992,11997,12034,12039,12086,12091],{"__ignoreMap":169},[86,11938,11939],{"class":174,"line":175},[86,11940,11941],{"class":1360},"# 1. Clean - letters only, lowercase\n",[86,11943,11944,11947,11949,11952,11954,11957,11959,11961,11964,11966,11968,11971,11973,11975,11978,11980,11983,11986,11989],{"class":174,"line":192},[86,11945,11946],{"class":182},"text ",[86,11948,258],{"class":219},[86,11950,11951],{"class":182}," re",[86,11953,61],{"class":219},[86,11955,11956],{"class":182},"sub",[86,11958,243],{"class":219},[86,11960,10971],{"class":575},[86,11962,11963],{"class":579},"[^a-zA-Z]",[86,11965,10971],{"class":575},[86,11967,291],{"class":219},[86,11969,11970],{"class":575}," '",[86,11972,11970],{"class":575},[86,11974,291],{"class":219},[86,11976,11977],{"class":182}," text",[86,11979,789],{"class":219},[86,11981,11982],{"class":182},"lower",[86,11984,11985],{"class":219},"().",[86,11987,11988],{"class":182},"split",[86,11990,11991],{"class":219},"()\n",[86,11993,11994],{"class":174,"line":205},[86,11995,11996],{"class":1360},"# 2. Remove stopwords\n",[86,11998,11999,12001,12003,12005,12008,12010,12013,12016,12019,12022,12024,12027,12029,12032],{"class":174,"line":212},[86,12000,11946],{"class":182},[86,12002,258],{"class":219},[86,12004,726],{"class":219},[86,12006,12007],{"class":182},"w ",[86,12009,9680],{"class":178},[86,12011,12012],{"class":182}," w ",[86,12014,12015],{"class":178},"in",[86,12017,12018],{"class":182}," text ",[86,12020,12021],{"class":178},"if",[86,12023,12012],{"class":182},[86,12025,12026],{"class":235},"not",[86,12028,9686],{"class":235},[86,12030,12031],{"class":182}," stop_words",[86,12033,752],{"class":219},[86,12035,12036],{"class":174,"line":227},[86,12037,12038],{"class":1360},"# 3. Lemmatize\n",[86,12040,12041,12043,12045,12047,12050,12052,12055,12057,12060,12062,12065,12067,12069,12071,12073,12075,12078,12080,12082,12084],{"class":174,"line":232},[86,12042,11946],{"class":182},[86,12044,258],{"class":219},[86,12046,726],{"class":219},[86,12048,12049],{"class":182},"lemmatizer",[86,12051,61],{"class":219},[86,12053,12054],{"class":182},"lemmatize",[86,12056,243],{"class":219},[86,12058,12059],{"class":182},"w",[86,12061,291],{"class":219},[86,12063,12064],{"class":304}," pos",[86,12066,258],{"class":219},[86,12068,10971],{"class":575},[86,12070,7912],{"class":579},[86,12072,10971],{"class":575},[86,12074,867],{"class":219},[86,12076,12077],{"class":178}," for",[86,12079,12012],{"class":182},[86,12081,12015],{"class":178},[86,12083,11977],{"class":182},[86,12085,752],{"class":219},[86,12087,12088],{"class":174,"line":252},[86,12089,12090],{"class":1360},"# 4. TF-IDF vectorization\n",[86,12092,12093,12096,12098,12101,12103,12105,12107,12110,12112,12114,12116,12119],{"class":174,"line":276},[86,12094,12095],{"class":182},"X ",[86,12097,258],{"class":219},[86,12099,12100],{"class":182}," TfidfVectorizer",[86,12102,243],{"class":219},[86,12104,1499],{"class":304},[86,12106,258],{"class":219},[86,12108,12109],{"class":223},"3000",[86,12111,789],{"class":219},[86,12113,11003],{"class":182},[86,12115,243],{"class":219},[86,12117,12118],{"class":182},"corpus",[86,12120,273],{"class":219},[12,12122,12123],{},"Se comparan cuatro clasificadores utilizando las mismas características:",[12,12125,12126,12130],{},[1945,12127],{"alt":12128,"src":12129},"Distribución de clases de spam en SMS","\u002Fblog\u002Fprobability-and-machine-learning\u002Fshared\u002Fnb_spam_distribution.webp",[901,12131,12132],{},"SMS dataset: muy desequilibrado hacia los mensajes legítimos (aproximadamente 87 % legítimos, aproximadamente 13 % spam).",[461,12134,12135,12153],{},[464,12136,12137],{},[467,12138,12139,12141,12144,12147,12150],{},[470,12140,11749],{},[470,12142,12143],{},"Precision",[470,12145,12146],{},"Recall",[470,12148,12149],{},"F1",[470,12151,12152],{},"CV Accuracy (10x)",[480,12154,12155,12284,12411,12540],{},[467,12156,12157,12159,12192,12223,12254],{},[485,12158,10517],{},[485,12160,12161,12191],{},[86,12162,12164,12178],{"className":12163},[955],[86,12165,12167],{"className":12166},[959],[961,12168,12169],{"xmlns":963},[965,12170,12171,12175],{},[968,12172,12173],{},[3191,12174,9443],{},[982,12176,12177],{"encoding":984},"\\approx",[86,12179,12181],{"className":12180,"ariaHidden":990},[989],[86,12182,12184,12188],{"className":12183},[994],[86,12185],{"className":12186,"style":12187},[998],"height:0.4831em;",[86,12189,9443],{"className":12190},[3226]," 0.97",[485,12193,12194,12222],{},[86,12195,12197,12210],{"className":12196},[955],[86,12198,12200],{"className":12199},[959],[961,12201,12202],{"xmlns":963},[965,12203,12204,12208],{},[968,12205,12206],{},[3191,12207,9443],{},[982,12209,12177],{"encoding":984},[86,12211,12213],{"className":12212,"ariaHidden":990},[989],[86,12214,12216,12219],{"className":12215},[994],[86,12217],{"className":12218,"style":12187},[998],[86,12220,9443],{"className":12221},[3226]," 0.94",[485,12224,12225,12253],{},[86,12226,12228,12241],{"className":12227},[955],[86,12229,12231],{"className":12230},[959],[961,12232,12233],{"xmlns":963},[965,12234,12235,12239],{},[968,12236,12237],{},[3191,12238,9443],{},[982,12240,12177],{"encoding":984},[86,12242,12244],{"className":12243,"ariaHidden":990},[989],[86,12245,12247,12250],{"className":12246},[994],[86,12248],{"className":12249,"style":12187},[998],[86,12251,9443],{"className":12252},[3226]," 0.95",[485,12255,12256,12191],{},[86,12257,12259,12272],{"className":12258},[955],[86,12260,12262],{"className":12261},[959],[961,12263,12264],{"xmlns":963},[965,12265,12266,12270],{},[968,12267,12268],{},[3191,12269,9443],{},[982,12271,12177],{"encoding":984},[86,12273,12275],{"className":12274,"ariaHidden":990},[989],[86,12276,12278,12281],{"className":12277},[994],[86,12279],{"className":12280,"style":12187},[998],[86,12282,9443],{"className":12283},[3226],[467,12285,12286,12289,12320,12350,12381],{},[485,12287,12288],{},"RandomForest",[485,12290,12291,12319],{},[86,12292,12294,12307],{"className":12293},[955],[86,12295,12297],{"className":12296},[959],[961,12298,12299],{"xmlns":963},[965,12300,12301,12305],{},[968,12302,12303],{},[3191,12304,9443],{},[982,12306,12177],{"encoding":984},[86,12308,12310],{"className":12309,"ariaHidden":990},[989],[86,12311,12313,12316],{"className":12312},[994],[86,12314],{"className":12315,"style":12187},[998],[86,12317,9443],{"className":12318},[3226]," 0.98",[485,12321,12322,12222],{},[86,12323,12325,12338],{"className":12324},[955],[86,12326,12328],{"className":12327},[959],[961,12329,12330],{"xmlns":963},[965,12331,12332,12336],{},[968,12333,12334],{},[3191,12335,9443],{},[982,12337,12177],{"encoding":984},[86,12339,12341],{"className":12340,"ariaHidden":990},[989],[86,12342,12344,12347],{"className":12343},[994],[86,12345],{"className":12346,"style":12187},[998],[86,12348,9443],{"className":12349},[3226],[485,12351,12352,12380],{},[86,12353,12355,12368],{"className":12354},[955],[86,12356,12358],{"className":12357},[959],[961,12359,12360],{"xmlns":963},[965,12361,12362,12366],{},[968,12363,12364],{},[3191,12365,9443],{},[982,12367,12177],{"encoding":984},[86,12369,12371],{"className":12370,"ariaHidden":990},[989],[86,12372,12374,12377],{"className":12373},[994],[86,12375],{"className":12376,"style":12187},[998],[86,12378,9443],{"className":12379},[3226]," 0.96",[485,12382,12383,12191],{},[86,12384,12386,12399],{"className":12385},[955],[86,12387,12389],{"className":12388},[959],[961,12390,12391],{"xmlns":963},[965,12392,12393,12397],{},[968,12394,12395],{},[3191,12396,9443],{},[982,12398,12177],{"encoding":984},[86,12400,12402],{"className":12401,"ariaHidden":990},[989],[86,12403,12405,12408],{"className":12404},[994],[86,12406],{"className":12407,"style":12187},[998],[86,12409,9443],{"className":12410},[3226],[467,12412,12413,12416,12447,12478,12509],{},[485,12414,12415],{},"KNeighbors",[485,12417,12418,12446],{},[86,12419,12421,12434],{"className":12420},[955],[86,12422,12424],{"className":12423},[959],[961,12425,12426],{"xmlns":963},[965,12427,12428,12432],{},[968,12429,12430],{},[3191,12431,9443],{},[982,12433,12177],{"encoding":984},[86,12435,12437],{"className":12436,"ariaHidden":990},[989],[86,12438,12440,12443],{"className":12439},[994],[86,12441],{"className":12442,"style":12187},[998],[86,12444,9443],{"className":12445},[3226]," 0.92",[485,12448,12449,12477],{},[86,12450,12452,12465],{"className":12451},[955],[86,12453,12455],{"className":12454},[959],[961,12456,12457],{"xmlns":963},[965,12458,12459,12463],{},[968,12460,12461],{},[3191,12462,9443],{},[982,12464,12177],{"encoding":984},[86,12466,12468],{"className":12467,"ariaHidden":990},[989],[86,12469,12471,12474],{"className":12470},[994],[86,12472],{"className":12473,"style":12187},[998],[86,12475,9443],{"className":12476},[3226]," 0.79",[485,12479,12480,12508],{},[86,12481,12483,12496],{"className":12482},[955],[86,12484,12486],{"className":12485},[959],[961,12487,12488],{"xmlns":963},[965,12489,12490,12494],{},[968,12491,12492],{},[3191,12493,9443],{},[982,12495,12177],{"encoding":984},[86,12497,12499],{"className":12498,"ariaHidden":990},[989],[86,12500,12502,12505],{"className":12501},[994],[86,12503],{"className":12504,"style":12187},[998],[86,12506,9443],{"className":12507},[3226]," 0.85",[485,12510,12511,12539],{},[86,12512,12514,12527],{"className":12513},[955],[86,12515,12517],{"className":12516},[959],[961,12518,12519],{"xmlns":963},[965,12520,12521,12525],{},[968,12522,12523],{},[3191,12524,9443],{},[982,12526,12177],{"encoding":984},[86,12528,12530],{"className":12529,"ariaHidden":990},[989],[86,12531,12533,12536],{"className":12532},[994],[86,12534],{"className":12535,"style":12187},[998],[86,12537,9443],{"className":12538},[3226]," 0.91",[467,12541,12542,12545,12575,12605,12635],{},[485,12543,12544],{},"SVC",[485,12546,12547,12319],{},[86,12548,12550,12563],{"className":12549},[955],[86,12551,12553],{"className":12552},[959],[961,12554,12555],{"xmlns":963},[965,12556,12557,12561],{},[968,12558,12559],{},[3191,12560,9443],{},[982,12562,12177],{"encoding":984},[86,12564,12566],{"className":12565,"ariaHidden":990},[989],[86,12567,12569,12572],{"className":12568},[994],[86,12570],{"className":12571,"style":12187},[998],[86,12573,9443],{"className":12574},[3226],[485,12576,12577,12380],{},[86,12578,12580,12593],{"className":12579},[955],[86,12581,12583],{"className":12582},[959],[961,12584,12585],{"xmlns":963},[965,12586,12587,12591],{},[968,12588,12589],{},[3191,12590,9443],{},[982,12592,12177],{"encoding":984},[86,12594,12596],{"className":12595,"ariaHidden":990},[989],[86,12597,12599,12602],{"className":12598},[994],[86,12600],{"className":12601,"style":12187},[998],[86,12603,9443],{"className":12604},[3226],[485,12606,12607,12191],{},[86,12608,12610,12623],{"className":12609},[955],[86,12611,12613],{"className":12612},[959],[961,12614,12615],{"xmlns":963},[965,12616,12617,12621],{},[968,12618,12619],{},[3191,12620,9443],{},[982,12622,12177],{"encoding":984},[86,12624,12626],{"className":12625,"ariaHidden":990},[989],[86,12627,12629,12632],{"className":12628},[994],[86,12630],{"className":12631,"style":12187},[998],[86,12633,9443],{"className":12634},[3226],[485,12636,12637,12191],{},[86,12638,12640,12653],{"className":12639},[955],[86,12641,12643],{"className":12642},[959],[961,12644,12645],{"xmlns":963},[965,12646,12647,12651],{},[968,12648,12649],{},[3191,12650,9443],{},[982,12652,12177],{"encoding":984},[86,12654,12656],{"className":12655,"ariaHidden":990},[989],[86,12657,12659,12662],{"className":12658},[994],[86,12660],{"className":12661,"style":12187},[998],[86,12663,9443],{"className":12664},[3226],[12,12666,12667,12668,12670],{},"MultinomialNB ofrece un rendimiento competitivo frente a Random Forest y SVC, requiriendo solo una fracción del tiempo de entrenamiento. Sus parámetros ",[145,12669,11074],{}," son directamente interpretables, lo que permite analizar qué palabras contribuyeron en mayor medida a la predicción de spam.",[12,12672,12673,12677],{},[1945,12674],{"alt":12675,"src":12676},"Matrices de confusión para los cuatro clasificadores","\u002Fblog\u002Fprobability-and-machine-learning\u002Fshared\u002Fnb_spam_confusion_matrices.webp",[901,12678,12679],{},"Matrices de confusión: Random Forest logra el mejor equilibrio general y no produce falsos positivos, mientras que MultinomialNB y SVC siguen siendo altamente competitivos. KNN tiene un rendimiento sustancialmente peor debido a su baja precisión en la clase minoritaria.",[12,12681,12682],{},"Naive Bayes es el punto de partida ideal antes de recurrir a modelos más complejos. Es rápido, interpretable y sorprendentemente competitivo en tareas de clasificación de texto, precisamente la aplicación donde la suposición de independencia \"ingenua\" tiende a ser menos perjudicial.",[43,12684],{},[12,12686,12687],{},"En el próximo artículo, exploraremos las pruebas estadísticas y su papel en el aprendizaje automático.",[2218,12689,12690],{},"html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .sfsYZ, html code.shiki .sfsYZ{--shiki-default:#A65E2B;--shiki-dark:#C99076}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .s5TCs, html code.shiki .s5TCs{--shiki-default:#AB5959;--shiki-dark:#CB7676}html pre.shiki code .s9nN2, html code.shiki .s9nN2{--shiki-default:#B07D48;--shiki-dark:#BD976A}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .scnC2, html code.shiki .scnC2{--shiki-default:#B5695977;--shiki-dark:#C98A7D77}html pre.shiki code .spP0B, html code.shiki .spP0B{--shiki-default:#B56959;--shiki-dark:#C98A7D}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}",{"title":169,"searchDepth":205,"depth":205,"links":12692},[12693,12704,12707,12708,12711,12712,12713],{"id":3696,"depth":192,"text":3697,"children":12694},[12695,12698,12699,12700,12701],{"id":4031,"depth":205,"text":4032,"children":12696},[12697],{"id":4600,"depth":212,"text":4601},{"id":4617,"depth":205,"text":4618},{"id":4776,"depth":205,"text":4777},{"id":5172,"depth":205,"text":5173},{"id":5438,"depth":205,"text":5439,"children":12702},[12703],{"id":7747,"depth":212,"text":7748},{"id":7773,"depth":192,"text":7774,"children":12705},[12706],{"id":7780,"depth":205,"text":7781},{"id":169,"depth":192,"text":169},{"id":7803,"depth":192,"text":169,"children":12709},[12710],{"id":7809,"depth":205,"text":7810},{"id":7836,"depth":192,"text":7837},{"id":7843,"depth":192,"text":169},{"id":9654,"depth":192,"text":9655,"children":12714},[12715,12716,12717,12718,12719],{"id":9666,"depth":205,"text":9667},{"id":10516,"depth":205,"text":10517},{"id":11103,"depth":205,"text":11104},{"id":11821,"depth":205,"text":11822},{"id":11921,"depth":205,"text":11922},"2026-05-05","\u002Fblog\u002Fprobability-and-machine-learning\u002Fshared\u002Fprobability-machine-learning.webp",{},"\u002Fblog\u002Fblog\u002Fprobability-and-machine-learning",{"title":3641,"description":3684},{"loc":12726,"priority":2259,"lastmod":3661},"\u002Fes\u002Fblog\u002Fprobability-and-machine-learning","probability-and-machine-learning","blog\u002Fblog\u002Fprobability-and-machine-learning","La probabilidad nos permite modelar la incertidumbre y tomar decisiones informadas. En este artículo, exploraremos cómo se utiliza esta herramienta en el contexto del aprendizaje automático.",[3625,12731,3675,2264,3676],"probabilidad","ElMhUwz1pbfc3iFwUziqYuRJw4N14Mr17bjXK5SGd8M",{"id":12734,"title":3649,"author":7,"body":12735,"date":19763,"description":19764,"extension":2250,"image":19765,"lastmod":19763,"meta":19766,"navigation":208,"order":276,"path":19767,"seo":19768,"sitemap":19769,"slug":19771,"stem":19772,"summary":19773,"tags":19774,"__hash__":19776},"content_es\u002Fblog\u002Fblog\u002Fstatistics-and-machine-learning.md",{"type":9,"value":12736,"toc":19749},[12737,12744,12751,12753,12755,12759,12778,12781,12813,12817,12820,12862,12866,12873,12879,12884,12888,12891,12931,12935,12938,13071,13074,13080,13087,13664,13707,13712,13719,13723,13734,13737,13744,13747,13754,13757,13764,13767,13774,13777,13784,13787,13967,14029,14036,14039,14041,14045,14056,14059,14318,14320,14479,14482,14485,14736,14738,14895,14898,14916,14919,14974,14977,14982,14985,15211,15307,15388,15391,15475,15481,15483,15487,15494,15501,15580,15587,15662,15669,15702,15786,15791,15863,15868,16109,16183,16186,16192,16195,16237,16242,16361,16511,16516,16745,16747,16906,17101,17218,17272,17277,17280,17313,17316,17390,17393,17400,17411,17414,17487,17492,17573,17576,17581,17583,17586,17589,17592,17842,18079,18298,18394,18478,18483,18486,18559,18562,18564,18567,18572,18575,18761,18764,18949,18952,19322,19481,19486,19490,19644,19648,19655,19658,19678,19685,19688,19693,19696,19704,19707,19710,19713,19721,19724,19744,19746],[12,12738,12739,12740,12743],{},"Ya hemos explorado el flujo de trabajo de un proyecto de aprendizaje automático, y hemos experimentado con el análisis exploratorio de datos (EDA) y la ingeniería de características (FE), ahora profundizaremos un poco más en algunos conceptos estadísticos que son fundamentales, y veremos ",[145,12741,12742],{},"qué"," deberíamos tener en cuenta al analizar nuestros datos con el fin de asegurar que nuestros modelos tengan el mejor desempeño posible.",[12,12745,3636,12746],{},[22,12747,12750],{"href":12748,"rel":12749},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fvectors-matrices-machine-learning",[26],"Vectores y Aprendizaje Automático",[40,12752],{},[43,12754],{},[46,12756,12758],{"id":12757},"estadística-descriptiva","Estadística Descriptiva",[12,12760,1938,12761,12764,12765,93,12768,93,12771,392,12774,12777],{},[122,12762,12763],{},"estadística descriptiva"," es la rama de la estadística que se centra en ",[122,12766,12767],{},"recolectar",[122,12769,12770],{},"organizar",[122,12772,12773],{},"resumir",[122,12775,12776],{},"visualizar"," un conjunto de datos. Su objetivo principal es transformar datos brutos en información estructurada y comprensible, permitiéndonos entender \"qué pasó\" con la información que estamos analizando.",[12,12779,12780],{},"Podemos dividir sus tareas principales en 5 pasos fundamentales:",[117,12782,12783,12789,12795,12801,12807],{},[33,12784,12785,12788],{},[122,12786,12787],{},"Recolectar:"," Obtener los datos de diversas fuentes, como bases de datos, archivos CSV, APIs, etc. Este paso es crucial para asegurar que tenemos una muestra representativa y de calidad para nuestro análisis.",[33,12790,12791,12794],{},[122,12792,12793],{},"Organizar:"," Consiste en ordenar la información recolectada para poder analizarla: clasificar las variables o construir tablas de frecuencia o distribución.",[33,12796,12797,12800],{},[122,12798,12799],{},"Presentar:"," Mostrar los datos de manera clara y ordenada, utilizando tablas, resúmenes numéricos o gráficos. Esto facilita la interpretación y comunicación de los resultados a otros.",[33,12802,12803,12806],{},[122,12804,12805],{},"Resumir:"," Utilizar métricas numéricas para describir grandes volúmenes de datos con unos pocos valores clave. Aquí es donde destacan las medidas de tendencia central y dispersión.",[33,12808,12809,12812],{},[122,12810,12811],{},"Interpretar:"," Analizar los datos y extraer conclusiones significativas, utilizando tanto métricas numéricas como visualizaciones para comunicar los hallazgos de manera efectiva.",[323,12814,12816],{"id":12815},"clasificación-de-variables","Clasificación de Variables",[12,12818,12819],{},"El tipo de variable influye en cómo analizamos y qué métricas utilizamos:",[30,12821,12822,12842],{},[33,12823,12824,12827,12828],{},[122,12825,12826],{},"Variables Categóricas:"," Representan categorías o grupos. Pueden ser:\n",[30,12829,12830,12836],{},[33,12831,12832,12835],{},[122,12833,12834],{},"Nominales:"," No tienen un orden específico (colores, tipos de frutas).",[33,12837,12838,12841],{},[122,12839,12840],{},"Ordinales:"," Tienen un orden o jerarquía (niveles de satisfacción: bajo, medio, alto).",[33,12843,12844,12847,12848],{},[122,12845,12846],{},"Variables Numéricas:"," Representan cantidades o medidas. Pueden ser:\n",[30,12849,12850,12856],{},[33,12851,12852,12855],{},[122,12853,12854],{},"Discretas:"," Toman valores enteros (número de hijos, cantidad de coches).",[33,12857,12858,12861],{},[122,12859,12860],{},"Continuas:"," Pueden tomar cualquier valor dentro de un rango (altura, peso, salario).",[323,12863,12865],{"id":12864},"tablas-de-frecuencia-y-distribución","Tablas de Frecuencia y Distribución",[12,12867,12868,12869,12872],{},"Las ",[122,12870,12871],{},"tablas de frecuencia"," son una herramienta fundamental para organizar y presentar datos categóricos. Nos permiten contar cuántas veces ocurre cada categoría en nuestro conjunto de datos, lo que facilita la identificación de patrones y tendencias. Por ejemplo, si tenemos una variable \"Color de Auto\" con categorías \"Rojo\", \"Azul\" y \"Negro\", una tabla de frecuencia nos mostraría cuántos autos de cada color hay en nuestro dataset.",[12,12874,12868,12875,12878],{},[122,12876,12877],{},"tablas de distribución",", por otro lado, se utilizan para variables numéricas. Nos permiten organizar los datos en intervalos o rangos y contar cuántos valores caen dentro de cada intervalo. Esto es especialmente útil para entender la forma de la distribución de los datos, identificar sesgos o detectar la presencia de outliers.",[16,12880,12881],{},[12,12882,12883],{},"Este tipo de tablas (y gráficos) nos permiten detectar casos como distribuciones sesgadas, presencia de outliers, o la necesidad de transformar los datos para mejorar el rendimiento de nuestros modelos de aprendizaje automático.",[323,12885,12887],{"id":12886},"presentación-de-datos","Presentación de Datos",[12,12889,12890],{},"La presentación de datos es crucial para comunicar eficazmente los hallazgos estadísticos. Podemos usar:",[30,12892,12893,12899],{},[33,12894,12895,12898],{},[122,12896,12897],{},"Tablas:"," Para mostrar información de manera estructurada y detallada.",[33,12900,12901,12904,12905],{},[122,12902,12903],{},"Gráficos:"," Para visualizar patrones, tendencias y relaciones en los datos:\n",[30,12906,12907,12913,12919,12925],{},[33,12908,12909,12912],{},[122,12910,12911],{},"Histogramas:"," Muestran la distribución de una variable continua.",[33,12914,12915,12918],{},[122,12916,12917],{},"Diagramas de caja (Box plots):"," Muestran la dispersión y la presencia de outliers.",[33,12920,12921,12924],{},[122,12922,12923],{},"Gráficos de barras:"," Muestran comparaciones entre categorías.",[33,12926,12927,12930],{},[122,12928,12929],{},"Gráficos de líneas:"," Muestran tendencias a lo largo del tiempo.",[323,12932,12934],{"id":12933},"medidas-estadísticas","Medidas Estadísticas",[12,12936,12937],{},"Para resumir los datos numéricos, se emplean principalmente dos familias de métricas:",[30,12939,12940,13019],{},[33,12941,12942,12945,12946],{},[122,12943,12944],{},"Medidas de Tendencia Central:"," Indican hacia dónde se agrupan los datos.\n",[30,12947,12948,12973,13013],{},[33,12949,12950,12953,12954],{},[122,12951,12952],{},"Media (Promedio):"," La suma de todos los valores dividida por el total de datos. Es sensible a valores extremos (outliers).\n",[16,12955,12956],{},[12,12957,12958,12961,12962,392,12965,12968,12969,12972],{},[122,12959,12960],{},"¿Como le afectan los outliers?"," Si tenemos un conjunto de datos con valores atípicos, la media puede darnos una impresión errónea del \"centro\" de los datos. Por ejemplo, si la mayoría de los empleados gana entre ",[145,12963,12964],{},"$2K",[145,12966,12967],{},"$3.5K",", pero hay un directivo que gana ",[145,12970,12971],{},"$15K",", la media se elevará, dando la falsa impresión de que el salario típico es mucho más alto de lo que realmente es para la mayoría.",[33,12974,12975,12978,12979],{},[122,12976,12977],{},"Mediana:"," Es el valor central de un conjunto de datos ordenados de menor a mayor. Es robusta y no se deja engañar fácilmente por anomalías.\n",[16,12980,12981],{},[12,12982,12983,12986,12987,93,12989,93,12992,93,12995,93,12997,93,13000,93,13003,13005,13006,13008,13009,13012],{},[122,12984,12985],{},"¿Cómo se protege de los outliers?"," La mediana nos da una mejor idea del salario típico en el ejemplo anterior, si tenemos valores como ",[145,12988,12964],{},[145,12990,12991],{},"$2.2K",[145,12993,12994],{},"$2.5K",[145,12996,12994],{},[145,12998,12999],{},"$2.8K",[145,13001,13002],{},"$3.1K",[145,13004,12967],{}," y un outlier de ",[145,13007,12971],{},", la mediana sería ",[145,13010,13011],{},"$2.65K",", reflejando mejor el salario típico de la mayoría de los empleados.",[33,13014,13015,13018],{},[122,13016,13017],{},"Moda:"," El valor (o valores) que más se repite en el conjunto de datos.",[33,13020,13021,13024,13025,13028,13029],{},[122,13022,13023],{},"Medidas de Dispersión:"," Proporcionan información sobre la ",[122,13026,13027],{},"variabilidad"," o qué tan separados están los datos.\n",[30,13030,13031,13037,13051,13057],{},[33,13032,13033,13036],{},[122,13034,13035],{},"Rango:"," La diferencia entre el valor máximo y el mínimo.",[33,13038,13039,13042,13043],{},[122,13040,13041],{},"Varianza:"," Mide el promedio de las desviaciones al cuadrado respecto a la media.\n",[16,13044,13045],{},[12,13046,13047,13050],{},[122,13048,13049],{},"¿Por qué al cuadrado?"," Porque si simplemente sumamos las desviaciones (valores - media), estas se cancelarán entre sí, dando un resultado de cero. Al elevar al cuadrado, todas las desviaciones se vuelven positivas, permitiendo medir la dispersión sin que los valores se anulen.",[33,13052,13053,13056],{},[122,13054,13055],{},"Desviación Estándar:"," La raíz cuadrada de la varianza. Se usa comúnmente porque devuelve la medida a sus unidades originales.",[33,13058,13059,13062,13063],{},[122,13060,13061],{},"Rango Intercuartílico (IQR):"," La diferencia entre el percentil 75 (Q3) y el percentil 25 (Q1). Ayuda a comprender la dispersión del 50% central de los datos, ignorando colas o extremos.\n",[16,13064,13065],{},[12,13066,13067,13070],{},[122,13068,13069],{},"¿Por qué es útil?"," Porque nos permite entender la dispersión de la mayoría de los datos sin que los valores extremos (outliers) distorsionen nuestra percepción. En el ejemplo de salarios, el IQR nos mostraría la variabilidad entre el 25% y el 75% de los empleados, proporcionando una visión más clara de la distribución salarial típica.",[12,13072,13073],{},"¿Cómo afecta una baja o alta desviación estándar a nuestros modelos de aprendizaje automático? Una baja desviación estándar indica que los datos están muy agrupados alrededor de la media, lo que puede facilitar que los modelos aprendan patrones claros. Por otro lado, una alta desviación estándar sugiere que los datos están más dispersos, lo que puede hacer que sea más difícil para los modelos encontrar relaciones significativas y generalizar bien a nuevos datos.",[12,13075,13076],{},[1945,13077],{"alt":13078,"src":13079},"Gráfico de dispersión con baja y alta desviación estándar","\u002Fblog\u002Fstatistics-and-machine-learning\u002Fshared\u002Fstandard-deviation-comparison.webp",[12,13081,13082,13083,13086],{},"Veamos cómo generar y analizar estos estadísticos utilizando ",[145,13084,13085],{},"pandas",". Tomemos el ejemplo de los salarios de los empleados:",[164,13088,13090],{"className":166,"code":13089,"language":168,"meta":169,"style":169},"import pandas as pd\n\n# 1. Organizamos los datos\n# La mayoría gana entre $2K y $3.5K, pero un directivo gana $15,000 (nuestro outlier)\nsalarios = [2000, 2200, 2500, 2500, 2800, 3100, 3500, 15000]\ndf = pd.DataFrame({'Salario': salarios})\n\n# 2. Medidas de Tendencia Central\nmedia = df['Salario'].mean()\nmediana = df['Salario'].median()\nmoda = df['Salario'].mode()[0]\n\nprint(\"--- Tendencia Central ---\")\nprint(f\"Media: ${media:.2f}\")\nprint(f\"Mediana: ${mediana:.2f}\")\nprint(f\"Moda: ${moda:.2f}\\n\")\n\n# 3. Medidas de Dispersión\nrango = df['Salario'].max() - df['Salario'].min()\nvarianza = df['Salario'].var() # ddof=1 por defecto (muestral)\ndesv_std = df['Salario'].std()\niqr = df['Salario'].quantile(0.75) - df['Salario'].quantile(0.25)\n\nprint(\"--- Medidas de Dispersión ---\")\nprint(f\"Rango: ${rango:.2f}\")\nprint(f\"Varianza: {varianza:.2f}\")\nprint(f\"Desviación Estándar: ${desv_std:.2f}\")\nprint(f\"IQR: ${iqr:.2f}\")\n",[145,13091,13092,13102,13106,13111,13116,13164,13196,13200,13205,13230,13254,13284,13289,13306,13332,13357,13383,13388,13394,13439,13466,13490,13543,13548,13564,13589,13614,13639],{"__ignoreMap":169},[86,13093,13094,13096,13098,13100],{"class":174,"line":175},[86,13095,179],{"class":178},[86,13097,197],{"class":182},[86,13099,186],{"class":178},[86,13101,202],{"class":182},[86,13103,13104],{"class":174,"line":192},[86,13105,209],{"emptyLinePlaceholder":208},[86,13107,13108],{"class":174,"line":205},[86,13109,13110],{"class":1360},"# 1. Organizamos los datos\n",[86,13112,13113],{"class":174,"line":212},[86,13114,13115],{"class":1360},"# La mayoría gana entre $2K y $3.5K, pero un directivo gana $15,000 (nuestro outlier)\n",[86,13117,13118,13121,13123,13125,13128,13130,13133,13135,13138,13140,13142,13144,13147,13149,13152,13154,13157,13159,13162],{"class":174,"line":227},[86,13119,13120],{"class":182},"salarios ",[86,13122,258],{"class":219},[86,13124,726],{"class":219},[86,13126,13127],{"class":223},"2000",[86,13129,291],{"class":219},[86,13131,13132],{"class":223}," 2200",[86,13134,291],{"class":219},[86,13136,13137],{"class":223}," 2500",[86,13139,291],{"class":219},[86,13141,13137],{"class":223},[86,13143,291],{"class":219},[86,13145,13146],{"class":223}," 2800",[86,13148,291],{"class":219},[86,13150,13151],{"class":223}," 3100",[86,13153,291],{"class":219},[86,13155,13156],{"class":223}," 3500",[86,13158,291],{"class":219},[86,13160,13161],{"class":223}," 15000",[86,13163,752],{"class":219},[86,13165,13166,13169,13171,13173,13175,13178,13181,13183,13186,13188,13190,13193],{"class":174,"line":232},[86,13167,13168],{"class":182},"df ",[86,13170,258],{"class":219},[86,13172,261],{"class":182},[86,13174,61],{"class":219},[86,13176,13177],{"class":182},"DataFrame",[86,13179,13180],{"class":219},"({",[86,13182,10971],{"class":575},[86,13184,13185],{"class":579},"Salario",[86,13187,10971],{"class":575},[86,13189,162],{"class":219},[86,13191,13192],{"class":182}," salarios",[86,13194,13195],{"class":219},"})\n",[86,13197,13198],{"class":174,"line":252},[86,13199,209],{"emptyLinePlaceholder":208},[86,13201,13202],{"class":174,"line":276},[86,13203,13204],{"class":1360},"# 2. Medidas de Tendencia Central\n",[86,13206,13207,13210,13212,13214,13216,13218,13220,13222,13225,13228],{"class":174,"line":315},[86,13208,13209],{"class":182},"media ",[86,13211,258],{"class":219},[86,13213,590],{"class":182},[86,13215,572],{"class":219},[86,13217,10971],{"class":575},[86,13219,13185],{"class":579},[86,13221,10971],{"class":575},[86,13223,13224],{"class":219},"].",[86,13226,13227],{"class":182},"mean",[86,13229,11991],{"class":219},[86,13231,13232,13235,13237,13239,13241,13243,13245,13247,13249,13252],{"class":174,"line":3665},[86,13233,13234],{"class":182},"mediana ",[86,13236,258],{"class":219},[86,13238,590],{"class":182},[86,13240,572],{"class":219},[86,13242,10971],{"class":575},[86,13244,13185],{"class":579},[86,13246,10971],{"class":575},[86,13248,13224],{"class":219},[86,13250,13251],{"class":182},"median",[86,13253,11991],{"class":219},[86,13255,13257,13260,13262,13264,13266,13268,13270,13272,13274,13277,13280,13282],{"class":174,"line":13256},11,[86,13258,13259],{"class":182},"moda ",[86,13261,258],{"class":219},[86,13263,590],{"class":182},[86,13265,572],{"class":219},[86,13267,10971],{"class":575},[86,13269,13185],{"class":579},[86,13271,10971],{"class":575},[86,13273,13224],{"class":219},[86,13275,13276],{"class":182},"mode",[86,13278,13279],{"class":219},"()[",[86,13281,2553],{"class":223},[86,13283,752],{"class":219},[86,13285,13287],{"class":174,"line":13286},12,[86,13288,209],{"emptyLinePlaceholder":208},[86,13290,13292,13295,13297,13299,13302,13304],{"class":174,"line":13291},13,[86,13293,13294],{"class":812},"print",[86,13296,243],{"class":219},[86,13298,576],{"class":575},[86,13300,13301],{"class":579},"--- Tendencia Central ---",[86,13303,576],{"class":575},[86,13305,273],{"class":219},[86,13307,13309,13311,13313,13315,13318,13320,13323,13326,13328,13330],{"class":174,"line":13308},14,[86,13310,13294],{"class":812},[86,13312,243],{"class":219},[86,13314,6178],{"class":235},[86,13316,13317],{"class":579},"\"Media: $",[86,13319,4089],{"class":215},[86,13321,13322],{"class":182},"media",[86,13324,13325],{"class":235},":.2f",[86,13327,4117],{"class":215},[86,13329,576],{"class":579},[86,13331,273],{"class":219},[86,13333,13335,13337,13339,13341,13344,13346,13349,13351,13353,13355],{"class":174,"line":13334},15,[86,13336,13294],{"class":812},[86,13338,243],{"class":219},[86,13340,6178],{"class":235},[86,13342,13343],{"class":579},"\"Mediana: $",[86,13345,4089],{"class":215},[86,13347,13348],{"class":182},"mediana",[86,13350,13325],{"class":235},[86,13352,4117],{"class":215},[86,13354,576],{"class":579},[86,13356,273],{"class":219},[86,13358,13360,13362,13364,13366,13369,13371,13374,13376,13379,13381],{"class":174,"line":13359},16,[86,13361,13294],{"class":812},[86,13363,243],{"class":219},[86,13365,6178],{"class":235},[86,13367,13368],{"class":579},"\"Moda: $",[86,13370,4089],{"class":215},[86,13372,13373],{"class":182},"moda",[86,13375,13325],{"class":235},[86,13377,13378],{"class":215},"}\\n",[86,13380,576],{"class":579},[86,13382,273],{"class":219},[86,13384,13386],{"class":174,"line":13385},17,[86,13387,209],{"emptyLinePlaceholder":208},[86,13389,13391],{"class":174,"line":13390},18,[86,13392,13393],{"class":1360},"# 3. Medidas de Dispersión\n",[86,13395,13397,13400,13402,13404,13406,13408,13410,13412,13414,13416,13419,13422,13424,13426,13428,13430,13432,13434,13437],{"class":174,"line":13396},19,[86,13398,13399],{"class":182},"rango ",[86,13401,258],{"class":219},[86,13403,590],{"class":182},[86,13405,572],{"class":219},[86,13407,10971],{"class":575},[86,13409,13185],{"class":579},[86,13411,10971],{"class":575},[86,13413,13224],{"class":219},[86,13415,7260],{"class":182},[86,13417,13418],{"class":219},"()",[86,13420,13421],{"class":235}," -",[86,13423,590],{"class":182},[86,13425,572],{"class":219},[86,13427,10971],{"class":575},[86,13429,13185],{"class":579},[86,13431,10971],{"class":575},[86,13433,13224],{"class":219},[86,13435,13436],{"class":182},"min",[86,13438,11991],{"class":219},[86,13440,13441,13444,13446,13448,13450,13452,13454,13456,13458,13461,13463],{"class":174,"line":3615},[86,13442,13443],{"class":182},"varianza ",[86,13445,258],{"class":219},[86,13447,590],{"class":182},[86,13449,572],{"class":219},[86,13451,10971],{"class":575},[86,13453,13185],{"class":579},[86,13455,10971],{"class":575},[86,13457,13224],{"class":219},[86,13459,13460],{"class":182},"var",[86,13462,13418],{"class":219},[86,13464,13465],{"class":1360}," # ddof=1 por defecto (muestral)\n",[86,13467,13468,13471,13473,13475,13477,13479,13481,13483,13485,13488],{"class":174,"line":2254},[86,13469,13470],{"class":182},"desv_std ",[86,13472,258],{"class":219},[86,13474,590],{"class":182},[86,13476,572],{"class":219},[86,13478,10971],{"class":575},[86,13480,13185],{"class":579},[86,13482,10971],{"class":575},[86,13484,13224],{"class":219},[86,13486,13487],{"class":182},"std",[86,13489,11991],{"class":219},[86,13491,13493,13496,13498,13500,13502,13504,13506,13508,13510,13513,13515,13518,13520,13522,13524,13526,13528,13530,13532,13534,13536,13538,13541],{"class":174,"line":13492},22,[86,13494,13495],{"class":182},"iqr ",[86,13497,258],{"class":219},[86,13499,590],{"class":182},[86,13501,572],{"class":219},[86,13503,10971],{"class":575},[86,13505,13185],{"class":579},[86,13507,10971],{"class":575},[86,13509,13224],{"class":219},[86,13511,13512],{"class":182},"quantile",[86,13514,243],{"class":219},[86,13516,13517],{"class":223},"0.75",[86,13519,867],{"class":219},[86,13521,13421],{"class":235},[86,13523,590],{"class":182},[86,13525,572],{"class":219},[86,13527,10971],{"class":575},[86,13529,13185],{"class":579},[86,13531,10971],{"class":575},[86,13533,13224],{"class":219},[86,13535,13512],{"class":182},[86,13537,243],{"class":219},[86,13539,13540],{"class":223},"0.25",[86,13542,273],{"class":219},[86,13544,13546],{"class":174,"line":13545},23,[86,13547,209],{"emptyLinePlaceholder":208},[86,13549,13551,13553,13555,13557,13560,13562],{"class":174,"line":13550},24,[86,13552,13294],{"class":812},[86,13554,243],{"class":219},[86,13556,576],{"class":575},[86,13558,13559],{"class":579},"--- Medidas de Dispersión ---",[86,13561,576],{"class":575},[86,13563,273],{"class":219},[86,13565,13567,13569,13571,13573,13576,13578,13581,13583,13585,13587],{"class":174,"line":13566},25,[86,13568,13294],{"class":812},[86,13570,243],{"class":219},[86,13572,6178],{"class":235},[86,13574,13575],{"class":579},"\"Rango: $",[86,13577,4089],{"class":215},[86,13579,13580],{"class":182},"rango",[86,13582,13325],{"class":235},[86,13584,4117],{"class":215},[86,13586,576],{"class":579},[86,13588,273],{"class":219},[86,13590,13592,13594,13596,13598,13601,13603,13606,13608,13610,13612],{"class":174,"line":13591},26,[86,13593,13294],{"class":812},[86,13595,243],{"class":219},[86,13597,6178],{"class":235},[86,13599,13600],{"class":579},"\"Varianza: ",[86,13602,4089],{"class":215},[86,13604,13605],{"class":182},"varianza",[86,13607,13325],{"class":235},[86,13609,4117],{"class":215},[86,13611,576],{"class":579},[86,13613,273],{"class":219},[86,13615,13617,13619,13621,13623,13626,13628,13631,13633,13635,13637],{"class":174,"line":13616},27,[86,13618,13294],{"class":812},[86,13620,243],{"class":219},[86,13622,6178],{"class":235},[86,13624,13625],{"class":579},"\"Desviación Estándar: $",[86,13627,4089],{"class":215},[86,13629,13630],{"class":182},"desv_std",[86,13632,13325],{"class":235},[86,13634,4117],{"class":215},[86,13636,576],{"class":579},[86,13638,273],{"class":219},[86,13640,13642,13644,13646,13648,13651,13653,13656,13658,13660,13662],{"class":174,"line":13641},28,[86,13643,13294],{"class":812},[86,13645,243],{"class":219},[86,13647,6178],{"class":235},[86,13649,13650],{"class":579},"\"IQR: $",[86,13652,4089],{"class":215},[86,13654,13655],{"class":182},"iqr",[86,13657,13325],{"class":235},[86,13659,4117],{"class":215},[86,13661,576],{"class":579},[86,13663,273],{"class":219},[30,13665,13666,13680,13688,13697],{},[33,13667,13668,13671,13672,13675,13676,13679],{},[122,13669,13670],{},"Media vs. Mediana:"," La media es ",[122,13673,13674],{},"$4,200",", inflada por los exagerados $15,000. Sin embargo, la mediana es ",[122,13677,13678],{},"$2,650",", mucho más representativa de un empleado promedio. Al hacer análisis de datos, siempre debes chequear ambas frente a posibles sesgos.",[33,13681,13682,13684,13685,61],{},[122,13683,13017],{}," El estatus salarial más repetido es ",[122,13686,13687],{},"$2,500",[33,13689,13690,13692,13693,13696],{},[122,13691,13055],{}," Obtendremos aproximadamente ",[122,13694,13695],{},"$4,390.25",". Es una dispersión enorme provocado nuevamente por el sueldo alto alejado de los demás.",[33,13698,13699,13702,13703,13706],{},[122,13700,13701],{},"IQR:"," El Rango Intercuartílico nos da ",[122,13704,13705],{},"$775",", reafirmando que el \"grueso\" del núcleo normal de empleados (el 50% del medio) varía sus salarios en un margen mucho menor y más manejable.",[16,13708,13709],{},[12,13710,13711],{},"Una regla práctica (pero NO absoluta): Si la media \u003C la mediana, entonces la distribución es sesgada a la izquierda (negativamente sesgada). Si la media > la mediana, entonces la distribución es sesgada a la derecha (positivamente sesgada).",[12,13713,13714,13715,61],{},"Puedes practicar con otros ejemplos en el siguiente ",[22,13716,7763],{"href":13717,"rel":13718},"https:\u002F\u002Fcolab.research.google.com\u002Fdrive\u002F1jD0kH9z9oVHrM4HwN1dykpjwfKO2S5ge?usp=sharing",[26],[46,13720,13722],{"id":13721},"estadística-inferencial","Estadística Inferencial",[12,13724,13725,13726,13729,13730,13733],{},"Otra rama muy importante es la ",[122,13727,13728],{},"estadística inferencial",". Mientras que la estadística descriptiva se limita a describir los datos que tenemos, la inferencial nos permite ",[122,13731,13732],{},"sacar conclusiones sobre una población a partir de una muestra",". Esto es crucial en el aprendizaje automático, ya que a menudo trabajamos con conjuntos de datos limitados y queremos generalizar nuestros hallazgos a un contexto más amplio.",[12,13735,13736],{},"Empecemos por definir algunos conceptos clave:",[117,13738,13739],{},[33,13740,13741],{},[122,13742,13743],{},"Población",[12,13745,13746],{},"Lo entenderemos como el conjunto total de individuos o elementos que queremos estudiar. Por ejemplo todos los estudiantes de una universidad.",[117,13748,13749],{"start":192},[33,13750,13751],{},[122,13752,13753],{},"Muestra",[12,13755,13756],{},"Un subconjunto de la población que realmente se está estudiando. De todos los estudiantes, tomamos 200 seleccionados al azar.",[117,13758,13759],{"start":205},[33,13760,13761],{},[122,13762,13763],{},"Parámetro",[12,13765,13766],{},"Es un valor numérico que describe una característica de la población. Podríamos por ejemplo tomar la media de estatura de todos los estudiantes.",[117,13768,13769],{"start":212},[33,13770,13771],{},[122,13772,13773],{},"Estadístico",[12,13775,13776],{},"Al contrario del parámetro, el estadístico es calculado a partir de la muestra. Podríamos tener por ejemplo la media de estatura de los 200 estudiantes.",[117,13778,13779],{"start":227},[33,13780,13781],{},[122,13782,13783],{},"Error muestral",[12,13785,13786],{},"Diferencia entre el parámetro real y el estadístico estimado. Si la media real de estatura de la población es 1.70m y la media de nuestra muestra es 1.68m, el error muestral sería 0.02m. PERO, en la práctica lo más seguro es que no conozcamos el parámetro real, por lo que el error muestral no puede calcularse directamente. En su lugar, se suele calcular el error estándar, que es una estimación de la variabilidad del estadístico debido al muestreo aleatorio. El error estándar se calcula como:",[86,13788,13790],{"className":13789},[3173],[86,13791,13793,13819],{"className":13792},[955],[86,13794,13796],{"className":13795},[959],[961,13797,13798],{"xmlns":963,"display":3182},[965,13799,13800,13816],{},[968,13801,13802,13804,13806,13808],{},[974,13803,4084],{},[974,13805,7871],{},[3191,13807,258],{},[3749,13809,13810,13812],{},[974,13811,9839],{},[9825,13813,13814],{},[974,13815,6896],{},[982,13817,13818],{"encoding":984},"SE = \\frac{\\sigma}{\\sqrt{n}}",[86,13820,13822,13843],{"className":13821,"ariaHidden":990},[989],[86,13823,13825,13828,13831,13834,13837,13840],{"className":13824},[994],[86,13826],{"className":13827,"style":3575},[998],[86,13829,4084],{"className":13830,"style":4133},[1003,1007],[86,13832,7871],{"className":13833,"style":4133},[1003,1007],[86,13835],{"className":13836,"style":3222},[3221],[86,13838,258],{"className":13839},[3226],[86,13841],{"className":13842,"style":3222},[3221],[86,13844,13846,13850],{"className":13845},[994],[86,13847],{"className":13848,"style":13849},[998],"height:2.0376em;vertical-align:-0.93em;",[86,13851,13853,13856,13964],{"className":13852},[1003],[86,13854],{"className":13855},[3320,3829],[86,13857,13859],{"className":13858},[3749],[86,13860,13862,13955],{"className":13861},[1016,3836],[86,13863,13865,13952],{"className":13864},[1020],[86,13866,13869,13933,13941],{"className":13867,"style":13868},[1024],"height:1.1076em;",[86,13870,13872,13875],{"style":13871},"top:-2.3097em;",[86,13873],{"className":13874,"style":3850},[1031],[86,13876,13878],{"className":13877},[1003],[86,13879,13881],{"className":13880},[1003,10044],[86,13882,13884,13924],{"className":13883},[1016,3836],[86,13885,13887,13921],{"className":13886},[1020],[86,13888,13891,13904],{"className":13889,"style":13890},[1024],"height:0.8003em;",[86,13892,13894,13897],{"className":13893,"style":3876},[10058],[86,13895],{"className":13896,"style":3850},[1031],[86,13898,13901],{"className":13899,"style":13900},[1003],"padding-left:0.833em;",[86,13902,6896],{"className":13903},[1003,1007],[86,13905,13907,13910],{"style":13906},"top:-2.7603em;",[86,13908],{"className":13909,"style":3850},[1031],[86,13911,13914],{"className":13912,"style":13913},[10147],"min-width:0.853em;height:1.08em;",[10150,13915,13918],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},"1.08em","0 0 400000 1080",[246,13919],{"d":13920},"M95,702\nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14\nc0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54\nc44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10\ns173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429\nc69,-144,104.5,-217.7,106.5,-221\nl0 -0\nc5.3,-9.3,12,-14,20,-14\nH400000v40H845.2724\ns-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7\nc-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z\nM834 80h400000v40h-400000z",[86,13922,3963],{"className":13923},[3962],[86,13925,13927],{"className":13926},[1020],[86,13928,13931],{"className":13929,"style":13930},[1024],"height:0.2397em;",[86,13932],{},[86,13934,13935,13938],{"style":3901},[86,13936],{"className":13937,"style":3850},[1031],[86,13939],{"className":13940,"style":3909},[3908],[86,13942,13943,13946],{"style":3912},[86,13944],{"className":13945,"style":3850},[1031],[86,13947,13949],{"className":13948},[1003],[86,13950,9839],{"className":13951,"style":8109},[1003,1007],[86,13953,3963],{"className":13954},[3962],[86,13956,13958],{"className":13957},[1020],[86,13959,13962],{"className":13960,"style":13961},[1024],"height:0.93em;",[86,13963],{},[86,13965],{"className":13966},[3356,3829],[12,13968,13969,13970,13999,14000,14028],{},"Donde ",[86,13971,13973,13987],{"className":13972},[955],[86,13974,13976],{"className":13975},[959],[961,13977,13978],{"xmlns":963},[965,13979,13980,13984],{},[968,13981,13982],{},[974,13983,9839],{},[982,13985,13986],{"encoding":984},"\\sigma",[86,13988,13990],{"className":13989,"ariaHidden":990},[989],[86,13991,13993,13996],{"className":13992},[994],[86,13994],{"className":13995,"style":7401},[998],[86,13997,9839],{"className":13998,"style":8109},[1003,1007]," es la desviación estándar de la población (o una estimación basada en la muestra) y ",[86,14001,14003,14016],{"className":14002},[955],[86,14004,14006],{"className":14005},[959],[961,14007,14008],{"xmlns":963},[965,14009,14010,14014],{},[968,14011,14012],{},[974,14013,6896],{},[982,14015,6896],{"encoding":984},[86,14017,14019],{"className":14018,"ariaHidden":990},[989],[86,14020,14022,14025],{"className":14021},[994],[86,14023],{"className":14024,"style":7401},[998],[86,14026,6896],{"className":14027},[1003,1007]," es el tamaño de la muestra.",[117,14030,14031],{"start":232},[33,14032,14033],{},[122,14034,14035],{},"Nivel de confianza",[12,14037,14038],{},"Probabilidad de que una estimación contenga el verdadero parámetro. Si decimos que tenemos un intervalo de confianza del 95%, significa que si repitiéramos el proceso de muestreo muchas veces, aproximadamente el 95% de esos intervalos incluirían el verdadero parámetro poblacional. Es una medida de cuán seguros estamos de nuestras estimaciones.",[43,14040],{},[323,14042,14044],{"id":14043},"intervalo-de-confianza","Intervalo de confianza",[12,14046,14047,14048,14051,14052,14055],{},"Un ",[122,14049,14050],{},"intervalo de confianza (IC)"," es un rango de valores dentro del cual se espera que esté el parámetro poblacional con cierto ",[122,14053,14054],{},"nivel de confianza",". En términos simples, es una forma de expresar la incertidumbre de nuestras estimaciones. Por ejemplo, si calculamos un intervalo de confianza del 95% para la media de estatura de los estudiantes y obtenemos (1.65m, 1.75m), podemos decir que estamos 95% seguros de que la verdadera media de estatura de todos los estudiantes está entre esos dos valores.",[12,14057,14058],{},"Fórmula básica:",[86,14060,14062],{"className":14061},[3173],[86,14063,14065,14111],{"className":14064},[955],[86,14066,14068],{"className":14067},[959],[961,14069,14070],{"xmlns":963,"display":3182},[965,14071,14072,14108],{},[968,14073,14074,14077,14079,14081,14088,14091,14094],{},[974,14075,14076],{},"I",[974,14078,1514],{},[3191,14080,258],{},[3758,14082,14083,14085],{"accent":990},[974,14084,3189],{},[3191,14086,14087],{},"ˉ",[3191,14089,14090],{},"±",[974,14092,14093],{},"Z",[968,14095,14096,14098,14106],{},[3191,14097,243],{"fence":990},[3749,14099,14100,14102],{},[974,14101,9839],{},[9825,14103,14104],{},[974,14105,6896],{},[3191,14107,867],{"fence":990},[982,14109,14110],{"encoding":984},"IC = \\bar{x} \\pm Z \\left(\\frac{\\sigma}{\\sqrt{n}}\\right)",[86,14112,14114,14135,14184],{"className":14113,"ariaHidden":990},[989],[86,14115,14117,14120,14123,14126,14129,14132],{"className":14116},[994],[86,14118],{"className":14119,"style":3575},[998],[86,14121,14076],{"className":14122,"style":4685},[1003,1007],[86,14124,1514],{"className":14125,"style":3512},[1003,1007],[86,14127],{"className":14128,"style":3222},[3221],[86,14130,258],{"className":14131},[3226],[86,14133],{"className":14134,"style":3222},[3221],[86,14136,14138,14142,14175,14178,14181],{"className":14137},[994],[86,14139],{"className":14140,"style":14141},[998],"height:0.6667em;vertical-align:-0.0833em;",[86,14143,14145],{"className":14144},[1003,3863],[86,14146,14148],{"className":14147},[1016],[86,14149,14151],{"className":14150},[1020],[86,14152,14155,14163],{"className":14153,"style":14154},[1024],"height:0.5678em;",[86,14156,14157,14160],{"style":3876},[86,14158],{"className":14159,"style":3850},[1031],[86,14161,3189],{"className":14162},[1003,1007],[86,14164,14165,14168],{"style":3876},[86,14166],{"className":14167,"style":3850},[1031],[86,14169,14172],{"className":14170,"style":14171},[3891],"left:-0.2222em;",[86,14173,14087],{"className":14174},[1003],[86,14176],{"className":14177,"style":5012},[3221],[86,14179,14090],{"className":14180},[5016],[86,14182],{"className":14183,"style":5012},[3221],[86,14185,14187,14191,14194,14197],{"className":14186},[994],[86,14188],{"className":14189,"style":14190},[998],"height:2.4em;vertical-align:-0.95em;",[86,14192,14093],{"className":14193,"style":3512},[1003,1007],[86,14195],{"className":14196,"style":4162},[3221],[86,14198,14200,14206,14312],{"className":14199},[7131],[86,14201,14203],{"className":14202,"style":10228},[3320,10227],[86,14204,243],{"className":14205},[10232,1038],[86,14207,14209,14212,14309],{"className":14208},[1003],[86,14210],{"className":14211},[3320,3829],[86,14213,14215],{"className":14214},[3749],[86,14216,14218,14301],{"className":14217},[1016,3836],[86,14219,14221,14298],{"className":14220},[1020],[86,14222,14224,14279,14287],{"className":14223,"style":13868},[1024],[86,14225,14226,14229],{"style":13871},[86,14227],{"className":14228,"style":3850},[1031],[86,14230,14232],{"className":14231},[1003],[86,14233,14235],{"className":14234},[1003,10044],[86,14236,14238,14271],{"className":14237},[1016,3836],[86,14239,14241,14268],{"className":14240},[1020],[86,14242,14244,14256],{"className":14243,"style":13890},[1024],[86,14245,14247,14250],{"className":14246,"style":3876},[10058],[86,14248],{"className":14249,"style":3850},[1031],[86,14251,14253],{"className":14252,"style":13900},[1003],[86,14254,6896],{"className":14255},[1003,1007],[86,14257,14258,14261],{"style":13906},[86,14259],{"className":14260,"style":3850},[1031],[86,14262,14264],{"className":14263,"style":13913},[10147],[10150,14265,14266],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,14267],{"d":13920},[86,14269,3963],{"className":14270},[3962],[86,14272,14274],{"className":14273},[1020],[86,14275,14277],{"className":14276,"style":13930},[1024],[86,14278],{},[86,14280,14281,14284],{"style":3901},[86,14282],{"className":14283,"style":3850},[1031],[86,14285],{"className":14286,"style":3909},[3908],[86,14288,14289,14292],{"style":3912},[86,14290],{"className":14291,"style":3850},[1031],[86,14293,14295],{"className":14294},[1003],[86,14296,9839],{"className":14297,"style":8109},[1003,1007],[86,14299,3963],{"className":14300},[3962],[86,14302,14304],{"className":14303},[1020],[86,14305,14307],{"className":14306,"style":13961},[1024],[86,14308],{},[86,14310],{"className":14311},[3356,3829],[86,14313,14315],{"className":14314,"style":10228},[3356,10227],[86,14316,867],{"className":14317},[10232,1038],[12,14319,3273],{},[30,14321,14322,14386,14417,14448],{},[33,14323,14324,14385],{},[86,14325,14327,14345],{"className":14326},[955],[86,14328,14330],{"className":14329},[959],[961,14331,14332],{"xmlns":963},[965,14333,14334,14342],{},[968,14335,14336],{},[3758,14337,14338,14340],{"accent":990},[974,14339,3189],{},[3191,14341,14087],{},[982,14343,14344],{"encoding":984},"\\bar{x}",[86,14346,14348],{"className":14347,"ariaHidden":990},[989],[86,14349,14351,14354],{"className":14350},[994],[86,14352],{"className":14353,"style":14154},[998],[86,14355,14357],{"className":14356},[1003,3863],[86,14358,14360],{"className":14359},[1016],[86,14361,14363],{"className":14362},[1020],[86,14364,14366,14374],{"className":14365,"style":14154},[1024],[86,14367,14368,14371],{"style":3876},[86,14369],{"className":14370,"style":3850},[1031],[86,14372,3189],{"className":14373},[1003,1007],[86,14375,14376,14379],{"style":3876},[86,14377],{"className":14378,"style":3850},[1031],[86,14380,14382],{"className":14381,"style":14171},[3891],[86,14383,14087],{"className":14384},[1003]," = media muestral",[33,14387,14388,14416],{},[86,14389,14391,14404],{"className":14390},[955],[86,14392,14394],{"className":14393},[959],[961,14395,14396],{"xmlns":963},[965,14397,14398,14402],{},[968,14399,14400],{},[974,14401,14093],{},[982,14403,14093],{"encoding":984},[86,14405,14407],{"className":14406,"ariaHidden":990},[989],[86,14408,14410,14413],{"className":14409},[994],[86,14411],{"className":14412,"style":3575},[998],[86,14414,14093],{"className":14415,"style":3512},[1003,1007]," = valor crítico",[33,14418,14419,14447],{},[86,14420,14422,14435],{"className":14421},[955],[86,14423,14425],{"className":14424},[959],[961,14426,14427],{"xmlns":963},[965,14428,14429,14433],{},[968,14430,14431],{},[974,14432,9839],{},[982,14434,13986],{"encoding":984},[86,14436,14438],{"className":14437,"ariaHidden":990},[989],[86,14439,14441,14444],{"className":14440},[994],[86,14442],{"className":14443,"style":7401},[998],[86,14445,9839],{"className":14446,"style":8109},[1003,1007]," = desviación estándar",[33,14449,14450,14478],{},[86,14451,14453,14466],{"className":14452},[955],[86,14454,14456],{"className":14455},[959],[961,14457,14458],{"xmlns":963},[965,14459,14460,14464],{},[968,14461,14462],{},[974,14463,6896],{},[982,14465,6896],{"encoding":984},[86,14467,14469],{"className":14468,"ariaHidden":990},[989],[86,14470,14472,14475],{"className":14471},[994],[86,14473],{"className":14474,"style":7401},[998],[86,14476,6896],{"className":14477},[1003,1007]," = tamaño de muestra",[12,14480,14481],{},"Esta fórmula se utiliza para calcular el intervalo de confianza para la media de una población cuando la desviación estándar es conocida y la muestra es suficientemente grande (n > 30).",[12,14483,14484],{},"En la práctica, a menudo no conocemos la desviación estándar de la población, por lo que utilizamos la desviación estándar muestral y el valor crítico de la distribución t de Student en lugar de Z. La fórmula se ajusta a:",[86,14486,14488],{"className":14487},[3173],[86,14489,14491,14533],{"className":14490},[955],[86,14492,14494],{"className":14493},[959],[961,14495,14496],{"xmlns":963,"display":3182},[965,14497,14498,14530],{},[968,14499,14500,14502,14504,14506,14512,14514,14516],{},[974,14501,14076],{},[974,14503,1514],{},[3191,14505,258],{},[3758,14507,14508,14510],{"accent":990},[974,14509,3189],{},[3191,14511,14087],{},[3191,14513,14090],{},[974,14515,6187],{},[968,14517,14518,14520,14528],{},[3191,14519,243],{"fence":990},[3749,14521,14522,14524],{},[974,14523,7892],{},[9825,14525,14526],{},[974,14527,6896],{},[3191,14529,867],{"fence":990},[982,14531,14532],{"encoding":984},"IC = \\bar{x} \\pm t \\left(\\frac{s}{\\sqrt{n}}\\right)",[86,14534,14536,14557,14603],{"className":14535,"ariaHidden":990},[989],[86,14537,14539,14542,14545,14548,14551,14554],{"className":14538},[994],[86,14540],{"className":14541,"style":3575},[998],[86,14543,14076],{"className":14544,"style":4685},[1003,1007],[86,14546,1514],{"className":14547,"style":3512},[1003,1007],[86,14549],{"className":14550,"style":3222},[3221],[86,14552,258],{"className":14553},[3226],[86,14555],{"className":14556,"style":3222},[3221],[86,14558,14560,14563,14594,14597,14600],{"className":14559},[994],[86,14561],{"className":14562,"style":14141},[998],[86,14564,14566],{"className":14565},[1003,3863],[86,14567,14569],{"className":14568},[1016],[86,14570,14572],{"className":14571},[1020],[86,14573,14575,14583],{"className":14574,"style":14154},[1024],[86,14576,14577,14580],{"style":3876},[86,14578],{"className":14579,"style":3850},[1031],[86,14581,3189],{"className":14582},[1003,1007],[86,14584,14585,14588],{"style":3876},[86,14586],{"className":14587,"style":3850},[1031],[86,14589,14591],{"className":14590,"style":14171},[3891],[86,14592,14087],{"className":14593},[1003],[86,14595],{"className":14596,"style":5012},[3221],[86,14598,14090],{"className":14599},[5016],[86,14601],{"className":14602,"style":5012},[3221],[86,14604,14606,14609,14612,14615],{"className":14605},[994],[86,14607],{"className":14608,"style":14190},[998],[86,14610,6187],{"className":14611},[1003,1007],[86,14613],{"className":14614,"style":4162},[3221],[86,14616,14618,14624,14730],{"className":14617},[7131],[86,14619,14621],{"className":14620,"style":10228},[3320,10227],[86,14622,243],{"className":14623},[10232,1038],[86,14625,14627,14630,14727],{"className":14626},[1003],[86,14628],{"className":14629},[3320,3829],[86,14631,14633],{"className":14632},[3749],[86,14634,14636,14719],{"className":14635},[1016,3836],[86,14637,14639,14716],{"className":14638},[1020],[86,14640,14642,14697,14705],{"className":14641,"style":13868},[1024],[86,14643,14644,14647],{"style":13871},[86,14645],{"className":14646,"style":3850},[1031],[86,14648,14650],{"className":14649},[1003],[86,14651,14653],{"className":14652},[1003,10044],[86,14654,14656,14689],{"className":14655},[1016,3836],[86,14657,14659,14686],{"className":14658},[1020],[86,14660,14662,14674],{"className":14661,"style":13890},[1024],[86,14663,14665,14668],{"className":14664,"style":3876},[10058],[86,14666],{"className":14667,"style":3850},[1031],[86,14669,14671],{"className":14670,"style":13900},[1003],[86,14672,6896],{"className":14673},[1003,1007],[86,14675,14676,14679],{"style":13906},[86,14677],{"className":14678,"style":3850},[1031],[86,14680,14682],{"className":14681,"style":13913},[10147],[10150,14683,14684],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,14685],{"d":13920},[86,14687,3963],{"className":14688},[3962],[86,14690,14692],{"className":14691},[1020],[86,14693,14695],{"className":14694,"style":13930},[1024],[86,14696],{},[86,14698,14699,14702],{"style":3901},[86,14700],{"className":14701,"style":3850},[1031],[86,14703],{"className":14704,"style":3909},[3908],[86,14706,14707,14710],{"style":3912},[86,14708],{"className":14709,"style":3850},[1031],[86,14711,14713],{"className":14712},[1003],[86,14714,7892],{"className":14715},[1003,1007],[86,14717,3963],{"className":14718},[3962],[86,14720,14722],{"className":14721},[1020],[86,14723,14725],{"className":14724,"style":13961},[1024],[86,14726],{},[86,14728],{"className":14729},[3356,3829],[86,14731,14733],{"className":14732,"style":10228},[3356,10227],[86,14734,867],{"className":14735},[10232,1038],[12,14737,3273],{},[30,14739,14740,14802,14834,14865],{},[33,14741,14742,14385],{},[86,14743,14745,14762],{"className":14744},[955],[86,14746,14748],{"className":14747},[959],[961,14749,14750],{"xmlns":963},[965,14751,14752,14760],{},[968,14753,14754],{},[3758,14755,14756,14758],{"accent":990},[974,14757,3189],{},[3191,14759,14087],{},[982,14761,14344],{"encoding":984},[86,14763,14765],{"className":14764,"ariaHidden":990},[989],[86,14766,14768,14771],{"className":14767},[994],[86,14769],{"className":14770,"style":14154},[998],[86,14772,14774],{"className":14773},[1003,3863],[86,14775,14777],{"className":14776},[1016],[86,14778,14780],{"className":14779},[1020],[86,14781,14783,14791],{"className":14782,"style":14154},[1024],[86,14784,14785,14788],{"style":3876},[86,14786],{"className":14787,"style":3850},[1031],[86,14789,3189],{"className":14790},[1003,1007],[86,14792,14793,14796],{"style":3876},[86,14794],{"className":14795,"style":3850},[1031],[86,14797,14799],{"className":14798,"style":14171},[3891],[86,14800,14087],{"className":14801},[1003],[33,14803,14804,14833],{},[86,14805,14807,14820],{"className":14806},[955],[86,14808,14810],{"className":14809},[959],[961,14811,14812],{"xmlns":963},[965,14813,14814,14818],{},[968,14815,14816],{},[974,14817,6187],{},[982,14819,6187],{"encoding":984},[86,14821,14823],{"className":14822,"ariaHidden":990},[989],[86,14824,14826,14830],{"className":14825},[994],[86,14827],{"className":14828,"style":14829},[998],"height:0.6151em;",[86,14831,6187],{"className":14832},[1003,1007]," = valor crítico de la distribución t de Student",[33,14835,14836,14864],{},[86,14837,14839,14852],{"className":14838},[955],[86,14840,14842],{"className":14841},[959],[961,14843,14844],{"xmlns":963},[965,14845,14846,14850],{},[968,14847,14848],{},[974,14849,7892],{},[982,14851,7892],{"encoding":984},[86,14853,14855],{"className":14854,"ariaHidden":990},[989],[86,14856,14858,14861],{"className":14857},[994],[86,14859],{"className":14860,"style":7401},[998],[86,14862,7892],{"className":14863},[1003,1007]," = desviación estándar muestral",[33,14866,14867,14478],{},[86,14868,14870,14883],{"className":14869},[955],[86,14871,14873],{"className":14872},[959],[961,14874,14875],{"xmlns":963},[965,14876,14877,14881],{},[968,14878,14879],{},[974,14880,6896],{},[982,14882,6896],{"encoding":984},[86,14884,14886],{"className":14885,"ariaHidden":990},[989],[86,14887,14889,14892],{"className":14888},[994],[86,14890],{"className":14891,"style":7401},[998],[86,14893,6896],{"className":14894},[1003,1007],[12,14896,14897],{},"Con eso aclarado, veámos un ejemplo práctico:",[12,14899,14900,14901,14904,14905,14908,14909,14912,14913,61],{},"Se encuesta a ",[122,14902,14903],{},"100 personas"," y se obtiene que la media de gasto mensual es ",[122,14906,14907],{},"$50",", con una desviación estándar de ",[122,14910,14911],{},"$10"," y con un nivel de confianza del ",[122,14914,14915],{},"95%",[12,14917,14918],{},"Sabemos que:",[86,14920,14922],{"className":14921},[3173],[86,14923,14925,14944],{"className":14924},[955],[86,14926,14928],{"className":14927},[959],[961,14929,14930],{"xmlns":963,"display":3182},[965,14931,14932,14941],{},[968,14933,14934,14936,14938],{},[974,14935,14093],{},[3191,14937,258],{},[978,14939,14940],{},"1.96",[982,14942,14943],{"encoding":984},"Z = 1.96",[86,14945,14947,14965],{"className":14946,"ariaHidden":990},[989],[86,14948,14950,14953,14956,14959,14962],{"className":14949},[994],[86,14951],{"className":14952,"style":3575},[998],[86,14954,14093],{"className":14955,"style":3512},[1003,1007],[86,14957],{"className":14958,"style":3222},[3221],[86,14960,258],{"className":14961},[3226],[86,14963],{"className":14964,"style":3222},[3221],[86,14966,14968,14971],{"className":14967},[994],[86,14969],{"className":14970,"style":5994},[998],[86,14972,14940],{"className":14973},[1003],[12,14975,14976],{},"Para un nivel de confianza del 95%, el valor crítico Z es aproximadamente 1.96 (esto se obtiene de la tabla de distribución normal estándar).",[16,14978,14979],{},[12,14980,14981],{},"Puedes buscar más sobre como obtener este valor investigando sobre la distribución normal estándar y las tablas Z (espero publicar un artículo sobre esto pronto).",[12,14983,14984],{},"Calculamos:",[86,14986,14988],{"className":14987},[3173],[86,14989,14991,15032],{"className":14990},[955],[86,14992,14994],{"className":14993},[959],[961,14995,14996],{"xmlns":963,"display":3182},[965,14997,14998,15029],{},[968,14999,15000,15002,15004,15006,15009,15011,15013],{},[974,15001,14076],{},[974,15003,1514],{},[3191,15005,258],{},[978,15007,15008],{},"50",[3191,15010,14090],{},[978,15012,14940],{},[968,15014,15015,15017,15027],{},[3191,15016,243],{"fence":990},[3749,15018,15019,15022],{},[978,15020,15021],{},"10",[9825,15023,15024],{},[978,15025,15026],{},"100",[3191,15028,867],{"fence":990},[982,15030,15031],{"encoding":984},"IC = 50 \\pm 1.96 \\left(\\frac{10}{\\sqrt{100}}\\right)",[86,15033,15035,15056,15074],{"className":15034,"ariaHidden":990},[989],[86,15036,15038,15041,15044,15047,15050,15053],{"className":15037},[994],[86,15039],{"className":15040,"style":3575},[998],[86,15042,14076],{"className":15043,"style":4685},[1003,1007],[86,15045,1514],{"className":15046,"style":3512},[1003,1007],[86,15048],{"className":15049,"style":3222},[3221],[86,15051,258],{"className":15052},[3226],[86,15054],{"className":15055,"style":3222},[3221],[86,15057,15059,15062,15065,15068,15071],{"className":15058},[994],[86,15060],{"className":15061,"style":9303},[998],[86,15063,15008],{"className":15064},[1003],[86,15066],{"className":15067,"style":5012},[3221],[86,15069,14090],{"className":15070},[5016],[86,15072],{"className":15073,"style":5012},[3221],[86,15075,15077,15080,15083,15086],{"className":15076},[994],[86,15078],{"className":15079,"style":14190},[998],[86,15081,14940],{"className":15082},[1003],[86,15084],{"className":15085,"style":4162},[3221],[86,15087,15089,15095,15205],{"className":15088},[7131],[86,15090,15092],{"className":15091,"style":10228},[3320,10227],[86,15093,243],{"className":15094},[10232,1038],[86,15096,15098,15101,15202],{"className":15097},[1003],[86,15099],{"className":15100},[3320,3829],[86,15102,15104],{"className":15103},[3749],[86,15105,15107,15194],{"className":15106},[1016,3836],[86,15108,15110,15191],{"className":15109},[1020],[86,15111,15113,15172,15180],{"className":15112,"style":9568},[1024],[86,15114,15116,15119],{"style":15115},"top:-2.2028em;",[86,15117],{"className":15118,"style":3850},[1031],[86,15120,15122],{"className":15121},[1003],[86,15123,15125],{"className":15124},[1003,10044],[86,15126,15128,15163],{"className":15127},[1016,3836],[86,15129,15131,15160],{"className":15130},[1020],[86,15132,15135,15147],{"className":15133,"style":15134},[1024],"height:0.9072em;",[86,15136,15138,15141],{"className":15137,"style":3876},[10058],[86,15139],{"className":15140,"style":3850},[1031],[86,15142,15144],{"className":15143,"style":13900},[1003],[86,15145,15026],{"className":15146},[1003],[86,15148,15150,15153],{"style":15149},"top:-2.8672em;",[86,15151],{"className":15152,"style":3850},[1031],[86,15154,15156],{"className":15155,"style":13913},[10147],[10150,15157,15158],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,15159],{"d":13920},[86,15161,3963],{"className":15162},[3962],[86,15164,15166],{"className":15165},[1020],[86,15167,15170],{"className":15168,"style":15169},[1024],"height:0.1328em;",[86,15171],{},[86,15173,15174,15177],{"style":3901},[86,15175],{"className":15176,"style":3850},[1031],[86,15178],{"className":15179,"style":3909},[3908],[86,15181,15182,15185],{"style":3912},[86,15183],{"className":15184,"style":3850},[1031],[86,15186,15188],{"className":15187},[1003],[86,15189,15021],{"className":15190},[1003],[86,15192,3963],{"className":15193},[3962],[86,15195,15197],{"className":15196},[1020],[86,15198,15200],{"className":15199,"style":13961},[1024],[86,15201],{},[86,15203],{"className":15204},[3356,3829],[86,15206,15208],{"className":15207,"style":10228},[3356,10227],[86,15209,867],{"className":15210},[10232,1038],[86,15212,15214],{"className":15213},[3173],[86,15215,15217,15247],{"className":15216},[955],[86,15218,15220],{"className":15219},[959],[961,15221,15222],{"xmlns":963,"display":3182},[965,15223,15224,15244],{},[968,15225,15226,15228,15230,15232,15234,15236,15238,15240,15242],{},[974,15227,14076],{},[974,15229,1514],{},[3191,15231,258],{},[978,15233,15008],{},[3191,15235,14090],{},[978,15237,14940],{},[3191,15239,243],{"stretchy":3295},[978,15241,802],{},[3191,15243,867],{"stretchy":3295},[982,15245,15246],{"encoding":984},"IC = 50 \\pm 1.96 (1)",[86,15248,15250,15271,15289],{"className":15249,"ariaHidden":990},[989],[86,15251,15253,15256,15259,15262,15265,15268],{"className":15252},[994],[86,15254],{"className":15255,"style":3575},[998],[86,15257,14076],{"className":15258,"style":4685},[1003,1007],[86,15260,1514],{"className":15261,"style":3512},[1003,1007],[86,15263],{"className":15264,"style":3222},[3221],[86,15266,258],{"className":15267},[3226],[86,15269],{"className":15270,"style":3222},[3221],[86,15272,15274,15277,15280,15283,15286],{"className":15273},[994],[86,15275],{"className":15276,"style":9303},[998],[86,15278,15008],{"className":15279},[1003],[86,15281],{"className":15282,"style":5012},[3221],[86,15284,14090],{"className":15285},[5016],[86,15287],{"className":15288,"style":5012},[3221],[86,15290,15292,15295,15298,15301,15304],{"className":15291},[994],[86,15293],{"className":15294,"style":3794},[998],[86,15296,14940],{"className":15297},[1003],[86,15299,243],{"className":15300},[3320],[86,15302,802],{"className":15303},[1003],[86,15305,867],{"className":15306},[3356],[86,15308,15310],{"className":15309},[3173],[86,15311,15313,15337],{"className":15312},[955],[86,15314,15316],{"className":15315},[959],[961,15317,15318],{"xmlns":963,"display":3182},[965,15319,15320,15334],{},[968,15321,15322,15324,15326,15328,15330,15332],{},[974,15323,14076],{},[974,15325,1514],{},[3191,15327,258],{},[978,15329,15008],{},[3191,15331,14090],{},[978,15333,14940],{},[982,15335,15336],{"encoding":984},"IC = 50 \\pm 1.96",[86,15338,15340,15361,15379],{"className":15339,"ariaHidden":990},[989],[86,15341,15343,15346,15349,15352,15355,15358],{"className":15342},[994],[86,15344],{"className":15345,"style":3575},[998],[86,15347,14076],{"className":15348,"style":4685},[1003,1007],[86,15350,1514],{"className":15351,"style":3512},[1003,1007],[86,15353],{"className":15354,"style":3222},[3221],[86,15356,258],{"className":15357},[3226],[86,15359],{"className":15360,"style":3222},[3221],[86,15362,15364,15367,15370,15373,15376],{"className":15363},[994],[86,15365],{"className":15366,"style":9303},[998],[86,15368,15008],{"className":15369},[1003],[86,15371],{"className":15372,"style":5012},[3221],[86,15374,14090],{"className":15375},[5016],[86,15377],{"className":15378,"style":5012},[3221],[86,15380,15382,15385],{"className":15381},[994],[86,15383],{"className":15384,"style":5994},[998],[86,15386,14940],{"className":15387},[1003],[12,15389,15390],{},"Resultado:",[86,15392,15394],{"className":15393},[3173],[86,15395,15397,15427],{"className":15396},[955],[86,15398,15400],{"className":15399},[959],[961,15401,15402],{"xmlns":963,"display":3182},[965,15403,15404,15424],{},[968,15405,15406,15408,15410,15412,15414,15417,15419,15422],{},[974,15407,14076],{},[974,15409,1514],{},[3191,15411,258],{},[3191,15413,243],{"stretchy":3295},[978,15415,15416],{},"48.04",[3191,15418,291],{"separator":990},[978,15420,15421],{},"51.96",[3191,15423,867],{"stretchy":3295},[982,15425,15426],{"encoding":984},"IC = (48.04 , 51.96)",[86,15428,15430,15451],{"className":15429,"ariaHidden":990},[989],[86,15431,15433,15436,15439,15442,15445,15448],{"className":15432},[994],[86,15434],{"className":15435,"style":3575},[998],[86,15437,14076],{"className":15438,"style":4685},[1003,1007],[86,15440,1514],{"className":15441,"style":3512},[1003,1007],[86,15443],{"className":15444,"style":3222},[3221],[86,15446,258],{"className":15447},[3226],[86,15449],{"className":15450,"style":3222},[3221],[86,15452,15454,15457,15460,15463,15466,15469,15472],{"className":15453},[994],[86,15455],{"className":15456,"style":3794},[998],[86,15458,243],{"className":15459},[3320],[86,15461,15416],{"className":15462},[1003],[86,15464,291],{"className":15465},[4158],[86,15467],{"className":15468,"style":4162},[3221],[86,15470,15421],{"className":15471},[1003],[86,15473,867],{"className":15474},[3356],[12,15476,15477,15478,61],{},"Interpretación:\nCon 95% de confianza, el verdadero gasto promedio poblacional está entre ",[122,15479,15480],{},"$48.04 y $51.96",[43,15482],{},[323,15484,15486],{"id":15485},"pruebas-de-hipótesis","Pruebas de hipótesis",[12,15488,15489,15490,15493],{},"Estas pruebas sirven para ",[122,15491,15492],{},"tomar decisiones"," sobre una afirmación respecto a la población. Vamos por partes:",[117,15495,15496],{},[33,15497,15498],{},[122,15499,15500],{},"Componentes básicos",[12,15502,15503],{},[122,15504,15505,15506,867],{},"Hipótesis nula (",[86,15507,15509,15528],{"className":15508},[955],[86,15510,15512],{"className":15511},[959],[961,15513,15514],{"xmlns":963},[965,15515,15516,15525],{},[968,15517,15518],{},[6849,15519,15520,15523],{},[974,15521,15522],{},"H",[978,15524,2553],{},[982,15526,15527],{"encoding":984},"H_0",[86,15529,15531],{"className":15530,"ariaHidden":990},[989],[86,15532,15534,15538],{"className":15533},[994],[86,15535],{"className":15536,"style":15537},[998],"height:0.8333em;vertical-align:-0.15em;",[86,15539,15541,15545],{"className":15540},[1003],[86,15542,15522],{"className":15543,"style":15544},[1003,1007],"margin-right:0.0813em;",[86,15546,15548],{"className":15547},[1012],[86,15549,15551,15572],{"className":15550},[1016,3836],[86,15552,15554,15569],{"className":15553},[1020],[86,15555,15557],{"className":15556,"style":6984},[1024],[86,15558,15560,15563],{"style":15559},"top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;",[86,15561],{"className":15562,"style":1032},[1031],[86,15564,15566],{"className":15565},[1036,1037,1038,1039],[86,15567,2553],{"className":15568},[1003,1039],[86,15570,3963],{"className":15571},[3962],[86,15573,15575],{"className":15574},[1020],[86,15576,15578],{"className":15577,"style":7006},[1024],[86,15579],{},[12,15581,15582,15583,15586],{},"Una afirmación que ponemos a prueba, generalmente una afirmación de \"no diferencia\", \"no efecto\" o \"igualdad\". Ejemplo: \"La media es ",[122,15584,15585],{},"igual"," a 50\".",[12,15588,15589],{},[122,15590,15591,15592,867],{},"Hipótesis alternativa (",[86,15593,15595,15613],{"className":15594},[955],[86,15596,15598],{"className":15597},[959],[961,15599,15600],{"xmlns":963},[965,15601,15602,15610],{},[968,15603,15604],{},[6849,15605,15606,15608],{},[974,15607,15522],{},[978,15609,802],{},[982,15611,15612],{"encoding":984},"H_1",[86,15614,15616],{"className":15615,"ariaHidden":990},[989],[86,15617,15619,15622],{"className":15618},[994],[86,15620],{"className":15621,"style":15537},[998],[86,15623,15625,15628],{"className":15624},[1003],[86,15626,15522],{"className":15627,"style":15544},[1003,1007],[86,15629,15631],{"className":15630},[1012],[86,15632,15634,15654],{"className":15633},[1016,3836],[86,15635,15637,15651],{"className":15636},[1020],[86,15638,15640],{"className":15639,"style":6984},[1024],[86,15641,15642,15645],{"style":15559},[86,15643],{"className":15644,"style":1032},[1031],[86,15646,15648],{"className":15647},[1036,1037,1038,1039],[86,15649,802],{"className":15650},[1003,1039],[86,15652,3963],{"className":15653},[3962],[86,15655,15657],{"className":15656},[1020],[86,15658,15660],{"className":15659,"style":7006},[1024],[86,15661],{},[12,15663,15664,15665,15668],{},"Representa la afirmación para la cuál buscamos evidencia. Contraria a la hipótesis nula. Por ejemplo: \"La media es ",[122,15666,15667],{},"diferente"," de 50\".",[12,15670,15671],{},[122,15672,15673,15674,867],{},"Nivel de significancia (",[86,15675,15677,15690],{"className":15676},[955],[86,15678,15680],{"className":15679},[959],[961,15681,15682],{"xmlns":963},[965,15683,15684,15688],{},[968,15685,15686],{},[974,15687,10574],{},[982,15689,10904],{"encoding":984},[86,15691,15693],{"className":15692,"ariaHidden":990},[989],[86,15694,15696,15699],{"className":15695},[994],[86,15697],{"className":15698,"style":7401},[998],[86,15700,10574],{"className":15701,"style":10771},[1003,1007],[12,15703,15704,15705,15774,15775,93,15778,15781,15782,15785],{},"Esta es la probabilidad de rechazar ",[86,15706,15708,15725],{"className":15707},[955],[86,15709,15711],{"className":15710},[959],[961,15712,15713],{"xmlns":963},[965,15714,15715,15723],{},[968,15716,15717],{},[6849,15718,15719,15721],{},[974,15720,15522],{},[978,15722,2553],{},[982,15724,15527],{"encoding":984},[86,15726,15728],{"className":15727,"ariaHidden":990},[989],[86,15729,15731,15734],{"className":15730},[994],[86,15732],{"className":15733,"style":15537},[998],[86,15735,15737,15740],{"className":15736},[1003],[86,15738,15522],{"className":15739,"style":15544},[1003,1007],[86,15741,15743],{"className":15742},[1012],[86,15744,15746,15766],{"className":15745},[1016,3836],[86,15747,15749,15763],{"className":15748},[1020],[86,15750,15752],{"className":15751,"style":6984},[1024],[86,15753,15754,15757],{"style":15559},[86,15755],{"className":15756,"style":1032},[1031],[86,15758,15760],{"className":15759},[1036,1037,1038,1039],[86,15761,2553],{"className":15762},[1003,1039],[86,15764,3963],{"className":15765},[3962],[86,15767,15769],{"className":15768},[1020],[86,15770,15772],{"className":15771,"style":7006},[1024],[86,15773],{}," cuando es verdadera. Es decir, el riesgo que estamos dispuestos a asumir de cometer un error tipo I (falso positivo). Comúnmente valores como: ",[122,15776,15777],{},"0.05 (5%)",[122,15779,15780],{},"0.01 (1%)"," o ",[122,15783,15784],{},"0.10 (10%)"," se utilizan como niveles de significancia.",[12,15787,15788],{},[122,15789,15790],{},"Estadístico de prueba",[12,15792,15793,15794,61],{},"Valor calculado para decidir si rechazamos ",[86,15795,15797,15814],{"className":15796},[955],[86,15798,15800],{"className":15799},[959],[961,15801,15802],{"xmlns":963},[965,15803,15804,15812],{},[968,15805,15806],{},[6849,15807,15808,15810],{},[974,15809,15522],{},[978,15811,2553],{},[982,15813,15527],{"encoding":984},[86,15815,15817],{"className":15816,"ariaHidden":990},[989],[86,15818,15820,15823],{"className":15819},[994],[86,15821],{"className":15822,"style":15537},[998],[86,15824,15826,15829],{"className":15825},[1003],[86,15827,15522],{"className":15828,"style":15544},[1003,1007],[86,15830,15832],{"className":15831},[1012],[86,15833,15835,15855],{"className":15834},[1016,3836],[86,15836,15838,15852],{"className":15837},[1020],[86,15839,15841],{"className":15840,"style":6984},[1024],[86,15842,15843,15846],{"style":15559},[86,15844],{"className":15845,"style":1032},[1031],[86,15847,15849],{"className":15848},[1036,1037,1038,1039],[86,15850,2553],{"className":15851},[1003,1039],[86,15853,3963],{"className":15854},[3962],[86,15856,15858],{"className":15857},[1020],[86,15859,15861],{"className":15860,"style":7006},[1024],[86,15862],{},[12,15864,15865],{},[122,15866,15867],{},"Valor p",[12,15869,15870,15871,15940,15941,15969,15970,16039,16040,61],{},"Probabilidad de obtener un resultado tan extremo como el observado si ",[86,15872,15874,15891],{"className":15873},[955],[86,15875,15877],{"className":15876},[959],[961,15878,15879],{"xmlns":963},[965,15880,15881,15889],{},[968,15882,15883],{},[6849,15884,15885,15887],{},[974,15886,15522],{},[978,15888,2553],{},[982,15890,15527],{"encoding":984},[86,15892,15894],{"className":15893,"ariaHidden":990},[989],[86,15895,15897,15900],{"className":15896},[994],[86,15898],{"className":15899,"style":15537},[998],[86,15901,15903,15906],{"className":15902},[1003],[86,15904,15522],{"className":15905,"style":15544},[1003,1007],[86,15907,15909],{"className":15908},[1012],[86,15910,15912,15932],{"className":15911},[1016,3836],[86,15913,15915,15929],{"className":15914},[1020],[86,15916,15918],{"className":15917,"style":6984},[1024],[86,15919,15920,15923],{"style":15559},[86,15921],{"className":15922,"style":1032},[1031],[86,15924,15926],{"className":15925},[1036,1037,1038,1039],[86,15927,2553],{"className":15928},[1003,1039],[86,15930,3963],{"className":15931},[3962],[86,15933,15935],{"className":15934},[1020],[86,15936,15938],{"className":15937,"style":7006},[1024],[86,15939],{}," fuera verdadera. Si el valor p es menor que ",[86,15942,15944,15957],{"className":15943},[955],[86,15945,15947],{"className":15946},[959],[961,15948,15949],{"xmlns":963},[965,15950,15951,15955],{},[968,15952,15953],{},[974,15954,10574],{},[982,15956,10904],{"encoding":984},[86,15958,15960],{"className":15959,"ariaHidden":990},[989],[86,15961,15963,15966],{"className":15962},[994],[86,15964],{"className":15965,"style":7401},[998],[86,15967,10574],{"className":15968,"style":10771},[1003,1007],", rechazamos ",[86,15971,15973,15990],{"className":15972},[955],[86,15974,15976],{"className":15975},[959],[961,15977,15978],{"xmlns":963},[965,15979,15980,15988],{},[968,15981,15982],{},[6849,15983,15984,15986],{},[974,15985,15522],{},[978,15987,2553],{},[982,15989,15527],{"encoding":984},[86,15991,15993],{"className":15992,"ariaHidden":990},[989],[86,15994,15996,15999],{"className":15995},[994],[86,15997],{"className":15998,"style":15537},[998],[86,16000,16002,16005],{"className":16001},[1003],[86,16003,15522],{"className":16004,"style":15544},[1003,1007],[86,16006,16008],{"className":16007},[1012],[86,16009,16011,16031],{"className":16010},[1016,3836],[86,16012,16014,16028],{"className":16013},[1020],[86,16015,16017],{"className":16016,"style":6984},[1024],[86,16018,16019,16022],{"style":15559},[86,16020],{"className":16021,"style":1032},[1031],[86,16023,16025],{"className":16024},[1036,1037,1038,1039],[86,16026,2553],{"className":16027},[1003,1039],[86,16029,3963],{"className":16030},[3962],[86,16032,16034],{"className":16033},[1020],[86,16035,16037],{"className":16036,"style":7006},[1024],[86,16038],{},", caso contrario, no rechazamos ",[86,16041,16043,16060],{"className":16042},[955],[86,16044,16046],{"className":16045},[959],[961,16047,16048],{"xmlns":963},[965,16049,16050,16058],{},[968,16051,16052],{},[6849,16053,16054,16056],{},[974,16055,15522],{},[978,16057,2553],{},[982,16059,15527],{"encoding":984},[86,16061,16063],{"className":16062,"ariaHidden":990},[989],[86,16064,16066,16069],{"className":16065},[994],[86,16067],{"className":16068,"style":15537},[998],[86,16070,16072,16075],{"className":16071},[1003],[86,16073,15522],{"className":16074,"style":15544},[1003,1007],[86,16076,16078],{"className":16077},[1012],[86,16079,16081,16101],{"className":16080},[1016,3836],[86,16082,16084,16098],{"className":16083},[1020],[86,16085,16087],{"className":16086,"style":6984},[1024],[86,16088,16089,16092],{"style":15559},[86,16090],{"className":16091,"style":1032},[1031],[86,16093,16095],{"className":16094},[1036,1037,1038,1039],[86,16096,2553],{"className":16097},[1003,1039],[86,16099,3963],{"className":16100},[3962],[86,16102,16104],{"className":16103},[1020],[86,16105,16107],{"className":16106,"style":7006},[1024],[86,16108],{},[16,16110,16111],{},[12,16112,16113,16114,61],{},"El valor p nos dice qué tan probable es obtener los resultados que tenemos (o más extremos) si la hipótesis nula fuera cierta. Si esta probabilidad es muy baja (menor que nuestro nivel de significancia), entonces tenemos suficiente evidencia para rechazar la hipótesis nula. Por dar un ejemplo, si obtenemos un valor p de 0.03 y nuestro nivel de significancia es 0.05, esto significa que hay solo un 3% de probabilidad de obtener esos resultados si la hipótesis nula fuera verdadera, lo que nos lleva a rechazar ",[86,16115,16117,16134],{"className":16116},[955],[86,16118,16120],{"className":16119},[959],[961,16121,16122],{"xmlns":963},[965,16123,16124,16132],{},[968,16125,16126],{},[6849,16127,16128,16130],{},[974,16129,15522],{},[978,16131,2553],{},[982,16133,15527],{"encoding":984},[86,16135,16137],{"className":16136,"ariaHidden":990},[989],[86,16138,16140,16143],{"className":16139},[994],[86,16141],{"className":16142,"style":15537},[998],[86,16144,16146,16149],{"className":16145},[1003],[86,16147,15522],{"className":16148,"style":15544},[1003,1007],[86,16150,16152],{"className":16151},[1012],[86,16153,16155,16175],{"className":16154},[1016,3836],[86,16156,16158,16172],{"className":16157},[1020],[86,16159,16161],{"className":16160,"style":6984},[1024],[86,16162,16163,16166],{"style":15559},[86,16164],{"className":16165,"style":1032},[1031],[86,16167,16169],{"className":16168},[1036,1037,1038,1039],[86,16170,2553],{"className":16171},[1003,1039],[86,16173,3963],{"className":16174},[3962],[86,16176,16178],{"className":16177},[1020],[86,16179,16181],{"className":16180,"style":7006},[1024],[86,16182],{},[12,16184,16185],{},"Hagámos un ejemplo práctico:",[12,16187,16188,16189,61],{},"Una empresa afirma que el tiempo promedio de entrega es ",[122,16190,16191],{},"30 minutos",[12,16193,16194],{},"Se toma una muestra y se obtiene:",[30,16196,16197,16200,16203,16206],{},[33,16198,16199],{},"n = 36",[33,16201,16202],{},"media = 32 minutos",[33,16204,16205],{},"desviación estándar = 6",[33,16207,16208,16236],{},[86,16209,16211,16224],{"className":16210},[955],[86,16212,16214],{"className":16213},[959],[961,16215,16216],{"xmlns":963},[965,16217,16218,16222],{},[968,16219,16220],{},[974,16221,10574],{},[982,16223,10904],{"encoding":984},[86,16225,16227],{"className":16226,"ariaHidden":990},[989],[86,16228,16230,16233],{"className":16229},[994],[86,16231],{"className":16232,"style":7401},[998],[86,16234,10574],{"className":16235,"style":10771},[1003,1007]," = 0.05",[117,16238,16239],{},[33,16240,16241],{},"Planteamos hipótesis",[86,16243,16245],{"className":16244},[3173],[86,16246,16248,16275],{"className":16247},[955],[86,16249,16251],{"className":16250},[959],[961,16252,16253],{"xmlns":963,"display":3182},[965,16254,16255,16272],{},[968,16256,16257,16263,16265,16267,16269],{},[6849,16258,16259,16261],{},[974,16260,15522],{},[978,16262,2553],{},[3191,16264,162],{},[974,16266,9883],{},[3191,16268,258],{},[978,16270,16271],{},"30",[982,16273,16274],{"encoding":984},"H_0: \\mu = 30",[86,16276,16278,16333,16352],{"className":16277,"ariaHidden":990},[989],[86,16279,16281,16284,16324,16327,16330],{"className":16280},[994],[86,16282],{"className":16283,"style":15537},[998],[86,16285,16287,16290],{"className":16286},[1003],[86,16288,15522],{"className":16289,"style":15544},[1003,1007],[86,16291,16293],{"className":16292},[1012],[86,16294,16296,16316],{"className":16295},[1016,3836],[86,16297,16299,16313],{"className":16298},[1020],[86,16300,16302],{"className":16301,"style":6984},[1024],[86,16303,16304,16307],{"style":15559},[86,16305],{"className":16306,"style":1032},[1031],[86,16308,16310],{"className":16309},[1036,1037,1038,1039],[86,16311,2553],{"className":16312},[1003,1039],[86,16314,3963],{"className":16315},[3962],[86,16317,16319],{"className":16318},[1020],[86,16320,16322],{"className":16321,"style":7006},[1024],[86,16323],{},[86,16325],{"className":16326,"style":3222},[3221],[86,16328,162],{"className":16329},[3226],[86,16331],{"className":16332,"style":3222},[3221],[86,16334,16336,16340,16343,16346,16349],{"className":16335},[994],[86,16337],{"className":16338,"style":16339},[998],"height:0.625em;vertical-align:-0.1944em;",[86,16341,9883],{"className":16342},[1003,1007],[86,16344],{"className":16345,"style":3222},[3221],[86,16347,258],{"className":16348},[3226],[86,16350],{"className":16351,"style":3222},[3221],[86,16353,16355,16358],{"className":16354},[994],[86,16356],{"className":16357,"style":5994},[998],[86,16359,16271],{"className":16360},[1003],[86,16362,16364],{"className":16363},[3173],[86,16365,16367,16393],{"className":16366},[955],[86,16368,16370],{"className":16369},[959],[961,16371,16372],{"xmlns":963,"display":3182},[965,16373,16374,16390],{},[968,16375,16376,16382,16384,16386,16388],{},[6849,16377,16378,16380],{},[974,16379,15522],{},[978,16381,802],{},[3191,16383,162],{},[974,16385,9883],{},[3191,16387,4812],{"mathvariant":4327},[978,16389,16271],{},[982,16391,16392],{"encoding":984},"H_1: \\mu \\neq 30",[86,16394,16396,16451,16502],{"className":16395,"ariaHidden":990},[989],[86,16397,16399,16402,16442,16445,16448],{"className":16398},[994],[86,16400],{"className":16401,"style":15537},[998],[86,16403,16405,16408],{"className":16404},[1003],[86,16406,15522],{"className":16407,"style":15544},[1003,1007],[86,16409,16411],{"className":16410},[1012],[86,16412,16414,16434],{"className":16413},[1016,3836],[86,16415,16417,16431],{"className":16416},[1020],[86,16418,16420],{"className":16419,"style":6984},[1024],[86,16421,16422,16425],{"style":15559},[86,16423],{"className":16424,"style":1032},[1031],[86,16426,16428],{"className":16427},[1036,1037,1038,1039],[86,16429,802],{"className":16430},[1003,1039],[86,16432,3963],{"className":16433},[3962],[86,16435,16437],{"className":16436},[1020],[86,16438,16440],{"className":16439,"style":7006},[1024],[86,16441],{},[86,16443],{"className":16444,"style":3222},[3221],[86,16446,162],{"className":16447},[3226],[86,16449],{"className":16450,"style":3222},[3221],[86,16452,16454,16457,16460,16463,16499],{"className":16453},[994],[86,16455],{"className":16456,"style":4888},[998],[86,16458,9883],{"className":16459},[1003,1007],[86,16461],{"className":16462,"style":3222},[3221],[86,16464,16466,16493,16496],{"className":16465},[3226],[86,16467,16469],{"className":16468},[3226],[86,16470,16472],{"className":16471},[1003,4876],[86,16473,16475],{"className":16474},[4880],[86,16476,16478,16481,16490],{"className":16477},[4884],[86,16479],{"className":16480,"style":4888},[998],[86,16482,16484],{"className":16483},[4892],[86,16485,16487],{"className":16486},[1003],[86,16488,4899],{"className":16489},[3226],[86,16491],{"className":16492},[4903],[86,16494],{"className":16495},[3221,4907],[86,16497,258],{"className":16498},[3226],[86,16500],{"className":16501,"style":3222},[3221],[86,16503,16505,16508],{"className":16504},[994],[86,16506],{"className":16507,"style":5994},[998],[86,16509,16271],{"className":16510},[1003],[117,16512,16513],{"start":192},[33,16514,16515],{},"Calculamos estadístico Z",[86,16517,16519],{"className":16518},[3173],[86,16520,16522,16563],{"className":16521},[955],[86,16523,16525],{"className":16524},[959],[961,16526,16527],{"xmlns":963,"display":3182},[965,16528,16529,16560],{},[968,16530,16531,16533,16535],{},[974,16532,14093],{},[3191,16534,258],{},[3749,16536,16537,16549],{},[968,16538,16539,16545,16547],{},[3758,16540,16541,16543],{"accent":990},[974,16542,3189],{},[3191,16544,14087],{},[3191,16546,9864],{},[974,16548,9883],{},[968,16550,16551,16553,16556],{},[974,16552,9839],{},[974,16554,16555],{"mathvariant":4327},"\u002F",[9825,16557,16558],{},[974,16559,6896],{},[982,16561,16562],{"encoding":984},"Z = \\frac{\\bar{x} - \\mu}{\\sigma\u002F\\sqrt{n}}",[86,16564,16566,16584],{"className":16565,"ariaHidden":990},[989],[86,16567,16569,16572,16575,16578,16581],{"className":16568},[994],[86,16570],{"className":16571,"style":3575},[998],[86,16573,14093],{"className":16574,"style":3512},[1003,1007],[86,16576],{"className":16577,"style":3222},[3221],[86,16579,258],{"className":16580},[3226],[86,16582],{"className":16583,"style":3222},[3221],[86,16585,16587,16591],{"className":16586},[994],[86,16588],{"className":16589,"style":16590},[998],"height:2.2006em;vertical-align:-0.9403em;",[86,16592,16594,16597,16742],{"className":16593},[1003],[86,16595],{"className":16596},[3320,3829],[86,16598,16600],{"className":16599},[3749],[86,16601,16603,16733],{"className":16602},[1016,3836],[86,16604,16606,16730],{"className":16605},[1020],[86,16607,16610,16671,16679],{"className":16608,"style":16609},[1024],"height:1.2603em;",[86,16611,16612,16615],{"style":13871},[86,16613],{"className":16614,"style":3850},[1031],[86,16616,16618,16621,16624],{"className":16617},[1003],[86,16619,9839],{"className":16620,"style":8109},[1003,1007],[86,16622,16555],{"className":16623},[1003],[86,16625,16627],{"className":16626},[1003,10044],[86,16628,16630,16663],{"className":16629},[1016,3836],[86,16631,16633,16660],{"className":16632},[1020],[86,16634,16636,16648],{"className":16635,"style":13890},[1024],[86,16637,16639,16642],{"className":16638,"style":3876},[10058],[86,16640],{"className":16641,"style":3850},[1031],[86,16643,16645],{"className":16644,"style":13900},[1003],[86,16646,6896],{"className":16647},[1003,1007],[86,16649,16650,16653],{"style":13906},[86,16651],{"className":16652,"style":3850},[1031],[86,16654,16656],{"className":16655,"style":13913},[10147],[10150,16657,16658],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,16659],{"d":13920},[86,16661,3963],{"className":16662},[3962],[86,16664,16666],{"className":16665},[1020],[86,16667,16669],{"className":16668,"style":13930},[1024],[86,16670],{},[86,16672,16673,16676],{"style":3901},[86,16674],{"className":16675,"style":3850},[1031],[86,16677],{"className":16678,"style":3909},[3908],[86,16680,16681,16684],{"style":3912},[86,16682],{"className":16683,"style":3850},[1031],[86,16685,16687,16718,16721,16724,16727],{"className":16686},[1003],[86,16688,16690],{"className":16689},[1003,3863],[86,16691,16693],{"className":16692},[1016],[86,16694,16696],{"className":16695},[1020],[86,16697,16699,16707],{"className":16698,"style":14154},[1024],[86,16700,16701,16704],{"style":3876},[86,16702],{"className":16703,"style":3850},[1031],[86,16705,3189],{"className":16706},[1003,1007],[86,16708,16709,16712],{"style":3876},[86,16710],{"className":16711,"style":3850},[1031],[86,16713,16715],{"className":16714,"style":14171},[3891],[86,16716,14087],{"className":16717},[1003],[86,16719],{"className":16720,"style":5012},[3221],[86,16722,9864],{"className":16723},[5016],[86,16725],{"className":16726,"style":5012},[3221],[86,16728,9883],{"className":16729},[1003,1007],[86,16731,3963],{"className":16732},[3962],[86,16734,16736],{"className":16735},[1020],[86,16737,16740],{"className":16738,"style":16739},[1024],"height:0.9403em;",[86,16741],{},[86,16743],{"className":16744},[3356,3829],[12,16746,4725],{},[30,16748,16749,16812,16844,16875],{},[33,16750,16751,16811],{},[86,16752,16754,16771],{"className":16753},[955],[86,16755,16757],{"className":16756},[959],[961,16758,16759],{"xmlns":963},[965,16760,16761,16769],{},[968,16762,16763],{},[3758,16764,16765,16767],{"accent":990},[974,16766,3189],{},[3191,16768,14087],{},[982,16770,14344],{"encoding":984},[86,16772,16774],{"className":16773,"ariaHidden":990},[989],[86,16775,16777,16780],{"className":16776},[994],[86,16778],{"className":16779,"style":14154},[998],[86,16781,16783],{"className":16782},[1003,3863],[86,16784,16786],{"className":16785},[1016],[86,16787,16789],{"className":16788},[1020],[86,16790,16792,16800],{"className":16791,"style":14154},[1024],[86,16793,16794,16797],{"style":3876},[86,16795],{"className":16796,"style":3850},[1031],[86,16798,3189],{"className":16799},[1003,1007],[86,16801,16802,16805],{"style":3876},[86,16803],{"className":16804,"style":3850},[1031],[86,16806,16808],{"className":16807,"style":14171},[3891],[86,16809,14087],{"className":16810},[1003]," = media muestral = 32",[33,16813,16814,16843],{},[86,16815,16817,16831],{"className":16816},[955],[86,16818,16820],{"className":16819},[959],[961,16821,16822],{"xmlns":963},[965,16823,16824,16828],{},[968,16825,16826],{},[974,16827,9883],{},[982,16829,16830],{"encoding":984},"\\mu",[86,16832,16834],{"className":16833,"ariaHidden":990},[989],[86,16835,16837,16840],{"className":16836},[994],[86,16838],{"className":16839,"style":16339},[998],[86,16841,9883],{"className":16842},[1003,1007]," = media hipotética = 30",[33,16845,16846,16874],{},[86,16847,16849,16862],{"className":16848},[955],[86,16850,16852],{"className":16851},[959],[961,16853,16854],{"xmlns":963},[965,16855,16856,16860],{},[968,16857,16858],{},[974,16859,9839],{},[982,16861,13986],{"encoding":984},[86,16863,16865],{"className":16864,"ariaHidden":990},[989],[86,16866,16868,16871],{"className":16867},[994],[86,16869],{"className":16870,"style":7401},[998],[86,16872,9839],{"className":16873,"style":8109},[1003,1007]," = desviación estándar = 6",[33,16876,16877,16905],{},[86,16878,16880,16893],{"className":16879},[955],[86,16881,16883],{"className":16882},[959],[961,16884,16885],{"xmlns":963},[965,16886,16887,16891],{},[968,16888,16889],{},[974,16890,6896],{},[982,16892,6896],{"encoding":984},[86,16894,16896],{"className":16895,"ariaHidden":990},[989],[86,16897,16899,16902],{"className":16898},[994],[86,16900],{"className":16901,"style":7401},[998],[86,16903,6896],{"className":16904},[1003,1007]," = tamaño de muestra = 36",[86,16907,16909],{"className":16908},[3173],[86,16910,16912,16950],{"className":16911},[955],[86,16913,16915],{"className":16914},[959],[961,16916,16917],{"xmlns":963,"display":3182},[965,16918,16919,16947],{},[968,16920,16921,16923,16925],{},[974,16922,14093],{},[3191,16924,258],{},[3749,16926,16927,16936],{},[968,16928,16929,16932,16934],{},[978,16930,16931],{},"32",[3191,16933,9864],{},[978,16935,16271],{},[968,16937,16938,16940,16942],{},[978,16939,4114],{},[974,16941,16555],{"mathvariant":4327},[9825,16943,16944],{},[978,16945,16946],{},"36",[982,16948,16949],{"encoding":984},"Z = \\frac{32 - 30}{6\u002F\\sqrt{36}}",[86,16951,16953,16971],{"className":16952,"ariaHidden":990},[989],[86,16954,16956,16959,16962,16965,16968],{"className":16955},[994],[86,16957],{"className":16958,"style":3575},[998],[86,16960,14093],{"className":16961,"style":3512},[1003,1007],[86,16963],{"className":16964,"style":3222},[3221],[86,16966,258],{"className":16967},[3226],[86,16969],{"className":16970,"style":3222},[3221],[86,16972,16974,16978],{"className":16973},[994],[86,16975],{"className":16976,"style":16977},[998],"height:2.3687em;vertical-align:-1.0472em;",[86,16979,16981,16984,17098],{"className":16980},[1003],[86,16982],{"className":16983},[3320,3829],[86,16985,16987],{"className":16986},[3749],[86,16988,16990,17089],{"className":16989},[1016,3836],[86,16991,16993,17086],{"className":16992},[1020],[86,16994,16996,17055,17063],{"className":16995,"style":9568},[1024],[86,16997,16998,17001],{"style":15115},[86,16999],{"className":17000,"style":3850},[1031],[86,17002,17004,17008],{"className":17003},[1003],[86,17005,17007],{"className":17006},[1003],"6\u002F",[86,17009,17011],{"className":17010},[1003,10044],[86,17012,17014,17047],{"className":17013},[1016,3836],[86,17015,17017,17044],{"className":17016},[1020],[86,17018,17020,17032],{"className":17019,"style":15134},[1024],[86,17021,17023,17026],{"className":17022,"style":3876},[10058],[86,17024],{"className":17025,"style":3850},[1031],[86,17027,17029],{"className":17028,"style":13900},[1003],[86,17030,16946],{"className":17031},[1003],[86,17033,17034,17037],{"style":15149},[86,17035],{"className":17036,"style":3850},[1031],[86,17038,17040],{"className":17039,"style":13913},[10147],[10150,17041,17042],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,17043],{"d":13920},[86,17045,3963],{"className":17046},[3962],[86,17048,17050],{"className":17049},[1020],[86,17051,17053],{"className":17052,"style":15169},[1024],[86,17054],{},[86,17056,17057,17060],{"style":3901},[86,17058],{"className":17059,"style":3850},[1031],[86,17061],{"className":17062,"style":3909},[3908],[86,17064,17065,17068],{"style":3912},[86,17066],{"className":17067,"style":3850},[1031],[86,17069,17071,17074,17077,17080,17083],{"className":17070},[1003],[86,17072,16931],{"className":17073},[1003],[86,17075],{"className":17076,"style":5012},[3221],[86,17078,9864],{"className":17079},[5016],[86,17081],{"className":17082,"style":5012},[3221],[86,17084,16271],{"className":17085},[1003],[86,17087,3963],{"className":17088},[3962],[86,17090,17092],{"className":17091},[1020],[86,17093,17096],{"className":17094,"style":17095},[1024],"height:1.0472em;",[86,17097],{},[86,17099],{"className":17100},[3356,3829],[86,17102,17104],{"className":17103},[3173],[86,17105,17107,17129],{"className":17106},[955],[86,17108,17110],{"className":17109},[959],[961,17111,17112],{"xmlns":963,"display":3182},[965,17113,17114,17126],{},[968,17115,17116,17118,17120],{},[974,17117,14093],{},[3191,17119,258],{},[3749,17121,17122,17124],{},[978,17123,980],{},[978,17125,802],{},[982,17127,17128],{"encoding":984},"Z = \\frac{2}{1}",[86,17130,17132,17150],{"className":17131,"ariaHidden":990},[989],[86,17133,17135,17138,17141,17144,17147],{"className":17134},[994],[86,17136],{"className":17137,"style":3575},[998],[86,17139,14093],{"className":17140,"style":3512},[1003,1007],[86,17142],{"className":17143,"style":3222},[3221],[86,17145,258],{"className":17146},[3226],[86,17148],{"className":17149,"style":3222},[3221],[86,17151,17153,17156],{"className":17152},[994],[86,17154],{"className":17155,"style":9549},[998],[86,17157,17159,17162,17215],{"className":17158},[1003],[86,17160],{"className":17161},[3320,3829],[86,17163,17165],{"className":17164},[3749],[86,17166,17168,17207],{"className":17167},[1016,3836],[86,17169,17171,17204],{"className":17170},[1020],[86,17172,17174,17185,17193],{"className":17173,"style":9568},[1024],[86,17175,17176,17179],{"style":3846},[86,17177],{"className":17178,"style":3850},[1031],[86,17180,17182],{"className":17181},[1003],[86,17183,802],{"className":17184},[1003],[86,17186,17187,17190],{"style":3901},[86,17188],{"className":17189,"style":3850},[1031],[86,17191],{"className":17192,"style":3909},[3908],[86,17194,17195,17198],{"style":3912},[86,17196],{"className":17197,"style":3850},[1031],[86,17199,17201],{"className":17200},[1003],[86,17202,980],{"className":17203},[1003],[86,17205,3963],{"className":17206},[3962],[86,17208,17210],{"className":17209},[1020],[86,17211,17213],{"className":17212,"style":9620},[1024],[86,17214],{},[86,17216],{"className":17217},[3356,3829],[86,17219,17221],{"className":17220},[3173],[86,17222,17224,17242],{"className":17223},[955],[86,17225,17227],{"className":17226},[959],[961,17228,17229],{"xmlns":963,"display":3182},[965,17230,17231,17239],{},[968,17232,17233,17235,17237],{},[974,17234,14093],{},[3191,17236,258],{},[978,17238,980],{},[982,17240,17241],{"encoding":984},"Z = 2",[86,17243,17245,17263],{"className":17244,"ariaHidden":990},[989],[86,17246,17248,17251,17254,17257,17260],{"className":17247},[994],[86,17249],{"className":17250,"style":3575},[998],[86,17252,14093],{"className":17253,"style":3512},[1003,1007],[86,17255],{"className":17256,"style":3222},[3221],[86,17258,258],{"className":17259},[3226],[86,17261],{"className":17262,"style":3222},[3221],[86,17264,17266,17269],{"className":17265},[994],[86,17267],{"className":17268,"style":5994},[998],[86,17270,980],{"className":17271},[1003],[117,17273,17274],{"start":205},[33,17275,17276],{},"Obtener el valor de p:",[12,17278,17279],{},"Para Z = 2, el valor p es aproximadamente 0.0455 (usando una tabla de distribución normal estándar o una calculadora estadística).",[117,17281,17282],{"start":212},[33,17283,17284,17285,162],{},"Comparar con ",[86,17286,17288,17301],{"className":17287},[955],[86,17289,17291],{"className":17290},[959],[961,17292,17293],{"xmlns":963},[965,17294,17295,17299],{},[968,17296,17297],{},[974,17298,10574],{},[982,17300,10904],{"encoding":984},[86,17302,17304],{"className":17303,"ariaHidden":990},[989],[86,17305,17307,17310],{"className":17306},[994],[86,17308],{"className":17309,"style":7401},[998],[86,17311,10574],{"className":17312,"style":10771},[1003,1007],[12,17314,17315],{},"Dado que 0.0455 \u003C 0.05, llegamos a la conclusión de que:",[12,17317,17318],{},[122,17319,17320,17321],{},"Se rechaza ",[86,17322,17324,17341],{"className":17323},[955],[86,17325,17327],{"className":17326},[959],[961,17328,17329],{"xmlns":963},[965,17330,17331,17339],{},[968,17332,17333],{},[6849,17334,17335,17337],{},[974,17336,15522],{},[978,17338,2553],{},[982,17340,15527],{"encoding":984},[86,17342,17344],{"className":17343,"ariaHidden":990},[989],[86,17345,17347,17350],{"className":17346},[994],[86,17348],{"className":17349,"style":15537},[998],[86,17351,17353,17356],{"className":17352},[1003],[86,17354,15522],{"className":17355,"style":15544},[1003,1007],[86,17357,17359],{"className":17358},[1012],[86,17360,17362,17382],{"className":17361},[1016,3836],[86,17363,17365,17379],{"className":17364},[1020],[86,17366,17368],{"className":17367,"style":6984},[1024],[86,17369,17370,17373],{"style":15559},[86,17371],{"className":17372,"style":1032},[1031],[86,17374,17376],{"className":17375},[1036,1037,1038,1039],[86,17377,2553],{"className":17378},[1003,1039],[86,17380,3963],{"className":17381},[3962],[86,17383,17385],{"className":17384},[1020],[86,17386,17388],{"className":17387,"style":7006},[1024],[86,17389],{},[12,17391,17392],{},"Ahora expliquemos un poco más a fondo como interpretar este resultado y los pasos que hemos realizado:",[12,17394,17395,17396,17399],{},"Primero que nada entendamos algo sobre este ejercicio: tenemos una ",[122,17397,17398],{},"población"," en la que el tiempo de entrega promedio es desconocido, pero la empresa afirma que es de 30 minutos. Entonces tomamos una muestra de 36 entregas y obtenemos una media de 32 minutos con una desviación estándar de 6 minutos. Queremos calcular que tan compatible es esta media muestral de 32 minutos con la afirmación de que el tiempo promedio de la población es de 30 minutos.",[12,17401,17402,17403,17406,17407,17410],{},"La fórmula para obtener Z lo que hace es estandarizar la diferencia entre la media muestral (32 minutos, ",[122,17404,17405],{},"LO OBSERVADO POR NOSOTROS",") y la media hipotética (30 minutos, ",[122,17408,17409],{},"LO AFIRMADO POR LA EMPRESA",") en términos de desviaciones estándar.",[12,17412,17413],{},"El Z calculado de 2 indica que la media muestral está a 2 desviaciones estándar por encima de la media hipotética de 30 minutos, es decir que: Si realmente el tiempo de entrega promedio fuera de 30 minutos, obtener una media muestral de 32 minutos (tal como nos sucede) sería un resultado que está 2 desviaciones estándar por encima de lo esperado.",[12,17415,17416,17417,17486],{},"Cuando trabajamos con una distribución normal estándar, aproximadamente un 95% de los valores están entre -1.96 y 1.96, el 5% está fuera de ese rango (2.5% en cada cola). Entonces, si asumiéramos que ",[86,17418,17420,17437],{"className":17419},[955],[86,17421,17423],{"className":17422},[959],[961,17424,17425],{"xmlns":963},[965,17426,17427,17435],{},[968,17428,17429],{},[6849,17430,17431,17433],{},[974,17432,15522],{},[978,17434,2553],{},[982,17436,15527],{"encoding":984},[86,17438,17440],{"className":17439,"ariaHidden":990},[989],[86,17441,17443,17446],{"className":17442},[994],[86,17444],{"className":17445,"style":15537},[998],[86,17447,17449,17452],{"className":17448},[1003],[86,17450,15522],{"className":17451,"style":15544},[1003,1007],[86,17453,17455],{"className":17454},[1012],[86,17456,17458,17478],{"className":17457},[1016,3836],[86,17459,17461,17475],{"className":17460},[1020],[86,17462,17464],{"className":17463,"style":6984},[1024],[86,17465,17466,17469],{"style":15559},[86,17467],{"className":17468,"style":1032},[1031],[86,17470,17472],{"className":17471},[1036,1037,1038,1039],[86,17473,2553],{"className":17474},[1003,1039],[86,17476,3963],{"className":17477},[3962],[86,17479,17481],{"className":17480},[1020],[86,17482,17484],{"className":17483,"style":7006},[1024],[86,17485],{}," es verdadera, esperaríamos que la media muestral normalmente caiga cerca de 30 minutos, pero obtener un Z de 2 implica que con ese valor de 32 minutos estamos en una zona que ocurre aproximadamente el 4.55% de las veces (valor p bilateral), lo que es menor que nuestro nivel de significancia del 5%.",[16,17488,17489],{},[12,17490,17491],{},"Es decir, si el promedio real fuera de 30, solo en un 4.55% de las muestras podríamos obtener una diferencia igual o mayor que 32 minutos por puro azar. O sea que esos 32 minutos serían muy raros de obtener si realmente el tiempo promedio fuera de 30 minutos.",[12,17493,17494,17495,17564,17565,17568,17569,17572],{},"Realmente una prueba de hipótesis no nos dice que ",[86,17496,17498,17515],{"className":17497},[955],[86,17499,17501],{"className":17500},[959],[961,17502,17503],{"xmlns":963},[965,17504,17505,17513],{},[968,17506,17507],{},[6849,17508,17509,17511],{},[974,17510,15522],{},[978,17512,2553],{},[982,17514,15527],{"encoding":984},[86,17516,17518],{"className":17517,"ariaHidden":990},[989],[86,17519,17521,17524],{"className":17520},[994],[86,17522],{"className":17523,"style":15537},[998],[86,17525,17527,17530],{"className":17526},[1003],[86,17528,15522],{"className":17529,"style":15544},[1003,1007],[86,17531,17533],{"className":17532},[1012],[86,17534,17536,17556],{"className":17535},[1016,3836],[86,17537,17539,17553],{"className":17538},[1020],[86,17540,17542],{"className":17541,"style":6984},[1024],[86,17543,17544,17547],{"style":15559},[86,17545],{"className":17546,"style":1032},[1031],[86,17548,17550],{"className":17549},[1036,1037,1038,1039],[86,17551,2553],{"className":17552},[1003,1039],[86,17554,3963],{"className":17555},[3962],[86,17557,17559],{"className":17558},[1020],[86,17560,17562],{"className":17561,"style":7006},[1024],[86,17563],{}," es verdadera o falsa, NO estamos diciendo que el tiempo de entrega es ",[122,17566,17567],{},"definitivamente"," diferente a 30 minutos, sino que estamos diciendo que ",[122,17570,17571],{},"existe evidencia estadística significativa"," para concluir que el tiempo promedio de entrega es diferente de 30 minutos.",[12,17574,17575],{},"La conclusión formal sería:",[16,17577,17578],{},[12,17579,17580],{},"Con un nivel de significancia del 5%, los datos observados son suficientemente incompatibles con la afirmación de que el tiempo promedio de entrega es de 30 minutos, por lo que rechazamos la hipótesis nula.",[43,17582],{},[12,17584,17585],{},"Haciendo un paréntesis.",[12,17587,17588],{},"Otra forma equivalente de analizar el problema es mediante un intervalo de confianza del 95% para la media poblacional.",[12,17590,17591],{},"La fórmula del intervalo es:",[86,17593,17595],{"className":17594},[3173],[86,17596,17598,17639],{"className":17597},[955],[86,17599,17601],{"className":17600},[959],[961,17602,17603],{"xmlns":963,"display":3182},[965,17604,17605,17637],{},[968,17606,17607,17609,17611,17613,17619,17621,17623],{},[974,17608,14076],{},[974,17610,1514],{},[3191,17612,258],{},[3758,17614,17615,17617],{"accent":990},[974,17616,3189],{},[3191,17618,14087],{},[3191,17620,14090],{},[974,17622,14093],{},[968,17624,17625,17627,17635],{},[3191,17626,243],{"fence":990},[3749,17628,17629,17631],{},[974,17630,9839],{},[9825,17632,17633],{},[974,17634,6896],{},[3191,17636,867],{"fence":990},[982,17638,14110],{"encoding":984},[86,17640,17642,17663,17709],{"className":17641,"ariaHidden":990},[989],[86,17643,17645,17648,17651,17654,17657,17660],{"className":17644},[994],[86,17646],{"className":17647,"style":3575},[998],[86,17649,14076],{"className":17650,"style":4685},[1003,1007],[86,17652,1514],{"className":17653,"style":3512},[1003,1007],[86,17655],{"className":17656,"style":3222},[3221],[86,17658,258],{"className":17659},[3226],[86,17661],{"className":17662,"style":3222},[3221],[86,17664,17666,17669,17700,17703,17706],{"className":17665},[994],[86,17667],{"className":17668,"style":14141},[998],[86,17670,17672],{"className":17671},[1003,3863],[86,17673,17675],{"className":17674},[1016],[86,17676,17678],{"className":17677},[1020],[86,17679,17681,17689],{"className":17680,"style":14154},[1024],[86,17682,17683,17686],{"style":3876},[86,17684],{"className":17685,"style":3850},[1031],[86,17687,3189],{"className":17688},[1003,1007],[86,17690,17691,17694],{"style":3876},[86,17692],{"className":17693,"style":3850},[1031],[86,17695,17697],{"className":17696,"style":14171},[3891],[86,17698,14087],{"className":17699},[1003],[86,17701],{"className":17702,"style":5012},[3221],[86,17704,14090],{"className":17705},[5016],[86,17707],{"className":17708,"style":5012},[3221],[86,17710,17712,17715,17718,17721],{"className":17711},[994],[86,17713],{"className":17714,"style":14190},[998],[86,17716,14093],{"className":17717,"style":3512},[1003,1007],[86,17719],{"className":17720,"style":4162},[3221],[86,17722,17724,17730,17836],{"className":17723},[7131],[86,17725,17727],{"className":17726,"style":10228},[3320,10227],[86,17728,243],{"className":17729},[10232,1038],[86,17731,17733,17736,17833],{"className":17732},[1003],[86,17734],{"className":17735},[3320,3829],[86,17737,17739],{"className":17738},[3749],[86,17740,17742,17825],{"className":17741},[1016,3836],[86,17743,17745,17822],{"className":17744},[1020],[86,17746,17748,17803,17811],{"className":17747,"style":13868},[1024],[86,17749,17750,17753],{"style":13871},[86,17751],{"className":17752,"style":3850},[1031],[86,17754,17756],{"className":17755},[1003],[86,17757,17759],{"className":17758},[1003,10044],[86,17760,17762,17795],{"className":17761},[1016,3836],[86,17763,17765,17792],{"className":17764},[1020],[86,17766,17768,17780],{"className":17767,"style":13890},[1024],[86,17769,17771,17774],{"className":17770,"style":3876},[10058],[86,17772],{"className":17773,"style":3850},[1031],[86,17775,17777],{"className":17776,"style":13900},[1003],[86,17778,6896],{"className":17779},[1003,1007],[86,17781,17782,17785],{"style":13906},[86,17783],{"className":17784,"style":3850},[1031],[86,17786,17788],{"className":17787,"style":13913},[10147],[10150,17789,17790],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,17791],{"d":13920},[86,17793,3963],{"className":17794},[3962],[86,17796,17798],{"className":17797},[1020],[86,17799,17801],{"className":17800,"style":13930},[1024],[86,17802],{},[86,17804,17805,17808],{"style":3901},[86,17806],{"className":17807,"style":3850},[1031],[86,17809],{"className":17810,"style":3909},[3908],[86,17812,17813,17816],{"style":3912},[86,17814],{"className":17815,"style":3850},[1031],[86,17817,17819],{"className":17818},[1003],[86,17820,9839],{"className":17821,"style":8109},[1003,1007],[86,17823,3963],{"className":17824},[3962],[86,17826,17828],{"className":17827},[1020],[86,17829,17831],{"className":17830,"style":13961},[1024],[86,17832],{},[86,17834],{"className":17835},[3356,3829],[86,17837,17839],{"className":17838,"style":10228},[3356,10227],[86,17840,867],{"className":17841},[10232,1038],[12,17843,17844,17845,93,17928,93,17978,392,18029,61],{},"Sabemos que ",[86,17846,17848,17870],{"className":17847},[955],[86,17849,17851],{"className":17850},[959],[961,17852,17853],{"xmlns":963},[965,17854,17855,17867],{},[968,17856,17857,17863,17865],{},[3758,17858,17859,17861],{"accent":990},[974,17860,3189],{},[3191,17862,14087],{},[3191,17864,258],{},[978,17866,16931],{},[982,17868,17869],{"encoding":984},"\\bar{x} = 32",[86,17871,17873,17919],{"className":17872,"ariaHidden":990},[989],[86,17874,17876,17879,17910,17913,17916],{"className":17875},[994],[86,17877],{"className":17878,"style":14154},[998],[86,17880,17882],{"className":17881},[1003,3863],[86,17883,17885],{"className":17884},[1016],[86,17886,17888],{"className":17887},[1020],[86,17889,17891,17899],{"className":17890,"style":14154},[1024],[86,17892,17893,17896],{"style":3876},[86,17894],{"className":17895,"style":3850},[1031],[86,17897,3189],{"className":17898},[1003,1007],[86,17900,17901,17904],{"style":3876},[86,17902],{"className":17903,"style":3850},[1031],[86,17905,17907],{"className":17906,"style":14171},[3891],[86,17908,14087],{"className":17909},[1003],[86,17911],{"className":17912,"style":3222},[3221],[86,17914,258],{"className":17915},[3226],[86,17917],{"className":17918,"style":3222},[3221],[86,17920,17922,17925],{"className":17921},[994],[86,17923],{"className":17924,"style":5994},[998],[86,17926,16931],{"className":17927},[1003],[86,17929,17931,17948],{"className":17930},[955],[86,17932,17934],{"className":17933},[959],[961,17935,17936],{"xmlns":963},[965,17937,17938,17946],{},[968,17939,17940,17942,17944],{},[974,17941,14093],{},[3191,17943,258],{},[978,17945,14940],{},[982,17947,14943],{"encoding":984},[86,17949,17951,17969],{"className":17950,"ariaHidden":990},[989],[86,17952,17954,17957,17960,17963,17966],{"className":17953},[994],[86,17955],{"className":17956,"style":3575},[998],[86,17958,14093],{"className":17959,"style":3512},[1003,1007],[86,17961],{"className":17962,"style":3222},[3221],[86,17964,258],{"className":17965},[3226],[86,17967],{"className":17968,"style":3222},[3221],[86,17970,17972,17975],{"className":17971},[994],[86,17973],{"className":17974,"style":5994},[998],[86,17976,14940],{"className":17977},[1003],[86,17979,17981,17999],{"className":17980},[955],[86,17982,17984],{"className":17983},[959],[961,17985,17986],{"xmlns":963},[965,17987,17988,17996],{},[968,17989,17990,17992,17994],{},[974,17991,9839],{},[3191,17993,258],{},[978,17995,4114],{},[982,17997,17998],{"encoding":984},"\\sigma = 6",[86,18000,18002,18020],{"className":18001,"ariaHidden":990},[989],[86,18003,18005,18008,18011,18014,18017],{"className":18004},[994],[86,18006],{"className":18007,"style":7401},[998],[86,18009,9839],{"className":18010,"style":8109},[1003,1007],[86,18012],{"className":18013,"style":3222},[3221],[86,18015,258],{"className":18016},[3226],[86,18018],{"className":18019,"style":3222},[3221],[86,18021,18023,18026],{"className":18022},[994],[86,18024],{"className":18025,"style":5994},[998],[86,18027,4114],{"className":18028},[1003],[86,18030,18032,18049],{"className":18031},[955],[86,18033,18035],{"className":18034},[959],[961,18036,18037],{"xmlns":963},[965,18038,18039,18047],{},[968,18040,18041,18043,18045],{},[974,18042,6896],{},[3191,18044,258],{},[978,18046,16946],{},[982,18048,16199],{"encoding":984},[86,18050,18052,18070],{"className":18051,"ariaHidden":990},[989],[86,18053,18055,18058,18061,18064,18067],{"className":18054},[994],[86,18056],{"className":18057,"style":7401},[998],[86,18059,6896],{"className":18060},[1003,1007],[86,18062],{"className":18063,"style":3222},[3221],[86,18065,258],{"className":18066},[3226],[86,18068],{"className":18069,"style":3222},[3221],[86,18071,18073,18076],{"className":18072},[994],[86,18074],{"className":18075,"style":5994},[998],[86,18077,16946],{"className":18078},[1003],[86,18080,18082],{"className":18081},[3173],[86,18083,18085,18123],{"className":18084},[955],[86,18086,18088],{"className":18087},[959],[961,18089,18090],{"xmlns":963,"display":3182},[965,18091,18092,18120],{},[968,18093,18094,18096,18098,18100,18102,18104,18106],{},[974,18095,14076],{},[974,18097,1514],{},[3191,18099,258],{},[978,18101,16931],{},[3191,18103,14090],{},[978,18105,14940],{},[968,18107,18108,18110,18118],{},[3191,18109,243],{"fence":990},[3749,18111,18112,18114],{},[978,18113,4114],{},[9825,18115,18116],{},[978,18117,16946],{},[3191,18119,867],{"fence":990},[982,18121,18122],{"encoding":984},"IC = 32 \\pm 1.96 \\left(\\frac{6}{\\sqrt{36}}\\right)",[86,18124,18126,18147,18165],{"className":18125,"ariaHidden":990},[989],[86,18127,18129,18132,18135,18138,18141,18144],{"className":18128},[994],[86,18130],{"className":18131,"style":3575},[998],[86,18133,14076],{"className":18134,"style":4685},[1003,1007],[86,18136,1514],{"className":18137,"style":3512},[1003,1007],[86,18139],{"className":18140,"style":3222},[3221],[86,18142,258],{"className":18143},[3226],[86,18145],{"className":18146,"style":3222},[3221],[86,18148,18150,18153,18156,18159,18162],{"className":18149},[994],[86,18151],{"className":18152,"style":9303},[998],[86,18154,16931],{"className":18155},[1003],[86,18157],{"className":18158,"style":5012},[3221],[86,18160,14090],{"className":18161},[5016],[86,18163],{"className":18164,"style":5012},[3221],[86,18166,18168,18171,18174,18177],{"className":18167},[994],[86,18169],{"className":18170,"style":14190},[998],[86,18172,14940],{"className":18173},[1003],[86,18175],{"className":18176,"style":4162},[3221],[86,18178,18180,18186,18292],{"className":18179},[7131],[86,18181,18183],{"className":18182,"style":10228},[3320,10227],[86,18184,243],{"className":18185},[10232,1038],[86,18187,18189,18192,18289],{"className":18188},[1003],[86,18190],{"className":18191},[3320,3829],[86,18193,18195],{"className":18194},[3749],[86,18196,18198,18281],{"className":18197},[1016,3836],[86,18199,18201,18278],{"className":18200},[1020],[86,18202,18204,18259,18267],{"className":18203,"style":9568},[1024],[86,18205,18206,18209],{"style":15115},[86,18207],{"className":18208,"style":3850},[1031],[86,18210,18212],{"className":18211},[1003],[86,18213,18215],{"className":18214},[1003,10044],[86,18216,18218,18251],{"className":18217},[1016,3836],[86,18219,18221,18248],{"className":18220},[1020],[86,18222,18224,18236],{"className":18223,"style":15134},[1024],[86,18225,18227,18230],{"className":18226,"style":3876},[10058],[86,18228],{"className":18229,"style":3850},[1031],[86,18231,18233],{"className":18232,"style":13900},[1003],[86,18234,16946],{"className":18235},[1003],[86,18237,18238,18241],{"style":15149},[86,18239],{"className":18240,"style":3850},[1031],[86,18242,18244],{"className":18243,"style":13913},[10147],[10150,18245,18246],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,18247],{"d":13920},[86,18249,3963],{"className":18250},[3962],[86,18252,18254],{"className":18253},[1020],[86,18255,18257],{"className":18256,"style":15169},[1024],[86,18258],{},[86,18260,18261,18264],{"style":3901},[86,18262],{"className":18263,"style":3850},[1031],[86,18265],{"className":18266,"style":3909},[3908],[86,18268,18269,18272],{"style":3912},[86,18270],{"className":18271,"style":3850},[1031],[86,18273,18275],{"className":18274},[1003],[86,18276,4114],{"className":18277},[1003],[86,18279,3963],{"className":18280},[3962],[86,18282,18284],{"className":18283},[1020],[86,18285,18287],{"className":18286,"style":13961},[1024],[86,18288],{},[86,18290],{"className":18291},[3356,3829],[86,18293,18295],{"className":18294,"style":10228},[3356,10227],[86,18296,867],{"className":18297},[10232,1038],[86,18299,18301],{"className":18300},[3173],[86,18302,18304,18334],{"className":18303},[955],[86,18305,18307],{"className":18306},[959],[961,18308,18309],{"xmlns":963,"display":3182},[965,18310,18311,18331],{},[968,18312,18313,18315,18317,18319,18321,18323,18325,18327,18329],{},[974,18314,14076],{},[974,18316,1514],{},[3191,18318,258],{},[978,18320,16931],{},[3191,18322,14090],{},[978,18324,14940],{},[3191,18326,243],{"stretchy":3295},[978,18328,802],{},[3191,18330,867],{"stretchy":3295},[982,18332,18333],{"encoding":984},"IC = 32 \\pm 1.96 (1)",[86,18335,18337,18358,18376],{"className":18336,"ariaHidden":990},[989],[86,18338,18340,18343,18346,18349,18352,18355],{"className":18339},[994],[86,18341],{"className":18342,"style":3575},[998],[86,18344,14076],{"className":18345,"style":4685},[1003,1007],[86,18347,1514],{"className":18348,"style":3512},[1003,1007],[86,18350],{"className":18351,"style":3222},[3221],[86,18353,258],{"className":18354},[3226],[86,18356],{"className":18357,"style":3222},[3221],[86,18359,18361,18364,18367,18370,18373],{"className":18360},[994],[86,18362],{"className":18363,"style":9303},[998],[86,18365,16931],{"className":18366},[1003],[86,18368],{"className":18369,"style":5012},[3221],[86,18371,14090],{"className":18372},[5016],[86,18374],{"className":18375,"style":5012},[3221],[86,18377,18379,18382,18385,18388,18391],{"className":18378},[994],[86,18380],{"className":18381,"style":3794},[998],[86,18383,14940],{"className":18384},[1003],[86,18386,243],{"className":18387},[3320],[86,18389,802],{"className":18390},[1003],[86,18392,867],{"className":18393},[3356],[86,18395,18397],{"className":18396},[3173],[86,18398,18400,18430],{"className":18399},[955],[86,18401,18403],{"className":18402},[959],[961,18404,18405],{"xmlns":963,"display":3182},[965,18406,18407,18427],{},[968,18408,18409,18411,18413,18415,18417,18420,18422,18425],{},[974,18410,14076],{},[974,18412,1514],{},[3191,18414,258],{},[3191,18416,243],{"stretchy":3295},[978,18418,18419],{},"30.04",[3191,18421,291],{"separator":990},[978,18423,18424],{},"33.96",[3191,18426,867],{"stretchy":3295},[982,18428,18429],{"encoding":984},"IC = (30.04 , 33.96)",[86,18431,18433,18454],{"className":18432,"ariaHidden":990},[989],[86,18434,18436,18439,18442,18445,18448,18451],{"className":18435},[994],[86,18437],{"className":18438,"style":3575},[998],[86,18440,14076],{"className":18441,"style":4685},[1003,1007],[86,18443,1514],{"className":18444,"style":3512},[1003,1007],[86,18446],{"className":18447,"style":3222},[3221],[86,18449,258],{"className":18450},[3226],[86,18452],{"className":18453,"style":3222},[3221],[86,18455,18457,18460,18463,18466,18469,18472,18475],{"className":18456},[994],[86,18458],{"className":18459,"style":3794},[998],[86,18461,243],{"className":18462},[3320],[86,18464,18419],{"className":18465},[1003],[86,18467,291],{"className":18468},[4158],[86,18470],{"className":18471,"style":4162},[3221],[86,18473,18424],{"className":18474},[1003],[86,18476,867],{"className":18477},[3356],[12,18479,18480],{},[122,18481,18482],{},"El valor 30 NO está dentro del intervalo de confianza",[12,18484,18485],{},"Eso significa que, con un 95% de confianza, el verdadero promedio no es 30 minutos.",[12,18487,18488,18489,18558],{},"Rechazar ",[86,18490,18492,18509],{"className":18491},[955],[86,18493,18495],{"className":18494},[959],[961,18496,18497],{"xmlns":963},[965,18498,18499,18507],{},[968,18500,18501],{},[6849,18502,18503,18505],{},[974,18504,15522],{},[978,18506,2553],{},[982,18508,15527],{"encoding":984},[86,18510,18512],{"className":18511,"ariaHidden":990},[989],[86,18513,18515,18518],{"className":18514},[994],[86,18516],{"className":18517,"style":15537},[998],[86,18519,18521,18524],{"className":18520},[1003],[86,18522,15522],{"className":18523,"style":15544},[1003,1007],[86,18525,18527],{"className":18526},[1012],[86,18528,18530,18550],{"className":18529},[1016,3836],[86,18531,18533,18547],{"className":18532},[1020],[86,18534,18536],{"className":18535,"style":6984},[1024],[86,18537,18538,18541],{"style":15559},[86,18539],{"className":18540,"style":1032},[1031],[86,18542,18544],{"className":18543},[1036,1037,1038,1039],[86,18545,2553],{"className":18546},[1003,1039],[86,18548,3963],{"className":18549},[3962],[86,18551,18553],{"className":18552},[1020],[86,18554,18556],{"className":18555,"style":7006},[1024],[86,18557],{}," al 5% es exactamente equivalente a que el valor hipotético (30) quede fuera del intervalo de confianza del 95%.",[12,18560,18561],{},"Las pruebas bilaterales y los intervalos de confianza cuentan la misma historia, solo desde perspectivas diferentes.",[43,18563],{},[12,18565,18566],{},"Regresando a la conclusión anterior:",[12,18568,18569],{},[122,18570,18571],{},"No es lo mismo a decir: \"Es poco probable que el tiempo de entrega promedio sea de 30 minutos\"",[12,18573,18574],{},"La prueba clásica no cálcula:",[12,18576,18577,18690,18691,18760],{},[86,18578,18580,18617],{"className":18579},[955],[86,18581,18583],{"className":18582},[959],[961,18584,18585],{"xmlns":963},[965,18586,18587,18614],{},[968,18588,18589,18591,18593,18599,18601,18604,18606,18608,18610,18612],{},[974,18590,3738],{},[3191,18592,243],{"stretchy":3295},[6849,18594,18595,18597],{},[974,18596,15522],{},[978,18598,2553],{},[974,18600,4804],{"mathvariant":4327},[974,18602,18603],{},"d",[974,18605,22],{},[974,18607,6187],{},[974,18609,6018],{},[974,18611,7892],{},[3191,18613,867],{"stretchy":3295},[982,18615,18616],{"encoding":984},"P(H_0 | datos)",[86,18618,18620],{"className":18619,"ariaHidden":990},[989],[86,18621,18623,18626,18629,18632,18672,18675,18678,18681,18684,18687],{"className":18622},[994],[86,18624],{"className":18625,"style":3794},[998],[86,18627,3738],{"className":18628,"style":3537},[1003,1007],[86,18630,243],{"className":18631},[3320],[86,18633,18635,18638],{"className":18634},[1003],[86,18636,15522],{"className":18637,"style":15544},[1003,1007],[86,18639,18641],{"className":18640},[1012],[86,18642,18644,18664],{"className":18643},[1016,3836],[86,18645,18647,18661],{"className":18646},[1020],[86,18648,18650],{"className":18649,"style":6984},[1024],[86,18651,18652,18655],{"style":15559},[86,18653],{"className":18654,"style":1032},[1031],[86,18656,18658],{"className":18657},[1036,1037,1038,1039],[86,18659,2553],{"className":18660},[1003,1039],[86,18662,3963],{"className":18663},[3962],[86,18665,18667],{"className":18666},[1020],[86,18668,18670],{"className":18669,"style":7006},[1024],[86,18671],{},[86,18673,4804],{"className":18674},[1003],[86,18676,18603],{"className":18677},[1003,1007],[86,18679,22],{"className":18680},[1003,1007],[86,18682,6187],{"className":18683},[1003,1007],[86,18685,8096],{"className":18686},[1003,1007],[86,18688,867],{"className":18689},[3356]," - es decir,  la probabilidad de que ",[86,18692,18694,18711],{"className":18693},[955],[86,18695,18697],{"className":18696},[959],[961,18698,18699],{"xmlns":963},[965,18700,18701,18709],{},[968,18702,18703],{},[6849,18704,18705,18707],{},[974,18706,15522],{},[978,18708,2553],{},[982,18710,15527],{"encoding":984},[86,18712,18714],{"className":18713,"ariaHidden":990},[989],[86,18715,18717,18720],{"className":18716},[994],[86,18718],{"className":18719,"style":15537},[998],[86,18721,18723,18726],{"className":18722},[1003],[86,18724,15522],{"className":18725,"style":15544},[1003,1007],[86,18727,18729],{"className":18728},[1012],[86,18730,18732,18752],{"className":18731},[1016,3836],[86,18733,18735,18749],{"className":18734},[1020],[86,18736,18738],{"className":18737,"style":6984},[1024],[86,18739,18740,18743],{"style":15559},[86,18741],{"className":18742,"style":1032},[1031],[86,18744,18746],{"className":18745},[1036,1037,1038,1039],[86,18747,2553],{"className":18748},[1003,1039],[86,18750,3963],{"className":18751},[3962],[86,18753,18755],{"className":18754},[1020],[86,18756,18758],{"className":18757,"style":7006},[1024],[86,18759],{}," sea verdadera dado los datos que tenemos",[12,18762,18763],{},"Sino:",[12,18765,18766,18878,18879,18948],{},[86,18767,18769,18805],{"className":18768},[955],[86,18770,18772],{"className":18771},[959],[961,18773,18774],{"xmlns":963},[965,18775,18776,18802],{},[968,18777,18778,18780,18782,18784,18786,18788,18790,18792,18794,18800],{},[974,18779,3738],{},[3191,18781,243],{"stretchy":3295},[974,18783,18603],{},[974,18785,22],{},[974,18787,6187],{},[974,18789,6018],{},[974,18791,7892],{},[974,18793,4804],{"mathvariant":4327},[6849,18795,18796,18798],{},[974,18797,15522],{},[978,18799,2553],{},[3191,18801,867],{"stretchy":3295},[982,18803,18804],{"encoding":984},"P(datos|H_0)",[86,18806,18808],{"className":18807,"ariaHidden":990},[989],[86,18809,18811,18814,18817,18820,18823,18826,18829,18832,18835,18875],{"className":18810},[994],[86,18812],{"className":18813,"style":3794},[998],[86,18815,3738],{"className":18816,"style":3537},[1003,1007],[86,18818,243],{"className":18819},[3320],[86,18821,18603],{"className":18822},[1003,1007],[86,18824,22],{"className":18825},[1003,1007],[86,18827,6187],{"className":18828},[1003,1007],[86,18830,8096],{"className":18831},[1003,1007],[86,18833,4804],{"className":18834},[1003],[86,18836,18838,18841],{"className":18837},[1003],[86,18839,15522],{"className":18840,"style":15544},[1003,1007],[86,18842,18844],{"className":18843},[1012],[86,18845,18847,18867],{"className":18846},[1016,3836],[86,18848,18850,18864],{"className":18849},[1020],[86,18851,18853],{"className":18852,"style":6984},[1024],[86,18854,18855,18858],{"style":15559},[86,18856],{"className":18857,"style":1032},[1031],[86,18859,18861],{"className":18860},[1036,1037,1038,1039],[86,18862,2553],{"className":18863},[1003,1039],[86,18865,3963],{"className":18866},[3962],[86,18868,18870],{"className":18869},[1020],[86,18871,18873],{"className":18872,"style":7006},[1024],[86,18874],{},[86,18876,867],{"className":18877},[3356]," - la probabilidad de obtener los datos que tenemos (o más extremos) asumiendo que ",[86,18880,18882,18899],{"className":18881},[955],[86,18883,18885],{"className":18884},[959],[961,18886,18887],{"xmlns":963},[965,18888,18889,18897],{},[968,18890,18891],{},[6849,18892,18893,18895],{},[974,18894,15522],{},[978,18896,2553],{},[982,18898,15527],{"encoding":984},[86,18900,18902],{"className":18901,"ariaHidden":990},[989],[86,18903,18905,18908],{"className":18904},[994],[86,18906],{"className":18907,"style":15537},[998],[86,18909,18911,18914],{"className":18910},[1003],[86,18912,15522],{"className":18913,"style":15544},[1003,1007],[86,18915,18917],{"className":18916},[1012],[86,18918,18920,18940],{"className":18919},[1016,3836],[86,18921,18923,18937],{"className":18922},[1020],[86,18924,18926],{"className":18925,"style":6984},[1024],[86,18927,18928,18931],{"style":15559},[86,18929],{"className":18930,"style":1032},[1031],[86,18932,18934],{"className":18933},[1036,1037,1038,1039],[86,18935,2553],{"className":18936},[1003,1039],[86,18938,3963],{"className":18939},[3962],[86,18941,18943],{"className":18942},[1020],[86,18944,18946],{"className":18945,"style":7006},[1024],[86,18947],{}," es verdadera.",[12,18950,18951],{},"Y además es importante tener claros estos 3 puntos:",[30,18953,18954,19239,19315],{},[33,18955,18956,19098,19099,19168,19169,19238],{},[122,18957,18958,18959,19028,19029],{},"Que no rechazar ",[86,18960,18962,18979],{"className":18961},[955],[86,18963,18965],{"className":18964},[959],[961,18966,18967],{"xmlns":963},[965,18968,18969,18977],{},[968,18970,18971],{},[6849,18972,18973,18975],{},[974,18974,15522],{},[978,18976,2553],{},[982,18978,15527],{"encoding":984},[86,18980,18982],{"className":18981,"ariaHidden":990},[989],[86,18983,18985,18988],{"className":18984},[994],[86,18986],{"className":18987,"style":15537},[998],[86,18989,18991,18994],{"className":18990},[1003],[86,18992,15522],{"className":18993,"style":15544},[1003,1007],[86,18995,18997],{"className":18996},[1012],[86,18998,19000,19020],{"className":18999},[1016,3836],[86,19001,19003,19017],{"className":19002},[1020],[86,19004,19006],{"className":19005,"style":6984},[1024],[86,19007,19008,19011],{"style":15559},[86,19009],{"className":19010,"style":1032},[1031],[86,19012,19014],{"className":19013},[1036,1037,1038,1039],[86,19015,2553],{"className":19016},[1003,1039],[86,19018,3963],{"className":19019},[3962],[86,19021,19023],{"className":19022},[1020],[86,19024,19026],{"className":19025,"style":7006},[1024],[86,19027],{}," no es lo mismo que aceptar ",[86,19030,19032,19049],{"className":19031},[955],[86,19033,19035],{"className":19034},[959],[961,19036,19037],{"xmlns":963},[965,19038,19039,19047],{},[968,19040,19041],{},[6849,19042,19043,19045],{},[974,19044,15522],{},[978,19046,2553],{},[982,19048,15527],{"encoding":984},[86,19050,19052],{"className":19051,"ariaHidden":990},[989],[86,19053,19055,19058],{"className":19054},[994],[86,19056],{"className":19057,"style":15537},[998],[86,19059,19061,19064],{"className":19060},[1003],[86,19062,15522],{"className":19063,"style":15544},[1003,1007],[86,19065,19067],{"className":19066},[1012],[86,19068,19070,19090],{"className":19069},[1016,3836],[86,19071,19073,19087],{"className":19072},[1020],[86,19074,19076],{"className":19075,"style":6984},[1024],[86,19077,19078,19081],{"style":15559},[86,19079],{"className":19080,"style":1032},[1031],[86,19082,19084],{"className":19083},[1036,1037,1038,1039],[86,19085,2553],{"className":19086},[1003,1039],[86,19088,3963],{"className":19089},[3962],[86,19091,19093],{"className":19092},[1020],[86,19094,19096],{"className":19095,"style":7006},[1024],[86,19097],{},". Si el valor p hubiera sido mayor que 0.05, simplemente no tendríamos suficiente evidencia para rechazar ",[86,19100,19102,19119],{"className":19101},[955],[86,19103,19105],{"className":19104},[959],[961,19106,19107],{"xmlns":963},[965,19108,19109,19117],{},[968,19110,19111],{},[6849,19112,19113,19115],{},[974,19114,15522],{},[978,19116,2553],{},[982,19118,15527],{"encoding":984},[86,19120,19122],{"className":19121,"ariaHidden":990},[989],[86,19123,19125,19128],{"className":19124},[994],[86,19126],{"className":19127,"style":15537},[998],[86,19129,19131,19134],{"className":19130},[1003],[86,19132,15522],{"className":19133,"style":15544},[1003,1007],[86,19135,19137],{"className":19136},[1012],[86,19138,19140,19160],{"className":19139},[1016,3836],[86,19141,19143,19157],{"className":19142},[1020],[86,19144,19146],{"className":19145,"style":6984},[1024],[86,19147,19148,19151],{"style":15559},[86,19149],{"className":19150,"style":1032},[1031],[86,19152,19154],{"className":19153},[1036,1037,1038,1039],[86,19155,2553],{"className":19156},[1003,1039],[86,19158,3963],{"className":19159},[3962],[86,19161,19163],{"className":19162},[1020],[86,19164,19166],{"className":19165,"style":7006},[1024],[86,19167],{},", pero eso no significa que ",[86,19170,19172,19189],{"className":19171},[955],[86,19173,19175],{"className":19174},[959],[961,19176,19177],{"xmlns":963},[965,19178,19179,19187],{},[968,19180,19181],{},[6849,19182,19183,19185],{},[974,19184,15522],{},[978,19186,2553],{},[982,19188,15527],{"encoding":984},[86,19190,19192],{"className":19191,"ariaHidden":990},[989],[86,19193,19195,19198],{"className":19194},[994],[86,19196],{"className":19197,"style":15537},[998],[86,19199,19201,19204],{"className":19200},[1003],[86,19202,15522],{"className":19203,"style":15544},[1003,1007],[86,19205,19207],{"className":19206},[1012],[86,19208,19210,19230],{"className":19209},[1016,3836],[86,19211,19213,19227],{"className":19212},[1020],[86,19214,19216],{"className":19215,"style":6984},[1024],[86,19217,19218,19221],{"style":15559},[86,19219],{"className":19220,"style":1032},[1031],[86,19222,19224],{"className":19223},[1036,1037,1038,1039],[86,19225,2553],{"className":19226},[1003,1039],[86,19228,3963],{"className":19229},[3962],[86,19231,19233],{"className":19232},[1020],[86,19234,19236],{"className":19235,"style":7006},[1024],[86,19237],{}," sea verdadera, sino que los datos no nos permiten concluir que es falsa. Recordemos que estamos trabajando con una muestra.",[33,19240,19241,19244,19245,19314],{},[122,19242,19243],{},"Que no existe certeza absoluta",". En este caso existe una probabilidad del 4.55% de cometer un error tipo I (rechazar ",[86,19246,19248,19265],{"className":19247},[955],[86,19249,19251],{"className":19250},[959],[961,19252,19253],{"xmlns":963},[965,19254,19255,19263],{},[968,19256,19257],{},[6849,19258,19259,19261],{},[974,19260,15522],{},[978,19262,2553],{},[982,19264,15527],{"encoding":984},[86,19266,19268],{"className":19267,"ariaHidden":990},[989],[86,19269,19271,19274],{"className":19270},[994],[86,19272],{"className":19273,"style":15537},[998],[86,19275,19277,19280],{"className":19276},[1003],[86,19278,15522],{"className":19279,"style":15544},[1003,1007],[86,19281,19283],{"className":19282},[1012],[86,19284,19286,19306],{"className":19285},[1016,3836],[86,19287,19289,19303],{"className":19288},[1020],[86,19290,19292],{"className":19291,"style":6984},[1024],[86,19293,19294,19297],{"style":15559},[86,19295],{"className":19296,"style":1032},[1031],[86,19298,19300],{"className":19299},[1036,1037,1038,1039],[86,19301,2553],{"className":19302},[1003,1039],[86,19304,3963],{"className":19305},[3962],[86,19307,19309],{"className":19308},[1020],[86,19310,19312],{"className":19311,"style":7006},[1024],[86,19313],{}," cuando es verdadera).",[33,19316,19317,19318,19321],{},"Y además existe la posibilidad de que la ",[122,19319,19320],{},"diferencia sea estadísticamente significativa pero no tenga relevancia práctica"," (es decir, que la diferencia de 2 minutos no sea importante en la realidad).",[12,19323,19324,19325,19411,19412,61],{},"Algo interesante que también podemos analizar es el tamaño del efecto. La diferencia que tenemos es de 2 minutos, pero el error estándar es de 1 minuto (es la parte de ",[86,19326,19328,19348],{"className":19327},[955],[86,19329,19331],{"className":19330},[959],[961,19332,19333],{"xmlns":963},[965,19334,19335,19345],{},[968,19336,19337,19339,19341],{},[974,19338,9839],{},[974,19340,16555],{"mathvariant":4327},[9825,19342,19343],{},[974,19344,6896],{},[982,19346,19347],{"encoding":984},"\\sigma\u002F\\sqrt{n}",[86,19349,19351],{"className":19350,"ariaHidden":990},[989],[86,19352,19354,19358,19361,19364],{"className":19353},[994],[86,19355],{"className":19356,"style":19357},[998],"height:1.0503em;vertical-align:-0.25em;",[86,19359,9839],{"className":19360,"style":8109},[1003,1007],[86,19362,16555],{"className":19363},[1003],[86,19365,19367],{"className":19366},[1003,10044],[86,19368,19370,19403],{"className":19369},[1016,3836],[86,19371,19373,19400],{"className":19372},[1020],[86,19374,19376,19388],{"className":19375,"style":13890},[1024],[86,19377,19379,19382],{"className":19378,"style":3876},[10058],[86,19380],{"className":19381,"style":3850},[1031],[86,19383,19385],{"className":19384,"style":13900},[1003],[86,19386,6896],{"className":19387},[1003,1007],[86,19389,19390,19393],{"style":13906},[86,19391],{"className":19392,"style":3850},[1031],[86,19394,19396],{"className":19395,"style":13913},[10147],[10150,19397,19398],{"xmlns":10152,"width":10153,"height":13916,"viewBox":13917,"preserveAspectRatio":10156},[246,19399],{"d":13920},[86,19401,3963],{"className":19402},[3962],[86,19404,19406],{"className":19405},[1020],[86,19407,19409],{"className":19408,"style":13930},[1024],[86,19410],{}," del cálculo de Z). Esto hace que la diferencia sea \"grande\" en términos estadísticos, pero si la muestra hubiera sido de solo 9 personas, el error estándar sería de 2 minutos, y el Z sería de 1, lo que no nos daría suficiente evidencia para rechazar ",[86,19413,19415,19432],{"className":19414},[955],[86,19416,19418],{"className":19417},[959],[961,19419,19420],{"xmlns":963},[965,19421,19422,19430],{},[968,19423,19424],{},[6849,19425,19426,19428],{},[974,19427,15522],{},[978,19429,2553],{},[982,19431,15527],{"encoding":984},[86,19433,19435],{"className":19434,"ariaHidden":990},[989],[86,19436,19438,19441],{"className":19437},[994],[86,19439],{"className":19440,"style":15537},[998],[86,19442,19444,19447],{"className":19443},[1003],[86,19445,15522],{"className":19446,"style":15544},[1003,1007],[86,19448,19450],{"className":19449},[1012],[86,19451,19453,19473],{"className":19452},[1016,3836],[86,19454,19456,19470],{"className":19455},[1020],[86,19457,19459],{"className":19458,"style":6984},[1024],[86,19460,19461,19464],{"style":15559},[86,19462],{"className":19463,"style":1032},[1031],[86,19465,19467],{"className":19466},[1036,1037,1038,1039],[86,19468,2553],{"className":19469},[1003,1039],[86,19471,3963],{"className":19472},[3962],[86,19474,19476],{"className":19475},[1020],[86,19477,19479],{"className":19478,"style":7006},[1024],[86,19480],{},[16,19482,19483],{},[12,19484,19485],{},"La significancia depende del tamaño de muestra. Una diferencia pequeña puede ser significativa si la muestra es grande.",[323,19487,19489],{"id":19488},"sobre-los-tipos-de-errores","Sobre los tipos de errores",[30,19491,19492,19568],{},[33,19493,19494,19497,19498,19567],{},[122,19495,19496],{},"Error tipo I (falso positivo)"," Rechazar ",[86,19499,19501,19518],{"className":19500},[955],[86,19502,19504],{"className":19503},[959],[961,19505,19506],{"xmlns":963},[965,19507,19508,19516],{},[968,19509,19510],{},[6849,19511,19512,19514],{},[974,19513,15522],{},[978,19515,2553],{},[982,19517,15527],{"encoding":984},[86,19519,19521],{"className":19520,"ariaHidden":990},[989],[86,19522,19524,19527],{"className":19523},[994],[86,19525],{"className":19526,"style":15537},[998],[86,19528,19530,19533],{"className":19529},[1003],[86,19531,15522],{"className":19532,"style":15544},[1003,1007],[86,19534,19536],{"className":19535},[1012],[86,19537,19539,19559],{"className":19538},[1016,3836],[86,19540,19542,19556],{"className":19541},[1020],[86,19543,19545],{"className":19544,"style":6984},[1024],[86,19546,19547,19550],{"style":15559},[86,19548],{"className":19549,"style":1032},[1031],[86,19551,19553],{"className":19552},[1036,1037,1038,1039],[86,19554,2553],{"className":19555},[1003,1039],[86,19557,3963],{"className":19558},[3962],[86,19560,19562],{"className":19561},[1020],[86,19563,19565],{"className":19564,"style":7006},[1024],[86,19566],{}," cuando es verdadera. Por ejemplo, concluir que el tiempo de entrega es diferente a 30 minutos cuando en realidad sí lo es.",[33,19569,19570,19573,19574,19643],{},[122,19571,19572],{},"Error tipo II (falso negativo)"," No rechazar ",[86,19575,19577,19594],{"className":19576},[955],[86,19578,19580],{"className":19579},[959],[961,19581,19582],{"xmlns":963},[965,19583,19584,19592],{},[968,19585,19586],{},[6849,19587,19588,19590],{},[974,19589,15522],{},[978,19591,2553],{},[982,19593,15527],{"encoding":984},[86,19595,19597],{"className":19596,"ariaHidden":990},[989],[86,19598,19600,19603],{"className":19599},[994],[86,19601],{"className":19602,"style":15537},[998],[86,19604,19606,19609],{"className":19605},[1003],[86,19607,15522],{"className":19608,"style":15544},[1003,1007],[86,19610,19612],{"className":19611},[1012],[86,19613,19615,19635],{"className":19614},[1016,3836],[86,19616,19618,19632],{"className":19617},[1020],[86,19619,19621],{"className":19620,"style":6984},[1024],[86,19622,19623,19626],{"style":15559},[86,19624],{"className":19625,"style":1032},[1031],[86,19627,19629],{"className":19628},[1036,1037,1038,1039],[86,19630,2553],{"className":19631},[1003,1039],[86,19633,3963],{"className":19634},[3962],[86,19636,19638],{"className":19637},[1020],[86,19639,19641],{"className":19640,"style":7006},[1024],[86,19642],{}," cuando es falsa. Por ejemplo, concluir que el tiempo de entrega es igual a 30 minutos cuando en realidad es diferente.",[46,19645,19647],{"id":19646},"importancia-en-el-aprendizaje-automático","Importancia en el aprendizaje automático",[12,19649,19650,19651,19654],{},"En aprendizaje automático no es suficiente con comparar métricas y elegir el modelo que tenga el valor más alto. Las métricas que obtenemos (accuracy, precisión, recall, AUC, etc.) son ",[122,19652,19653],{},"estimaciones muestrales"," del rendimiento real del modelo.",[12,19656,19657],{},"Es decir:",[30,19659,19660,19666,19672],{},[33,19661,19662,19663,61],{},"El dataset que usamos es una ",[122,19664,19665],{},"muestra del mundo real",[33,19667,19668,19669,61],{},"La métrica calculada es un ",[122,19670,19671],{},"estadístico",[33,19673,19674,19675,61],{},"El rendimiento real en producción es un ",[122,19676,19677],{},"parámetro poblacional desconocido",[12,19679,19680,19681,19684],{},"Entonces, toda comparación entre modelos está sujeta a ",[122,19682,19683],{},"variabilidad muestral",". Si tomáramos otra muestra distinta del mismo problema, las métricas cambiarían.",[12,19686,19687],{},"Aquí aparece exactamente el mismo problema que vimos antes:",[16,19689,19690],{},[12,19691,19692],{},"¿La diferencia observada es real o puede explicarse por azar?",[12,19694,19695],{},"Supongamos que comparamos dos modelos de clasificación binaria sobre un conjunto de prueba de 1000 observaciones:",[30,19697,19698,19701],{},[33,19699,19700],{},"Modelo A: accuracy = 0.85",[33,19702,19703],{},"Modelo B: accuracy = 0.80",[12,19705,19706],{},"La diferencia es del 5%, pero ¿es esa diferencia estadísticamente significativa? ¿Realmente el modelo A es mejor que el modelo B, o esa diferencia podría ser producto del azar?",[12,19708,19709],{},"Podríamos por ejemplo construir un intervalo de confianza para el accuracy que nos permita estimar un rango plausible para el rendimiento real del modelo.",[12,19711,19712],{},"Otro caso sería comparar dos modelos sobre el mismo conjunto de prueba (como comúnmente se hace), lo que introduce dependencia entre las observaciones, que es importante tenerlo en cuenta porque:",[30,19714,19715,19718],{},[33,19716,19717],{},"No podemos usar pruebas para muestras independientes.",[33,19719,19720],{},"Necesitamos pruebas para datos pareados.",[12,19722,19723],{},"Algunas herramientas comunes son:",[30,19725,19726,19732,19738],{},[33,19727,19728,19731],{},[122,19729,19730],{},"Prueba de McNemar",": para comparar accuracy en clasificación binaria.",[33,19733,19734,19737],{},[122,19735,19736],{},"t-test pareado",": cuando usamos validación cruzada y obtenemos múltiples mediciones.",[33,19739,19740,19743],{},[122,19741,19742],{},"Bootstrap",": para estimar la distribución empírica de la diferencia entre modelos.",[43,19745],{},[2218,19747,19748],{},"html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}html pre.shiki code .scnC2, html code.shiki .scnC2{--shiki-default:#B5695977;--shiki-dark:#C98A7D77}html pre.shiki code .spP0B, html code.shiki .spP0B{--shiki-default:#B56959;--shiki-dark:#C98A7D}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html pre.shiki code .s5TCs, html code.shiki .s5TCs{--shiki-default:#AB5959;--shiki-dark:#CB7676}html pre.shiki code .sfsYZ, html code.shiki .sfsYZ{--shiki-default:#A65E2B;--shiki-dark:#C99076}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":169,"searchDepth":205,"depth":205,"links":19750},[19751,19757,19762],{"id":12757,"depth":192,"text":12758,"children":19752},[19753,19754,19755,19756],{"id":12815,"depth":205,"text":12816},{"id":12864,"depth":205,"text":12865},{"id":12886,"depth":205,"text":12887},{"id":12933,"depth":205,"text":12934},{"id":13721,"depth":192,"text":13722,"children":19758},[19759,19760,19761],{"id":14043,"depth":205,"text":14044},{"id":15485,"depth":205,"text":15486},{"id":19488,"depth":205,"text":19489},{"id":19646,"depth":192,"text":19647},"2026-05-06","Ya hemos explorado el flujo de trabajo de un proyecto de aprendizaje automático, y hemos experimentado con el análisis exploratorio de datos (EDA) y la ingeniería de características (FE), ahora profundizaremos un poco más en algunos conceptos estadísticos que son fundamentales, y veremos qué deberíamos tener en cuenta al analizar nuestros datos con el fin de asegurar que nuestros modelos tengan el mejor desempeño posible.","\u002Fblog\u002Fstatistics-and-machine-learning\u002Fshared\u002Fstatistics-machine-learning.webp",{},"\u002Fblog\u002Fblog\u002Fstatistics-and-machine-learning",{"title":3649,"description":19764},{"loc":19770,"priority":2259,"lastmod":19763},"\u002Fes\u002Fblog\u002Fstatistics-and-machine-learning","statistics-and-machine-learning","blog\u002Fblog\u002Fstatistics-and-machine-learning","La estadística nos permite analizar y entender los datos. En este artículo, exploraremos un poco más sobre la estadística descriptiva e inferencial, y cómo estos conceptos son fundamentales para el aprendizaje automático.",[3625,19775,3675,2264,3676],"estadística","wXOQa-MSGLEUwr_Dviw8a8M6lATLKukxvtk8BjVqFGk",{"id":19778,"title":12750,"author":7,"body":19779,"date":32998,"description":19783,"extension":2250,"image":32999,"lastmod":32998,"meta":33000,"navigation":208,"order":252,"path":33001,"seo":33002,"sitemap":33003,"slug":33005,"stem":33006,"summary":33007,"tags":33008,"__hash__":33013},"content_es\u002Fblog\u002Fblog\u002Fvectors-matrices-machine-learning.md",{"type":9,"value":19780,"toc":32990},[19781,19784,19792,19794,19796,19800,19803,19832,19835,19873,19876,20330,20333,20337,20340,20556,20562,20565,20579,20582,20590,21017,21025,21408,21416,21729,21737,21929,21937,22240,22244,22247,22662,22674,22677,22685,24321,24329,28079,28087,29114,29122,29238,29246,29342,29350,30616,30619,30742,30754,30757,30760,30792,30797,31111,31117,31261,31269,31763,31906,31909,32761,32767,32806,32809,32813,32816,32834,32837,32970,32974,32982,32984,32987],[12,19782,19783],{},"En el artículo anterior de esta serie seguíamos experimentando con el flujo en proyectos de aprendizaje automático. Haremos una pausa para hablar sobre un tema fundamental: los vectores y matrices. Estos conceptos son esenciales para entender cómo se representan los datos y cómo funcionan los algoritmos de machine learning.",[12,19785,19786,19787],{},"Artículo anterior: ",[22,19788,19791],{"href":19789,"rel":19790},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fexperimenting-with-titanic-dataset",[26],"Experimentando con el dataset de supervivencia del Titanic",[40,19793],{},[43,19795],{},[46,19797,19799],{"id":19798},"representación-de-datos-en-machine-learning","Representación de Datos en Machine Learning",[12,19801,19802],{},"¿Cómo interpretar los datos una computadora?\nLos algoritmos de aprendizaje automático procesan información en forma de números. Para representar y procesar datos de manera eficiente, utilizamos estructuras matemáticas como vectores y matrices, básicamente se usan conceptos fundamentales para trabajar con datos en machine learning:",[30,19804,19805,19815,19821,19827],{},[33,19806,19807,19810,19811,19814],{},[122,19808,19809],{},"Vectores",": Un vector es una lista ordenada de números que representa una sola instancia de datos. Por ejemplo, si tenemos un conjunto de datos con características como altura, peso y edad, cada instancia de datos se puede representar como un vector. Por ejemplo, un vector podría ser ",[145,19812,19813],{},"[170, 65, 30]",", donde cada número representa una característica específica.",[33,19816,19817,19820],{},[122,19818,19819],{},"Matrices",": Una matriz es una colección de vectores organizados en filas y columnas. En el contexto del aprendizaje automático, una matriz se utiliza para representar un conjunto de datos completo. Por ejemplo, si tenemos 100 instancias de datos con 3 características cada una, podríamos representar este conjunto de datos como una matriz de 100 filas y 3 columnas.",[33,19822,19823,19826],{},[122,19824,19825],{},"Tensores",": Un tensor es una generalización de vectores y matrices a dimensiones superiores. En el aprendizaje automático, especialmente en redes neuronales, los tensores se utilizan para representar datos con múltiples dimensiones, como imágenes (que pueden tener dimensiones de altura, ancho y canales de color) o secuencias de texto (que pueden tener dimensiones de longitud y características).",[33,19828,19829,19831],{},[122,19830,7810],{},": Se realizan diversas operaciones con vectores y matrices, como la multiplicación de matrices, la transposición, la inversa y la descomposición. Estas operaciones son fundamentales para el entrenamiento de modelos, la optimización de parámetros y la realización de predicciones.",[12,19833,19834],{},"Los algoritmos convierten tablas en estructuras matemáticas para procesar la información. Por ejemplo:",[461,19836,19837,19850],{},[464,19838,19839],{},[467,19840,19841,19844,19847],{},[470,19842,19843],{},"Altura",[470,19845,19846],{},"Peso",[470,19848,19849],{},"Edad",[480,19851,19852,19862],{},[467,19853,19854,19857,19860],{},[485,19855,19856],{},"170",[485,19858,19859],{},"65",[485,19861,16271],{},[467,19863,19864,19867,19870],{},[485,19865,19866],{},"182",[485,19868,19869],{},"75",[485,19871,19872],{},"25",[12,19874,19875],{},"Se convierte en una matriz:",[86,19877,19879],{"className":19878},[3173],[86,19880,19882,19997],{"className":19881},[955],[86,19883,19885],{"className":19884},[959],[961,19886,19887],{"xmlns":963,"display":3182},[965,19888,19889,19994],{},[968,19890,19891,19894,19896],{},[974,19892,4624],{"mathvariant":19893},"bold",[3191,19895,258],{},[968,19897,19898,19900,19992],{},[3191,19899,572],{"fence":990},[19901,19902,19906,19929,19949],"mtable",{"rowspacing":19903,"columnalign":19904,"columnspacing":19905},"0.16em","center center center","1em",[19907,19908,19909,19917,19923],"mtr",{},[19910,19911,19912],"mtd",{},[19913,19914,19915],"mstyle",{"scriptlevel":2553,"displaystyle":3295},[978,19916,19856],{},[19910,19918,19919],{},[19913,19920,19921],{"scriptlevel":2553,"displaystyle":3295},[978,19922,19859],{},[19910,19924,19925],{},[19913,19926,19927],{"scriptlevel":2553,"displaystyle":3295},[978,19928,16271],{},[19907,19930,19931,19937,19943],{},[19910,19932,19933],{},[19913,19934,19935],{"scriptlevel":2553,"displaystyle":3295},[978,19936,19866],{},[19910,19938,19939],{},[19913,19940,19941],{"scriptlevel":2553,"displaystyle":3295},[978,19942,19869],{},[19910,19944,19945],{},[19913,19946,19947],{"scriptlevel":2553,"displaystyle":3295},[978,19948,19872],{},[19907,19950,19951,19968,19980],{},[19910,19952,19953],{},[19913,19954,19955],{"scriptlevel":2553,"displaystyle":3295},[968,19956,19957,19960],{},[974,19958,19959],{"mathvariant":4327},"⋮",[19961,19962,19964],"mpadded",{"height":19963,"voffset":19963},"0em",[3221,19965],{"mathbackground":19966,"width":19963,"height":19967},"black","1.5em",[19910,19969,19970],{},[19913,19971,19972],{"scriptlevel":2553,"displaystyle":3295},[968,19973,19974,19976],{},[974,19975,19959],{"mathvariant":4327},[19961,19977,19978],{"height":19963,"voffset":19963},[3221,19979],{"mathbackground":19966,"width":19963,"height":19967},[19910,19981,19982],{},[19913,19983,19984],{"scriptlevel":2553,"displaystyle":3295},[968,19985,19986,19988],{},[974,19987,19959],{"mathvariant":4327},[19961,19989,19990],{"height":19963,"voffset":19963},[3221,19991],{"mathbackground":19966,"width":19963,"height":19967},[3191,19993,585],{"fence":990},[982,19995,19996],{"encoding":984},"\\mathbf{X} =\n\\begin{bmatrix}\n170 & 65 & 30 \\\\\n182 & 75 & 25 \\\\\n\\vdots & \\vdots & \\vdots \\\\\n\\end{bmatrix}",[86,19998,20000,20020],{"className":19999,"ariaHidden":990},[989],[86,20001,20003,20007,20011,20014,20017],{"className":20002},[994],[86,20004],{"className":20005,"style":20006},[998],"height:0.6861em;",[86,20008,4624],{"className":20009},[1003,20010],"mathbf",[86,20012],{"className":20013,"style":3222},[3221],[86,20015,258],{"className":20016},[3226],[86,20018],{"className":20019,"style":3222},[3221],[86,20021,20023,20027],{"className":20022},[994],[86,20024],{"className":20025,"style":20026},[998],"height:4.26em;vertical-align:-1.88em;",[86,20028,20030,20077,20292],{"className":20029},[7131],[86,20031,20033],{"className":20032},[3320],[86,20034,20037],{"className":20035},[10232,20036],"mult",[86,20038,20040,20068],{"className":20039},[1016,3836],[86,20041,20043,20065],{"className":20042},[1020],[86,20044,20047],{"className":20045,"style":20046},[1024],"height:2.35em;",[86,20048,20050,20054],{"style":20049},"top:-4.35em;",[86,20051],{"className":20052,"style":20053},[1031],"height:6.2em;",[86,20055,20057],{"style":20056},"width:0.667em;height:4.2em;",[10150,20058,20062],{"xmlns":10152,"width":20059,"height":20060,"viewBox":20061},"0.667em","4.2em","0 0 667 4200",[246,20063],{"d":20064},"M403 1759 V84 H666 V0 H319 V1759 v600 v1759 h347 v-84\nH403z M403 1759 V0 H319 V1759 v600 v1759 h84z",[86,20066,3963],{"className":20067},[3962],[86,20069,20071],{"className":20070},[1020],[86,20072,20075],{"className":20073,"style":20074},[1024],"height:1.85em;",[86,20076],{},[86,20078,20080],{"className":20079},[1003],[86,20081,20083,20154,20159,20162,20224,20227,20230],{"className":20082},[19901],[86,20084,20087],{"className":20085},[20086],"col-align-c",[86,20088,20090,20145],{"className":20089},[1016,3836],[86,20091,20093,20142],{"className":20092},[1020],[86,20094,20097,20110,20122],{"className":20095,"style":20096},[1024],"height:2.38em;",[86,20098,20100,20104],{"style":20099},"top:-5.2275em;",[86,20101],{"className":20102,"style":20103},[1031],"height:3.6875em;",[86,20105,20107],{"className":20106},[1003],[86,20108,19856],{"className":20109},[1003],[86,20111,20113,20116],{"style":20112},"top:-4.0275em;",[86,20114],{"className":20115,"style":20103},[1031],[86,20117,20119],{"className":20118},[1003],[86,20120,19866],{"className":20121},[1003],[86,20123,20125,20128],{"style":20124},"top:-2.1675em;",[86,20126],{"className":20127,"style":20103},[1031],[86,20129,20131],{"className":20130},[1003],[86,20132,20134,20137],{"className":20133},[1003],[86,20135,19959],{"className":20136},[1003],[86,20138],{"className":20139,"style":20141},[1003,20140],"rule","border-right-width:0em;border-top-width:1.5em;bottom:0em;",[86,20143,3963],{"className":20144},[3962],[86,20146,20148],{"className":20147},[1020],[86,20149,20152],{"className":20150,"style":20151},[1024],"height:1.88em;",[86,20153],{},[86,20155],{"className":20156,"style":20158},[20157],"arraycolsep","width:0.5em;",[86,20160],{"className":20161,"style":20158},[20157],[86,20163,20165],{"className":20164},[20086],[86,20166,20168,20216],{"className":20167},[1016,3836],[86,20169,20171,20213],{"className":20170},[1020],[86,20172,20174,20185,20196],{"className":20173,"style":20096},[1024],[86,20175,20176,20179],{"style":20099},[86,20177],{"className":20178,"style":20103},[1031],[86,20180,20182],{"className":20181},[1003],[86,20183,19859],{"className":20184},[1003],[86,20186,20187,20190],{"style":20112},[86,20188],{"className":20189,"style":20103},[1031],[86,20191,20193],{"className":20192},[1003],[86,20194,19869],{"className":20195},[1003],[86,20197,20198,20201],{"style":20124},[86,20199],{"className":20200,"style":20103},[1031],[86,20202,20204],{"className":20203},[1003],[86,20205,20207,20210],{"className":20206},[1003],[86,20208,19959],{"className":20209},[1003],[86,20211],{"className":20212,"style":20141},[1003,20140],[86,20214,3963],{"className":20215},[3962],[86,20217,20219],{"className":20218},[1020],[86,20220,20222],{"className":20221,"style":20151},[1024],[86,20223],{},[86,20225],{"className":20226,"style":20158},[20157],[86,20228],{"className":20229,"style":20158},[20157],[86,20231,20233],{"className":20232},[20086],[86,20234,20236,20284],{"className":20235},[1016,3836],[86,20237,20239,20281],{"className":20238},[1020],[86,20240,20242,20253,20264],{"className":20241,"style":20096},[1024],[86,20243,20244,20247],{"style":20099},[86,20245],{"className":20246,"style":20103},[1031],[86,20248,20250],{"className":20249},[1003],[86,20251,16271],{"className":20252},[1003],[86,20254,20255,20258],{"style":20112},[86,20256],{"className":20257,"style":20103},[1031],[86,20259,20261],{"className":20260},[1003],[86,20262,19872],{"className":20263},[1003],[86,20265,20266,20269],{"style":20124},[86,20267],{"className":20268,"style":20103},[1031],[86,20270,20272],{"className":20271},[1003],[86,20273,20275,20278],{"className":20274},[1003],[86,20276,19959],{"className":20277},[1003],[86,20279],{"className":20280,"style":20141},[1003,20140],[86,20282,3963],{"className":20283},[3962],[86,20285,20287],{"className":20286},[1020],[86,20288,20290],{"className":20289,"style":20151},[1024],[86,20291],{},[86,20293,20295],{"className":20294},[3356],[86,20296,20298],{"className":20297},[10232,20036],[86,20299,20301,20322],{"className":20300},[1016,3836],[86,20302,20304,20319],{"className":20303},[1020],[86,20305,20307],{"className":20306,"style":20046},[1024],[86,20308,20309,20312],{"style":20049},[86,20310],{"className":20311,"style":20053},[1031],[86,20313,20314],{"style":20056},[10150,20315,20316],{"xmlns":10152,"width":20059,"height":20060,"viewBox":20061},[246,20317],{"d":20318},"M347 1759 V0 H0 V84 H263 V1759 v600 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v600 v1759 h84z",[86,20320,3963],{"className":20321},[3962],[86,20323,20325],{"className":20324},[1020],[86,20326,20328],{"className":20327,"style":20074},[1024],[86,20329],{},[12,20331,20332],{},"En esta matriz, cada fila representa una instancia de datos (una persona) y cada columna representa una característica (altura, peso, edad).",[323,20334,20336],{"id":20335},"vector","Vector",[12,20338,20339],{},"Un vector es una lista ordenada de números que representa una sola instancia de datos, esta puede ser cualquier serie de valores organizados en una sola dimensión (fila o columna). Por ejemplo, si tenemos un conjunto de datos con características como altura, peso y edad, cada instancia de datos se puede representar como un vector.",[86,20341,20343],{"className":20342},[3173],[86,20344,20346,20388],{"className":20345},[955],[86,20347,20349],{"className":20348},[959],[961,20350,20351],{"xmlns":963,"display":3182},[965,20352,20353,20385],{},[968,20354,20355,20357,20359,20361,20367,20369,20375,20377,20383],{},[974,20356,7912],{"mathvariant":19893},[3191,20358,258],{},[3191,20360,572],{"stretchy":3295},[6849,20362,20363,20365],{},[974,20364,7912],{},[978,20366,802],{},[3191,20368,291],{"separator":990},[6849,20370,20371,20373],{},[974,20372,7912],{},[978,20374,980],{},[3191,20376,291],{"separator":990},[6849,20378,20379,20381],{},[974,20380,7912],{},[978,20382,4100],{},[3191,20384,585],{"stretchy":3295},[982,20386,20387],{"encoding":984},"\\mathbf{v} = [v_1, v_2, v_3]",[86,20389,20391,20411],{"className":20390,"ariaHidden":990},[989],[86,20392,20394,20398,20402,20405,20408],{"className":20393},[994],[86,20395],{"className":20396,"style":20397},[998],"height:0.4444em;",[86,20399,7912],{"className":20400,"style":20401},[1003,20010],"margin-right:0.016em;",[86,20403],{"className":20404,"style":3222},[3221],[86,20406,258],{"className":20407},[3226],[86,20409],{"className":20410,"style":3222},[3221],[86,20412,20414,20417,20420,20461,20464,20467,20507,20510,20513,20553],{"className":20413},[994],[86,20415],{"className":20416,"style":3794},[998],[86,20418,572],{"className":20419},[3320],[86,20421,20423,20426],{"className":20422},[1003],[86,20424,7912],{"className":20425,"style":8109},[1003,1007],[86,20427,20429],{"className":20428},[1012],[86,20430,20432,20453],{"className":20431},[1016,3836],[86,20433,20435,20450],{"className":20434},[1020],[86,20436,20438],{"className":20437,"style":6984},[1024],[86,20439,20441,20444],{"style":20440},"top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;",[86,20442],{"className":20443,"style":1032},[1031],[86,20445,20447],{"className":20446},[1036,1037,1038,1039],[86,20448,802],{"className":20449},[1003,1039],[86,20451,3963],{"className":20452},[3962],[86,20454,20456],{"className":20455},[1020],[86,20457,20459],{"className":20458,"style":7006},[1024],[86,20460],{},[86,20462,291],{"className":20463},[4158],[86,20465],{"className":20466,"style":4162},[3221],[86,20468,20470,20473],{"className":20469},[1003],[86,20471,7912],{"className":20472,"style":8109},[1003,1007],[86,20474,20476],{"className":20475},[1012],[86,20477,20479,20499],{"className":20478},[1016,3836],[86,20480,20482,20496],{"className":20481},[1020],[86,20483,20485],{"className":20484,"style":6984},[1024],[86,20486,20487,20490],{"style":20440},[86,20488],{"className":20489,"style":1032},[1031],[86,20491,20493],{"className":20492},[1036,1037,1038,1039],[86,20494,980],{"className":20495},[1003,1039],[86,20497,3963],{"className":20498},[3962],[86,20500,20502],{"className":20501},[1020],[86,20503,20505],{"className":20504,"style":7006},[1024],[86,20506],{},[86,20508,291],{"className":20509},[4158],[86,20511],{"className":20512,"style":4162},[3221],[86,20514,20516,20519],{"className":20515},[1003],[86,20517,7912],{"className":20518,"style":8109},[1003,1007],[86,20520,20522],{"className":20521},[1012],[86,20523,20525,20545],{"className":20524},[1016,3836],[86,20526,20528,20542],{"className":20527},[1020],[86,20529,20531],{"className":20530,"style":6984},[1024],[86,20532,20533,20536],{"style":20440},[86,20534],{"className":20535,"style":1032},[1031],[86,20537,20539],{"className":20538},[1036,1037,1038,1039],[86,20540,4100],{"className":20541},[1003,1039],[86,20543,3963],{"className":20544},[3962],[86,20546,20548],{"className":20547},[1020],[86,20549,20551],{"className":20550,"style":7006},[1024],[86,20552],{},[86,20554,585],{"className":20555},[3356],[12,20557,20558,20559,20561],{},"La dimensión de un vector se refiere al número de elementos que contiene. En el ejemplo anterior, el vector ",[145,20560,7912],{}," tiene una dimensión de 3, ya que contiene tres elementos (altura, peso y edad). El orden de los elementos en un vector es importante, ya que cada posición representa una característica específica.",[12,20563,20564],{},"Dentro de los modelos los vectores se utilizan para:",[30,20566,20567,20573],{},[33,20568,20569,20572],{},[122,20570,20571],{},"Representar instancias de datos",": Cada fila de una matriz de datos puede ser un vector que representa una instancia específica.",[33,20574,20575,20578],{},[122,20576,20577],{},"Representar parámetros del modelo",": Los pesos y sesgos en modelos de machine learning también se representan como vectores.",[12,20580,20581],{},"Las operaciones comunes con vectores incluyen:",[30,20583,20584],{},[33,20585,20586,20589],{},[122,20587,20588],{},"Suma de vectores",": Se suman los elementos correspondientes de dos vectores.",[86,20591,20593],{"className":20592},[3173],[86,20594,20596,20666],{"className":20595},[955],[86,20597,20599],{"className":20598},[959],[961,20600,20601],{"xmlns":963,"display":3182},[965,20602,20603,20663],{},[968,20604,20605,20607,20609,20611,20613,20615,20621,20623,20629,20631,20637,20639,20645,20647,20653,20655,20661],{},[974,20606,7912],{"mathvariant":19893},[3191,20608,6565],{},[974,20610,12059],{"mathvariant":19893},[3191,20612,258],{},[3191,20614,572],{"stretchy":3295},[6849,20616,20617,20619],{},[974,20618,7912],{},[978,20620,802],{},[3191,20622,6565],{},[6849,20624,20625,20627],{},[974,20626,12059],{},[978,20628,802],{},[3191,20630,291],{"separator":990},[6849,20632,20633,20635],{},[974,20634,7912],{},[978,20636,980],{},[3191,20638,6565],{},[6849,20640,20641,20643],{},[974,20642,12059],{},[978,20644,980],{},[3191,20646,291],{"separator":990},[6849,20648,20649,20651],{},[974,20650,7912],{},[978,20652,4100],{},[3191,20654,6565],{},[6849,20656,20657,20659],{},[974,20658,12059],{},[978,20660,4100],{},[3191,20662,585],{"stretchy":3295},[982,20664,20665],{"encoding":984},"\\mathbf{v} + \\mathbf{w} = [v_1 + w_1, v_2 + w_2, v_3 + w_3]",[86,20667,20669,20687,20705,20763,20867,20968],{"className":20668,"ariaHidden":990},[989],[86,20670,20672,20675,20678,20681,20684],{"className":20671},[994],[86,20673],{"className":20674,"style":14141},[998],[86,20676,7912],{"className":20677,"style":20401},[1003,20010],[86,20679],{"className":20680,"style":5012},[3221],[86,20682,6565],{"className":20683},[5016],[86,20685],{"className":20686,"style":5012},[3221],[86,20688,20690,20693,20696,20699,20702],{"className":20689},[994],[86,20691],{"className":20692,"style":20397},[998],[86,20694,12059],{"className":20695,"style":20401},[1003,20010],[86,20697],{"className":20698,"style":3222},[3221],[86,20700,258],{"className":20701},[3226],[86,20703],{"className":20704,"style":3222},[3221],[86,20706,20708,20711,20714,20754,20757,20760],{"className":20707},[994],[86,20709],{"className":20710,"style":3794},[998],[86,20712,572],{"className":20713},[3320],[86,20715,20717,20720],{"className":20716},[1003],[86,20718,7912],{"className":20719,"style":8109},[1003,1007],[86,20721,20723],{"className":20722},[1012],[86,20724,20726,20746],{"className":20725},[1016,3836],[86,20727,20729,20743],{"className":20728},[1020],[86,20730,20732],{"className":20731,"style":6984},[1024],[86,20733,20734,20737],{"style":20440},[86,20735],{"className":20736,"style":1032},[1031],[86,20738,20740],{"className":20739},[1036,1037,1038,1039],[86,20741,802],{"className":20742},[1003,1039],[86,20744,3963],{"className":20745},[3962],[86,20747,20749],{"className":20748},[1020],[86,20750,20752],{"className":20751,"style":7006},[1024],[86,20753],{},[86,20755],{"className":20756,"style":5012},[3221],[86,20758,6565],{"className":20759},[5016],[86,20761],{"className":20762,"style":5012},[3221],[86,20764,20766,20770,20812,20815,20818,20858,20861,20864],{"className":20765},[994],[86,20767],{"className":20768,"style":20769},[998],"height:0.7778em;vertical-align:-0.1944em;",[86,20771,20773,20777],{"className":20772},[1003],[86,20774,12059],{"className":20775,"style":20776},[1003,1007],"margin-right:0.0269em;",[86,20778,20780],{"className":20779},[1012],[86,20781,20783,20804],{"className":20782},[1016,3836],[86,20784,20786,20801],{"className":20785},[1020],[86,20787,20789],{"className":20788,"style":6984},[1024],[86,20790,20792,20795],{"style":20791},"top:-2.55em;margin-left:-0.0269em;margin-right:0.05em;",[86,20793],{"className":20794,"style":1032},[1031],[86,20796,20798],{"className":20797},[1036,1037,1038,1039],[86,20799,802],{"className":20800},[1003,1039],[86,20802,3963],{"className":20803},[3962],[86,20805,20807],{"className":20806},[1020],[86,20808,20810],{"className":20809,"style":7006},[1024],[86,20811],{},[86,20813,291],{"className":20814},[4158],[86,20816],{"className":20817,"style":4162},[3221],[86,20819,20821,20824],{"className":20820},[1003],[86,20822,7912],{"className":20823,"style":8109},[1003,1007],[86,20825,20827],{"className":20826},[1012],[86,20828,20830,20850],{"className":20829},[1016,3836],[86,20831,20833,20847],{"className":20832},[1020],[86,20834,20836],{"className":20835,"style":6984},[1024],[86,20837,20838,20841],{"style":20440},[86,20839],{"className":20840,"style":1032},[1031],[86,20842,20844],{"className":20843},[1036,1037,1038,1039],[86,20845,980],{"className":20846},[1003,1039],[86,20848,3963],{"className":20849},[3962],[86,20851,20853],{"className":20852},[1020],[86,20854,20856],{"className":20855,"style":7006},[1024],[86,20857],{},[86,20859],{"className":20860,"style":5012},[3221],[86,20862,6565],{"className":20863},[5016],[86,20865],{"className":20866,"style":5012},[3221],[86,20868,20870,20873,20913,20916,20919,20959,20962,20965],{"className":20869},[994],[86,20871],{"className":20872,"style":20769},[998],[86,20874,20876,20879],{"className":20875},[1003],[86,20877,12059],{"className":20878,"style":20776},[1003,1007],[86,20880,20882],{"className":20881},[1012],[86,20883,20885,20905],{"className":20884},[1016,3836],[86,20886,20888,20902],{"className":20887},[1020],[86,20889,20891],{"className":20890,"style":6984},[1024],[86,20892,20893,20896],{"style":20791},[86,20894],{"className":20895,"style":1032},[1031],[86,20897,20899],{"className":20898},[1036,1037,1038,1039],[86,20900,980],{"className":20901},[1003,1039],[86,20903,3963],{"className":20904},[3962],[86,20906,20908],{"className":20907},[1020],[86,20909,20911],{"className":20910,"style":7006},[1024],[86,20912],{},[86,20914,291],{"className":20915},[4158],[86,20917],{"className":20918,"style":4162},[3221],[86,20920,20922,20925],{"className":20921},[1003],[86,20923,7912],{"className":20924,"style":8109},[1003,1007],[86,20926,20928],{"className":20927},[1012],[86,20929,20931,20951],{"className":20930},[1016,3836],[86,20932,20934,20948],{"className":20933},[1020],[86,20935,20937],{"className":20936,"style":6984},[1024],[86,20938,20939,20942],{"style":20440},[86,20940],{"className":20941,"style":1032},[1031],[86,20943,20945],{"className":20944},[1036,1037,1038,1039],[86,20946,4100],{"className":20947},[1003,1039],[86,20949,3963],{"className":20950},[3962],[86,20952,20954],{"className":20953},[1020],[86,20955,20957],{"className":20956,"style":7006},[1024],[86,20958],{},[86,20960],{"className":20961,"style":5012},[3221],[86,20963,6565],{"className":20964},[5016],[86,20966],{"className":20967,"style":5012},[3221],[86,20969,20971,20974,21014],{"className":20970},[994],[86,20972],{"className":20973,"style":3794},[998],[86,20975,20977,20980],{"className":20976},[1003],[86,20978,12059],{"className":20979,"style":20776},[1003,1007],[86,20981,20983],{"className":20982},[1012],[86,20984,20986,21006],{"className":20985},[1016,3836],[86,20987,20989,21003],{"className":20988},[1020],[86,20990,20992],{"className":20991,"style":6984},[1024],[86,20993,20994,20997],{"style":20791},[86,20995],{"className":20996,"style":1032},[1031],[86,20998,21000],{"className":20999},[1036,1037,1038,1039],[86,21001,4100],{"className":21002},[1003,1039],[86,21004,3963],{"className":21005},[3962],[86,21007,21009],{"className":21008},[1020],[86,21010,21012],{"className":21011,"style":7006},[1024],[86,21013],{},[86,21015,585],{"className":21016},[3356],[30,21018,21019],{},[33,21020,21021,21024],{},[122,21022,21023],{},"Producto escalar",": Se multiplican los elementos correspondientes de dos vectores y se suman los resultados.",[86,21026,21028],{"className":21027},[3173],[86,21029,21031,21091],{"className":21030},[955],[86,21032,21034],{"className":21033},[959],[961,21035,21036],{"xmlns":963,"display":3182},[965,21037,21038,21088],{},[968,21039,21040,21042,21044,21046,21048,21054,21060,21062,21068,21074,21076,21082],{},[974,21041,7912],{"mathvariant":19893},[3191,21043,4975],{},[974,21045,12059],{"mathvariant":19893},[3191,21047,258],{},[6849,21049,21050,21052],{},[974,21051,7912],{},[978,21053,802],{},[6849,21055,21056,21058],{},[974,21057,12059],{},[978,21059,802],{},[3191,21061,6565],{},[6849,21063,21064,21066],{},[974,21065,7912],{},[978,21067,980],{},[6849,21069,21070,21072],{},[974,21071,12059],{},[978,21073,980],{},[3191,21075,6565],{},[6849,21077,21078,21080],{},[974,21079,7912],{},[978,21081,4100],{},[6849,21083,21084,21086],{},[974,21085,12059],{},[978,21087,4100],{},[982,21089,21090],{"encoding":984},"\\mathbf{v} \\cdot \\mathbf{w} = v_1 w_1 + v_2 w_2 + v_3 w_3",[86,21092,21094,21112,21130,21226,21321],{"className":21093,"ariaHidden":990},[989],[86,21095,21097,21100,21103,21106,21109],{"className":21096},[994],[86,21098],{"className":21099,"style":7127},[998],[86,21101,7912],{"className":21102,"style":20401},[1003,20010],[86,21104],{"className":21105,"style":5012},[3221],[86,21107,4975],{"className":21108},[5016],[86,21110],{"className":21111,"style":5012},[3221],[86,21113,21115,21118,21121,21124,21127],{"className":21114},[994],[86,21116],{"className":21117,"style":20397},[998],[86,21119,12059],{"className":21120,"style":20401},[1003,20010],[86,21122],{"className":21123,"style":3222},[3221],[86,21125,258],{"className":21126},[3226],[86,21128],{"className":21129,"style":3222},[3221],[86,21131,21133,21137,21177,21217,21220,21223],{"className":21132},[994],[86,21134],{"className":21135,"style":21136},[998],"height:0.7333em;vertical-align:-0.15em;",[86,21138,21140,21143],{"className":21139},[1003],[86,21141,7912],{"className":21142,"style":8109},[1003,1007],[86,21144,21146],{"className":21145},[1012],[86,21147,21149,21169],{"className":21148},[1016,3836],[86,21150,21152,21166],{"className":21151},[1020],[86,21153,21155],{"className":21154,"style":6984},[1024],[86,21156,21157,21160],{"style":20440},[86,21158],{"className":21159,"style":1032},[1031],[86,21161,21163],{"className":21162},[1036,1037,1038,1039],[86,21164,802],{"className":21165},[1003,1039],[86,21167,3963],{"className":21168},[3962],[86,21170,21172],{"className":21171},[1020],[86,21173,21175],{"className":21174,"style":7006},[1024],[86,21176],{},[86,21178,21180,21183],{"className":21179},[1003],[86,21181,12059],{"className":21182,"style":20776},[1003,1007],[86,21184,21186],{"className":21185},[1012],[86,21187,21189,21209],{"className":21188},[1016,3836],[86,21190,21192,21206],{"className":21191},[1020],[86,21193,21195],{"className":21194,"style":6984},[1024],[86,21196,21197,21200],{"style":20791},[86,21198],{"className":21199,"style":1032},[1031],[86,21201,21203],{"className":21202},[1036,1037,1038,1039],[86,21204,802],{"className":21205},[1003,1039],[86,21207,3963],{"className":21208},[3962],[86,21210,21212],{"className":21211},[1020],[86,21213,21215],{"className":21214,"style":7006},[1024],[86,21216],{},[86,21218],{"className":21219,"style":5012},[3221],[86,21221,6565],{"className":21222},[5016],[86,21224],{"className":21225,"style":5012},[3221],[86,21227,21229,21232,21272,21312,21315,21318],{"className":21228},[994],[86,21230],{"className":21231,"style":21136},[998],[86,21233,21235,21238],{"className":21234},[1003],[86,21236,7912],{"className":21237,"style":8109},[1003,1007],[86,21239,21241],{"className":21240},[1012],[86,21242,21244,21264],{"className":21243},[1016,3836],[86,21245,21247,21261],{"className":21246},[1020],[86,21248,21250],{"className":21249,"style":6984},[1024],[86,21251,21252,21255],{"style":20440},[86,21253],{"className":21254,"style":1032},[1031],[86,21256,21258],{"className":21257},[1036,1037,1038,1039],[86,21259,980],{"className":21260},[1003,1039],[86,21262,3963],{"className":21263},[3962],[86,21265,21267],{"className":21266},[1020],[86,21268,21270],{"className":21269,"style":7006},[1024],[86,21271],{},[86,21273,21275,21278],{"className":21274},[1003],[86,21276,12059],{"className":21277,"style":20776},[1003,1007],[86,21279,21281],{"className":21280},[1012],[86,21282,21284,21304],{"className":21283},[1016,3836],[86,21285,21287,21301],{"className":21286},[1020],[86,21288,21290],{"className":21289,"style":6984},[1024],[86,21291,21292,21295],{"style":20791},[86,21293],{"className":21294,"style":1032},[1031],[86,21296,21298],{"className":21297},[1036,1037,1038,1039],[86,21299,980],{"className":21300},[1003,1039],[86,21302,3963],{"className":21303},[3962],[86,21305,21307],{"className":21306},[1020],[86,21308,21310],{"className":21309,"style":7006},[1024],[86,21311],{},[86,21313],{"className":21314,"style":5012},[3221],[86,21316,6565],{"className":21317},[5016],[86,21319],{"className":21320,"style":5012},[3221],[86,21322,21324,21328,21368],{"className":21323},[994],[86,21325],{"className":21326,"style":21327},[998],"height:0.5806em;vertical-align:-0.15em;",[86,21329,21331,21334],{"className":21330},[1003],[86,21332,7912],{"className":21333,"style":8109},[1003,1007],[86,21335,21337],{"className":21336},[1012],[86,21338,21340,21360],{"className":21339},[1016,3836],[86,21341,21343,21357],{"className":21342},[1020],[86,21344,21346],{"className":21345,"style":6984},[1024],[86,21347,21348,21351],{"style":20440},[86,21349],{"className":21350,"style":1032},[1031],[86,21352,21354],{"className":21353},[1036,1037,1038,1039],[86,21355,4100],{"className":21356},[1003,1039],[86,21358,3963],{"className":21359},[3962],[86,21361,21363],{"className":21362},[1020],[86,21364,21366],{"className":21365,"style":7006},[1024],[86,21367],{},[86,21369,21371,21374],{"className":21370},[1003],[86,21372,12059],{"className":21373,"style":20776},[1003,1007],[86,21375,21377],{"className":21376},[1012],[86,21378,21380,21400],{"className":21379},[1016,3836],[86,21381,21383,21397],{"className":21382},[1020],[86,21384,21386],{"className":21385,"style":6984},[1024],[86,21387,21388,21391],{"style":20791},[86,21389],{"className":21390,"style":1032},[1031],[86,21392,21394],{"className":21393},[1036,1037,1038,1039],[86,21395,4100],{"className":21396},[1003,1039],[86,21398,3963],{"className":21399},[3962],[86,21401,21403],{"className":21402},[1020],[86,21404,21406],{"className":21405,"style":7006},[1024],[86,21407],{},[30,21409,21410],{},[33,21411,21412,21415],{},[122,21413,21414],{},"Norma de un vector",": Se calcula la longitud o magnitud de un vector, lo que es útil para medir la distancia entre vectores.",[86,21417,21419],{"className":21418},[3173],[86,21420,21422,21475],{"className":21421},[955],[86,21423,21425],{"className":21424},[959],[961,21426,21427],{"xmlns":963,"display":3182},[965,21428,21429,21472],{},[968,21430,21431,21434,21436,21438,21440],{},[974,21432,21433],{"mathvariant":4327},"∥",[974,21435,7912],{"mathvariant":19893},[974,21437,21433],{"mathvariant":4327},[3191,21439,258],{},[9825,21441,21442],{},[968,21443,21444,21452,21454,21462,21464],{},[9835,21445,21446,21448,21450],{},[974,21447,7912],{},[978,21449,802],{},[978,21451,980],{},[3191,21453,6565],{},[9835,21455,21456,21458,21460],{},[974,21457,7912],{},[978,21459,980],{},[978,21461,980],{},[3191,21463,6565],{},[9835,21465,21466,21468,21470],{},[974,21467,7912],{},[978,21469,4100],{},[978,21471,980],{},[982,21473,21474],{"encoding":984},"\\|\\mathbf{v}\\| = \\sqrt{v_1^2 + v_2^2 + v_3^2}",[86,21476,21478,21502],{"className":21477,"ariaHidden":990},[989],[86,21479,21481,21484,21487,21490,21493,21496,21499],{"className":21480},[994],[86,21482],{"className":21483,"style":3794},[998],[86,21485,21433],{"className":21486},[1003],[86,21488,7912],{"className":21489,"style":20401},[1003,20010],[86,21491,21433],{"className":21492},[1003],[86,21494],{"className":21495,"style":3222},[3221],[86,21497,258],{"className":21498},[3226],[86,21500],{"className":21501,"style":3222},[3221],[86,21503,21505,21509],{"className":21504},[994],[86,21506],{"className":21507,"style":21508},[998],"height:1.84em;vertical-align:-0.5413em;",[86,21510,21512],{"className":21511},[1003,10044],[86,21513,21515,21720],{"className":21514},[1016,3836],[86,21516,21518,21717],{"className":21517},[1020],[86,21519,21522,21704],{"className":21520,"style":21521},[1024],"height:1.2987em;",[86,21523,21525,21528],{"className":21524,"style":10059},[10058],[86,21526],{"className":21527,"style":10063},[1031],[86,21529,21531,21584,21587,21590,21593,21644,21647,21650,21653],{"className":21530,"style":10067},[1003],[86,21532,21534,21537],{"className":21533},[1003],[86,21535,7912],{"className":21536,"style":8109},[1003,1007],[86,21538,21540],{"className":21539},[1012],[86,21541,21543,21575],{"className":21542},[1016,3836],[86,21544,21546,21572],{"className":21545},[1020],[86,21547,21549,21561],{"className":21548,"style":10092},[1024],[86,21550,21552,21555],{"style":21551},"top:-2.4337em;margin-left:-0.0359em;margin-right:0.05em;",[86,21553],{"className":21554,"style":1032},[1031],[86,21556,21558],{"className":21557},[1036,1037,1038,1039],[86,21559,802],{"className":21560},[1003,1039],[86,21562,21563,21566],{"style":10116},[86,21564],{"className":21565,"style":1032},[1031],[86,21567,21569],{"className":21568},[1036,1037,1038,1039],[86,21570,980],{"className":21571},[1003,1039],[86,21573,3963],{"className":21574},[3962],[86,21576,21578],{"className":21577},[1020],[86,21579,21582],{"className":21580,"style":21581},[1024],"height:0.2663em;",[86,21583],{},[86,21585],{"className":21586,"style":5012},[3221],[86,21588,6565],{"className":21589},[5016],[86,21591],{"className":21592,"style":5012},[3221],[86,21594,21596,21599],{"className":21595},[1003],[86,21597,7912],{"className":21598,"style":8109},[1003,1007],[86,21600,21602],{"className":21601},[1012],[86,21603,21605,21636],{"className":21604},[1016,3836],[86,21606,21608,21633],{"className":21607},[1020],[86,21609,21611,21622],{"className":21610,"style":10092},[1024],[86,21612,21613,21616],{"style":21551},[86,21614],{"className":21615,"style":1032},[1031],[86,21617,21619],{"className":21618},[1036,1037,1038,1039],[86,21620,980],{"className":21621},[1003,1039],[86,21623,21624,21627],{"style":10116},[86,21625],{"className":21626,"style":1032},[1031],[86,21628,21630],{"className":21629},[1036,1037,1038,1039],[86,21631,980],{"className":21632},[1003,1039],[86,21634,3963],{"className":21635},[3962],[86,21637,21639],{"className":21638},[1020],[86,21640,21642],{"className":21641,"style":21581},[1024],[86,21643],{},[86,21645],{"className":21646,"style":5012},[3221],[86,21648,6565],{"className":21649},[5016],[86,21651],{"className":21652,"style":5012},[3221],[86,21654,21656,21659],{"className":21655},[1003],[86,21657,7912],{"className":21658,"style":8109},[1003,1007],[86,21660,21662],{"className":21661},[1012],[86,21663,21665,21696],{"className":21664},[1016,3836],[86,21666,21668,21693],{"className":21667},[1020],[86,21669,21671,21682],{"className":21670,"style":10092},[1024],[86,21672,21673,21676],{"style":21551},[86,21674],{"className":21675,"style":1032},[1031],[86,21677,21679],{"className":21678},[1036,1037,1038,1039],[86,21680,4100],{"className":21681},[1003,1039],[86,21683,21684,21687],{"style":10116},[86,21685],{"className":21686,"style":1032},[1031],[86,21688,21690],{"className":21689},[1036,1037,1038,1039],[86,21691,980],{"className":21692},[1003,1039],[86,21694,3963],{"className":21695},[3962],[86,21697,21699],{"className":21698},[1020],[86,21700,21702],{"className":21701,"style":21581},[1024],[86,21703],{},[86,21705,21707,21710],{"style":21706},"top:-3.2587em;",[86,21708],{"className":21709,"style":10063},[1031],[86,21711,21713],{"className":21712,"style":10148},[10147],[10150,21714,21715],{"xmlns":10152,"width":10153,"height":10154,"viewBox":10155,"preserveAspectRatio":10156},[246,21716],{"d":10159},[86,21718,3963],{"className":21719},[3962],[86,21721,21723],{"className":21722},[1020],[86,21724,21727],{"className":21725,"style":21726},[1024],"height:0.5413em;",[86,21728],{},[30,21730,21731],{},[33,21732,21733,21736],{},[122,21734,21735],{},"Normalización",": Se ajusta un vector para que tenga una longitud de 1, lo que es útil para comparar vectores en diferentes escalas.",[86,21738,21740],{"className":21739},[3173],[86,21741,21743,21783],{"className":21742},[955],[86,21744,21746],{"className":21745},[959],[961,21747,21748],{"xmlns":963,"display":3182},[965,21749,21750,21780],{},[968,21751,21752,21766,21768],{},[6849,21753,21754,21756],{},[974,21755,7912],{"mathvariant":19893},[968,21757,21758,21760,21762,21764],{},[974,21759,6896],{},[974,21761,6018],{},[974,21763,6184],{},[974,21765,5940],{},[3191,21767,258],{},[3749,21769,21770,21772],{},[974,21771,7912],{"mathvariant":19893},[968,21773,21774,21776,21778],{},[974,21775,21433],{"mathvariant":4327},[974,21777,7912],{"mathvariant":19893},[974,21779,21433],{"mathvariant":4327},[982,21781,21782],{"encoding":984},"\\mathbf{v}_{norm} = \\frac{\\mathbf{v}}{\\|\\mathbf{v}\\|}",[86,21784,21786,21853],{"className":21785,"ariaHidden":990},[989],[86,21787,21789,21793,21844,21847,21850],{"className":21788},[994],[86,21790],{"className":21791,"style":21792},[998],"height:0.5944em;vertical-align:-0.15em;",[86,21794,21796,21799],{"className":21795},[1003],[86,21797,7912],{"className":21798,"style":20401},[1003,20010],[86,21800,21802],{"className":21801},[1012],[86,21803,21805,21836],{"className":21804},[1016,3836],[86,21806,21808,21833],{"className":21807},[1020],[86,21809,21811],{"className":21810,"style":7171},[1024],[86,21812,21814,21817],{"style":21813},"top:-2.55em;margin-left:-0.016em;margin-right:0.05em;",[86,21815],{"className":21816,"style":1032},[1031],[86,21818,21820],{"className":21819},[1036,1037,1038,1039],[86,21821,21823,21826,21830],{"className":21822},[1003,1039],[86,21824,6896],{"className":21825},[1003,1007,1039],[86,21827,21829],{"className":21828,"style":6235},[1003,1007,1039],"or",[86,21831,5940],{"className":21832},[1003,1007,1039],[86,21834,3963],{"className":21835},[3962],[86,21837,21839],{"className":21838},[1020],[86,21840,21842],{"className":21841,"style":7006},[1024],[86,21843],{},[86,21845],{"className":21846,"style":3222},[3221],[86,21848,258],{"className":21849},[3226],[86,21851],{"className":21852,"style":3222},[3221],[86,21854,21856,21860],{"className":21855},[994],[86,21857],{"className":21858,"style":21859},[998],"height:2.0574em;vertical-align:-0.936em;",[86,21861,21863,21866,21926],{"className":21862},[1003],[86,21864],{"className":21865},[3320,3829],[86,21867,21869],{"className":21868},[3749],[86,21870,21872,21918],{"className":21871},[1016,3836],[86,21873,21875,21915],{"className":21874},[1020],[86,21876,21879,21896,21904],{"className":21877,"style":21878},[1024],"height:1.1214em;",[86,21880,21881,21884],{"style":3846},[86,21882],{"className":21883,"style":3850},[1031],[86,21885,21887,21890,21893],{"className":21886},[1003],[86,21888,21433],{"className":21889},[1003],[86,21891,7912],{"className":21892,"style":20401},[1003,20010],[86,21894,21433],{"className":21895},[1003],[86,21897,21898,21901],{"style":3901},[86,21899],{"className":21900,"style":3850},[1031],[86,21902],{"className":21903,"style":3909},[3908],[86,21905,21906,21909],{"style":3912},[86,21907],{"className":21908,"style":3850},[1031],[86,21910,21912],{"className":21911},[1003],[86,21913,7912],{"className":21914,"style":20401},[1003,20010],[86,21916,3963],{"className":21917},[3962],[86,21919,21921],{"className":21920},[1020],[86,21922,21924],{"className":21923,"style":5797},[1024],[86,21925],{},[86,21927],{"className":21928},[3356,3829],[30,21930,21931],{},[33,21932,21933,21936],{},[122,21934,21935],{},"Mutiplicación por un escalar",": Se multiplican todos los elementos de un vector por un número (escalar).",[86,21938,21940],{"className":21939},[3173],[86,21941,21943,22002],{"className":21942},[955],[86,21944,21946],{"className":21945},[959],[961,21947,21948],{"xmlns":963,"display":3182},[965,21949,21950,21999],{},[968,21951,21952,21954,21956,21959,21961,21963,21969,21971,21973,21975,21981,21983,21985,21987,21993,21995,21997],{},[974,21953,7912],{"mathvariant":19893},[3191,21955,4975],{},[974,21957,21958],{},"c",[3191,21960,258],{},[3191,21962,572],{"stretchy":3295},[6849,21964,21965,21967],{},[974,21966,7912],{},[978,21968,802],{},[3191,21970,4975],{},[974,21972,21958],{},[3191,21974,291],{"separator":990},[6849,21976,21977,21979],{},[974,21978,7912],{},[978,21980,980],{},[3191,21982,4975],{},[974,21984,21958],{},[3191,21986,291],{"separator":990},[6849,21988,21989,21991],{},[974,21990,7912],{},[978,21992,4100],{},[3191,21994,4975],{},[974,21996,21958],{},[3191,21998,585],{"stretchy":3295},[982,22000,22001],{"encoding":984},"\\mathbf{v} \\cdot c = [v_1 \\cdot c, v_2 \\cdot c, v_3 \\cdot c]",[86,22003,22005,22023,22041,22099,22164,22228],{"className":22004,"ariaHidden":990},[989],[86,22006,22008,22011,22014,22017,22020],{"className":22007},[994],[86,22009],{"className":22010,"style":7127},[998],[86,22012,7912],{"className":22013,"style":20401},[1003,20010],[86,22015],{"className":22016,"style":5012},[3221],[86,22018,4975],{"className":22019},[5016],[86,22021],{"className":22022,"style":5012},[3221],[86,22024,22026,22029,22032,22035,22038],{"className":22025},[994],[86,22027],{"className":22028,"style":7401},[998],[86,22030,21958],{"className":22031},[1003,1007],[86,22033],{"className":22034,"style":3222},[3221],[86,22036,258],{"className":22037},[3226],[86,22039],{"className":22040,"style":3222},[3221],[86,22042,22044,22047,22050,22090,22093,22096],{"className":22043},[994],[86,22045],{"className":22046,"style":3794},[998],[86,22048,572],{"className":22049},[3320],[86,22051,22053,22056],{"className":22052},[1003],[86,22054,7912],{"className":22055,"style":8109},[1003,1007],[86,22057,22059],{"className":22058},[1012],[86,22060,22062,22082],{"className":22061},[1016,3836],[86,22063,22065,22079],{"className":22064},[1020],[86,22066,22068],{"className":22067,"style":6984},[1024],[86,22069,22070,22073],{"style":20440},[86,22071],{"className":22072,"style":1032},[1031],[86,22074,22076],{"className":22075},[1036,1037,1038,1039],[86,22077,802],{"className":22078},[1003,1039],[86,22080,3963],{"className":22081},[3962],[86,22083,22085],{"className":22084},[1020],[86,22086,22088],{"className":22087,"style":7006},[1024],[86,22089],{},[86,22091],{"className":22092,"style":5012},[3221],[86,22094,4975],{"className":22095},[5016],[86,22097],{"className":22098,"style":5012},[3221],[86,22100,22102,22106,22109,22112,22115,22155,22158,22161],{"className":22101},[994],[86,22103],{"className":22104,"style":22105},[998],"height:0.6389em;vertical-align:-0.1944em;",[86,22107,21958],{"className":22108},[1003,1007],[86,22110,291],{"className":22111},[4158],[86,22113],{"className":22114,"style":4162},[3221],[86,22116,22118,22121],{"className":22117},[1003],[86,22119,7912],{"className":22120,"style":8109},[1003,1007],[86,22122,22124],{"className":22123},[1012],[86,22125,22127,22147],{"className":22126},[1016,3836],[86,22128,22130,22144],{"className":22129},[1020],[86,22131,22133],{"className":22132,"style":6984},[1024],[86,22134,22135,22138],{"style":20440},[86,22136],{"className":22137,"style":1032},[1031],[86,22139,22141],{"className":22140},[1036,1037,1038,1039],[86,22142,980],{"className":22143},[1003,1039],[86,22145,3963],{"className":22146},[3962],[86,22148,22150],{"className":22149},[1020],[86,22151,22153],{"className":22152,"style":7006},[1024],[86,22154],{},[86,22156],{"className":22157,"style":5012},[3221],[86,22159,4975],{"className":22160},[5016],[86,22162],{"className":22163,"style":5012},[3221],[86,22165,22167,22170,22173,22176,22179,22219,22222,22225],{"className":22166},[994],[86,22168],{"className":22169,"style":22105},[998],[86,22171,21958],{"className":22172},[1003,1007],[86,22174,291],{"className":22175},[4158],[86,22177],{"className":22178,"style":4162},[3221],[86,22180,22182,22185],{"className":22181},[1003],[86,22183,7912],{"className":22184,"style":8109},[1003,1007],[86,22186,22188],{"className":22187},[1012],[86,22189,22191,22211],{"className":22190},[1016,3836],[86,22192,22194,22208],{"className":22193},[1020],[86,22195,22197],{"className":22196,"style":6984},[1024],[86,22198,22199,22202],{"style":20440},[86,22200],{"className":22201,"style":1032},[1031],[86,22203,22205],{"className":22204},[1036,1037,1038,1039],[86,22206,4100],{"className":22207},[1003,1039],[86,22209,3963],{"className":22210},[3962],[86,22212,22214],{"className":22213},[1020],[86,22215,22217],{"className":22216,"style":7006},[1024],[86,22218],{},[86,22220],{"className":22221,"style":5012},[3221],[86,22223,4975],{"className":22224},[5016],[86,22226],{"className":22227,"style":5012},[3221],[86,22229,22231,22234,22237],{"className":22230},[994],[86,22232],{"className":22233,"style":3794},[998],[86,22235,21958],{"className":22236},[1003,1007],[86,22238,585],{"className":22239},[3356],[323,22241,22243],{"id":22242},"matriz","Matriz",[12,22245,22246],{},"Una matriz es una colección de vectores organizados en filas y columnas. En el contexto del aprendizaje automático, una matriz se utiliza para representar un conjunto de datos completo. Por ejemplo, si tenemos 100 instancias de datos con 3 características cada una, podríamos representar este conjunto de datos como una matriz de 100 filas y 3 columnas.",[86,22248,22250],{"className":22249},[3173],[86,22251,22253,22354],{"className":22252},[955],[86,22254,22256],{"className":22255},[959],[961,22257,22258],{"xmlns":963,"display":3182},[965,22259,22260,22352],{},[968,22261,22262,22264,22266],{},[974,22263,4624],{"mathvariant":19893},[3191,22265,258],{},[968,22267,22268,22270,22350],{},[3191,22269,572],{"fence":990},[19901,22271,22272,22292,22312],{"rowspacing":19903,"columnalign":19904,"columnspacing":19905},[19907,22273,22274,22280,22286],{},[19910,22275,22276],{},[19913,22277,22278],{"scriptlevel":2553,"displaystyle":3295},[978,22279,19856],{},[19910,22281,22282],{},[19913,22283,22284],{"scriptlevel":2553,"displaystyle":3295},[978,22285,19859],{},[19910,22287,22288],{},[19913,22289,22290],{"scriptlevel":2553,"displaystyle":3295},[978,22291,16271],{},[19907,22293,22294,22300,22306],{},[19910,22295,22296],{},[19913,22297,22298],{"scriptlevel":2553,"displaystyle":3295},[978,22299,19866],{},[19910,22301,22302],{},[19913,22303,22304],{"scriptlevel":2553,"displaystyle":3295},[978,22305,19869],{},[19910,22307,22308],{},[19913,22309,22310],{"scriptlevel":2553,"displaystyle":3295},[978,22311,19872],{},[19907,22313,22314,22326,22338],{},[19910,22315,22316],{},[19913,22317,22318],{"scriptlevel":2553,"displaystyle":3295},[968,22319,22320,22322],{},[974,22321,19959],{"mathvariant":4327},[19961,22323,22324],{"height":19963,"voffset":19963},[3221,22325],{"mathbackground":19966,"width":19963,"height":19967},[19910,22327,22328],{},[19913,22329,22330],{"scriptlevel":2553,"displaystyle":3295},[968,22331,22332,22334],{},[974,22333,19959],{"mathvariant":4327},[19961,22335,22336],{"height":19963,"voffset":19963},[3221,22337],{"mathbackground":19966,"width":19963,"height":19967},[19910,22339,22340],{},[19913,22341,22342],{"scriptlevel":2553,"displaystyle":3295},[968,22343,22344,22346],{},[974,22345,19959],{"mathvariant":4327},[19961,22347,22348],{"height":19963,"voffset":19963},[3221,22349],{"mathbackground":19966,"width":19963,"height":19967},[3191,22351,585],{"fence":990},[982,22353,19996],{"encoding":984},[86,22355,22357,22375],{"className":22356,"ariaHidden":990},[989],[86,22358,22360,22363,22366,22369,22372],{"className":22359},[994],[86,22361],{"className":22362,"style":20006},[998],[86,22364,4624],{"className":22365},[1003,20010],[86,22367],{"className":22368,"style":3222},[3221],[86,22370,258],{"className":22371},[3226],[86,22373],{"className":22374,"style":3222},[3221],[86,22376,22378,22381],{"className":22377},[994],[86,22379],{"className":22380,"style":20026},[998],[86,22382,22384,22421,22625],{"className":22383},[7131],[86,22385,22387],{"className":22386},[3320],[86,22388,22390],{"className":22389},[10232,20036],[86,22391,22393,22413],{"className":22392},[1016,3836],[86,22394,22396,22410],{"className":22395},[1020],[86,22397,22399],{"className":22398,"style":20046},[1024],[86,22400,22401,22404],{"style":20049},[86,22402],{"className":22403,"style":20053},[1031],[86,22405,22406],{"style":20056},[10150,22407,22408],{"xmlns":10152,"width":20059,"height":20060,"viewBox":20061},[246,22409],{"d":20064},[86,22411,3963],{"className":22412},[3962],[86,22414,22416],{"className":22415},[1020],[86,22417,22419],{"className":22418,"style":20074},[1024],[86,22420],{},[86,22422,22424],{"className":22423},[1003],[86,22425,22427,22489,22492,22495,22557,22560,22563],{"className":22426},[19901],[86,22428,22430],{"className":22429},[20086],[86,22431,22433,22481],{"className":22432},[1016,3836],[86,22434,22436,22478],{"className":22435},[1020],[86,22437,22439,22450,22461],{"className":22438,"style":20096},[1024],[86,22440,22441,22444],{"style":20099},[86,22442],{"className":22443,"style":20103},[1031],[86,22445,22447],{"className":22446},[1003],[86,22448,19856],{"className":22449},[1003],[86,22451,22452,22455],{"style":20112},[86,22453],{"className":22454,"style":20103},[1031],[86,22456,22458],{"className":22457},[1003],[86,22459,19866],{"className":22460},[1003],[86,22462,22463,22466],{"style":20124},[86,22464],{"className":22465,"style":20103},[1031],[86,22467,22469],{"className":22468},[1003],[86,22470,22472,22475],{"className":22471},[1003],[86,22473,19959],{"className":22474},[1003],[86,22476],{"className":22477,"style":20141},[1003,20140],[86,22479,3963],{"className":22480},[3962],[86,22482,22484],{"className":22483},[1020],[86,22485,22487],{"className":22486,"style":20151},[1024],[86,22488],{},[86,22490],{"className":22491,"style":20158},[20157],[86,22493],{"className":22494,"style":20158},[20157],[86,22496,22498],{"className":22497},[20086],[86,22499,22501,22549],{"className":22500},[1016,3836],[86,22502,22504,22546],{"className":22503},[1020],[86,22505,22507,22518,22529],{"className":22506,"style":20096},[1024],[86,22508,22509,22512],{"style":20099},[86,22510],{"className":22511,"style":20103},[1031],[86,22513,22515],{"className":22514},[1003],[86,22516,19859],{"className":22517},[1003],[86,22519,22520,22523],{"style":20112},[86,22521],{"className":22522,"style":20103},[1031],[86,22524,22526],{"className":22525},[1003],[86,22527,19869],{"className":22528},[1003],[86,22530,22531,22534],{"style":20124},[86,22532],{"className":22533,"style":20103},[1031],[86,22535,22537],{"className":22536},[1003],[86,22538,22540,22543],{"className":22539},[1003],[86,22541,19959],{"className":22542},[1003],[86,22544],{"className":22545,"style":20141},[1003,20140],[86,22547,3963],{"className":22548},[3962],[86,22550,22552],{"className":22551},[1020],[86,22553,22555],{"className":22554,"style":20151},[1024],[86,22556],{},[86,22558],{"className":22559,"style":20158},[20157],[86,22561],{"className":22562,"style":20158},[20157],[86,22564,22566],{"className":22565},[20086],[86,22567,22569,22617],{"className":22568},[1016,3836],[86,22570,22572,22614],{"className":22571},[1020],[86,22573,22575,22586,22597],{"className":22574,"style":20096},[1024],[86,22576,22577,22580],{"style":20099},[86,22578],{"className":22579,"style":20103},[1031],[86,22581,22583],{"className":22582},[1003],[86,22584,16271],{"className":22585},[1003],[86,22587,22588,22591],{"style":20112},[86,22589],{"className":22590,"style":20103},[1031],[86,22592,22594],{"className":22593},[1003],[86,22595,19872],{"className":22596},[1003],[86,22598,22599,22602],{"style":20124},[86,22600],{"className":22601,"style":20103},[1031],[86,22603,22605],{"className":22604},[1003],[86,22606,22608,22611],{"className":22607},[1003],[86,22609,19959],{"className":22610},[1003],[86,22612],{"className":22613,"style":20141},[1003,20140],[86,22615,3963],{"className":22616},[3962],[86,22618,22620],{"className":22619},[1020],[86,22621,22623],{"className":22622,"style":20151},[1024],[86,22624],{},[86,22626,22628],{"className":22627},[3356],[86,22629,22631],{"className":22630},[10232,20036],[86,22632,22634,22654],{"className":22633},[1016,3836],[86,22635,22637,22651],{"className":22636},[1020],[86,22638,22640],{"className":22639,"style":20046},[1024],[86,22641,22642,22645],{"style":20049},[86,22643],{"className":22644,"style":20053},[1031],[86,22646,22647],{"style":20056},[10150,22648,22649],{"xmlns":10152,"width":20059,"height":20060,"viewBox":20061},[246,22650],{"d":20318},[86,22652,3963],{"className":22653},[3962],[86,22655,22657],{"className":22656},[1020],[86,22658,22660],{"className":22659,"style":20074},[1024],[86,22661],{},[12,22663,22664,22665,22667,22668,22670,22671,61],{},"Un dataset con ",[145,22666,5940],{}," instancias y ",[145,22669,6896],{}," características se representa como una matriz de dimensiones ",[145,22672,22673],{},"m x n",[12,22675,22676],{},"Las operaciones comunes con matrices incluyen:",[30,22678,22679],{},[33,22680,22681,22684],{},[122,22682,22683],{},"Suma de matrices",": Se suman los elementos correspondientes de dos matrices.",[86,22686,22688],{"className":22687},[3173],[86,22689,22691,23015],{"className":22690},[955],[86,22692,22694],{"className":22693},[959],[961,22695,22696],{"xmlns":963,"display":3182},[965,22697,22698,23012],{},[968,22699,22700,22702,22704,22706,22708],{},[974,22701,3743],{"mathvariant":19893},[3191,22703,6565],{},[974,22705,4807],{"mathvariant":19893},[3191,22707,258],{},[968,22709,22710,22712,23010],{},[3191,22711,572],{"fence":990},[19901,22713,22715,22795,22873,22918],{"rowspacing":19903,"columnalign":22714,"columnspacing":19905},"center center center center",[19907,22716,22717,22739,22760,22767],{},[19910,22718,22719],{},[19913,22720,22721],{"scriptlevel":2553,"displaystyle":3295},[968,22722,22723,22730,22732],{},[6849,22724,22725,22727],{},[974,22726,22],{},[978,22728,22729],{},"11",[3191,22731,6565],{},[6849,22733,22734,22737],{},[974,22735,22736],{},"b",[978,22738,22729],{},[19910,22740,22741],{},[19913,22742,22743],{"scriptlevel":2553,"displaystyle":3295},[968,22744,22745,22752,22754],{},[6849,22746,22747,22749],{},[974,22748,22],{},[978,22750,22751],{},"12",[3191,22753,6565],{},[6849,22755,22756,22758],{},[974,22757,22736],{},[978,22759,22751],{},[19910,22761,22762],{},[19913,22763,22764],{"scriptlevel":2553,"displaystyle":3295},[3191,22765,22766],{"lspace":19963,"rspace":19963},"⋯",[19910,22768,22769],{},[19913,22770,22771],{"scriptlevel":2553,"displaystyle":3295},[968,22772,22773,22783,22785],{},[6849,22774,22775,22777],{},[974,22776,22],{},[968,22778,22779,22781],{},[978,22780,802],{},[974,22782,6896],{},[3191,22784,6565],{},[6849,22786,22787,22789],{},[974,22788,22736],{},[968,22790,22791,22793],{},[978,22792,802],{},[974,22794,6896],{},[19907,22796,22797,22818,22839,22845],{},[19910,22798,22799],{},[19913,22800,22801],{"scriptlevel":2553,"displaystyle":3295},[968,22802,22803,22810,22812],{},[6849,22804,22805,22807],{},[974,22806,22],{},[978,22808,22809],{},"21",[3191,22811,6565],{},[6849,22813,22814,22816],{},[974,22815,22736],{},[978,22817,22809],{},[19910,22819,22820],{},[19913,22821,22822],{"scriptlevel":2553,"displaystyle":3295},[968,22823,22824,22831,22833],{},[6849,22825,22826,22828],{},[974,22827,22],{},[978,22829,22830],{},"22",[3191,22832,6565],{},[6849,22834,22835,22837],{},[974,22836,22736],{},[978,22838,22830],{},[19910,22840,22841],{},[19913,22842,22843],{"scriptlevel":2553,"displaystyle":3295},[3191,22844,22766],{"lspace":19963,"rspace":19963},[19910,22846,22847],{},[19913,22848,22849],{"scriptlevel":2553,"displaystyle":3295},[968,22850,22851,22861,22863],{},[6849,22852,22853,22855],{},[974,22854,22],{},[968,22856,22857,22859],{},[978,22858,980],{},[974,22860,6896],{},[3191,22862,6565],{},[6849,22864,22865,22867],{},[974,22866,22736],{},[968,22868,22869,22871],{},[978,22870,980],{},[974,22872,6896],{},[19907,22874,22875,22887,22899,22906],{},[19910,22876,22877],{},[19913,22878,22879],{"scriptlevel":2553,"displaystyle":3295},[968,22880,22881,22883],{},[974,22882,19959],{"mathvariant":4327},[19961,22884,22885],{"height":19963,"voffset":19963},[3221,22886],{"mathbackground":19966,"width":19963,"height":19967},[19910,22888,22889],{},[19913,22890,22891],{"scriptlevel":2553,"displaystyle":3295},[968,22892,22893,22895],{},[974,22894,19959],{"mathvariant":4327},[19961,22896,22897],{"height":19963,"voffset":19963},[3221,22898],{"mathbackground":19966,"width":19963,"height":19967},[19910,22900,22901],{},[19913,22902,22903],{"scriptlevel":2553,"displaystyle":3295},[3191,22904,22905],{"lspace":19963,"rspace":19963},"⋱",[19910,22907,22908],{},[19913,22909,22910],{"scriptlevel":2553,"displaystyle":3295},[968,22911,22912,22914],{},[974,22913,19959],{"mathvariant":4327},[19961,22915,22916],{"height":19963,"voffset":19963},[3221,22917],{"mathbackground":19966,"width":19963,"height":19967},[19907,22919,22920,22948,22976,22982],{},[19910,22921,22922],{},[19913,22923,22924],{"scriptlevel":2553,"displaystyle":3295},[968,22925,22926,22936,22938],{},[6849,22927,22928,22930],{},[974,22929,22],{},[968,22931,22932,22934],{},[974,22933,5940],{},[978,22935,802],{},[3191,22937,6565],{},[6849,22939,22940,22942],{},[974,22941,22736],{},[968,22943,22944,22946],{},[974,22945,5940],{},[978,22947,802],{},[19910,22949,22950],{},[19913,22951,22952],{"scriptlevel":2553,"displaystyle":3295},[968,22953,22954,22964,22966],{},[6849,22955,22956,22958],{},[974,22957,22],{},[968,22959,22960,22962],{},[974,22961,5940],{},[978,22963,980],{},[3191,22965,6565],{},[6849,22967,22968,22970],{},[974,22969,22736],{},[968,22971,22972,22974],{},[974,22973,5940],{},[978,22975,980],{},[19910,22977,22978],{},[19913,22979,22980],{"scriptlevel":2553,"displaystyle":3295},[3191,22981,22766],{"lspace":19963,"rspace":19963},[19910,22983,22984],{},[19913,22985,22986],{"scriptlevel":2553,"displaystyle":3295},[968,22987,22988,22998,23000],{},[6849,22989,22990,22992],{},[974,22991,22],{},[968,22993,22994,22996],{},[974,22995,5940],{},[974,22997,6896],{},[3191,22999,6565],{},[6849,23001,23002,23004],{},[974,23003,22736],{},[968,23005,23006,23008],{},[974,23007,5940],{},[974,23009,6896],{},[3191,23011,585],{"fence":990},[982,23013,23014],{"encoding":984},"\\mathbf{A} + \\mathbf{B} =\n\\begin{bmatrix}\na_{11} + b_{11} & a_{12} + b_{12} & \\cdots & a_{1n} + b_{1n} \\\\\na_{21} + b_{21} & a_{22} + b_{22} & \\cdots & a_{2n} + b_{2n} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{m1} + b_{m1} & a_{m2} + b_{m2} & \\cdots & a_{mn} + b_{mn} \\\\\n\\end{bmatrix}",[86,23016,23018,23037,23055],{"className":23017,"ariaHidden":990},[989],[86,23019,23021,23025,23028,23031,23034],{"className":23020},[994],[86,23022],{"className":23023,"style":23024},[998],"height:0.7694em;vertical-align:-0.0833em;",[86,23026,3743],{"className":23027},[1003,20010],[86,23029],{"className":23030,"style":5012},[3221],[86,23032,6565],{"className":23033},[5016],[86,23035],{"className":23036,"style":5012},[3221],[86,23038,23040,23043,23046,23049,23052],{"className":23039},[994],[86,23041],{"className":23042,"style":20006},[998],[86,23044,4807],{"className":23045},[1003,20010],[86,23047],{"className":23048,"style":3222},[3221],[86,23050,258],{"className":23051},[3226],[86,23053],{"className":23054,"style":3222},[3221],[86,23056,23058,23062],{"className":23057},[994],[86,23059],{"className":23060,"style":23061},[998],"height:5.46em;vertical-align:-2.48em;",[86,23063,23065,23110,24283],{"className":23064},[7131],[86,23066,23068],{"className":23067},[3320],[86,23069,23071],{"className":23070},[10232,20036],[86,23072,23074,23101],{"className":23073},[1016,3836],[86,23075,23077,23098],{"className":23076},[1020],[86,23078,23081],{"className":23079,"style":23080},[1024],"height:2.95em;",[86,23082,23084,23088],{"style":23083},"top:-4.95em;",[86,23085],{"className":23086,"style":23087},[1031],"height:7.4em;",[86,23089,23091],{"style":23090},"width:0.667em;height:5.4em;",[10150,23092,23095],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},"5.4em","0 0 667 5400",[246,23096],{"d":23097},"M403 1759 V84 H666 V0 H319 V1759 v1800 v1759 h347 v-84\nH403z M403 1759 V0 H319 V1759 v1800 v1759 h84z",[86,23099,3963],{"className":23100},[3962],[86,23102,23104],{"className":23103},[1020],[86,23105,23108],{"className":23106,"style":23107},[1024],"height:2.45em;",[86,23109],{},[86,23111,23113],{"className":23112},[1003],[86,23114,23116,23477,23480,23483,23838,23841,23844,23916,23919,23922],{"className":23115},[19901],[86,23117,23119],{"className":23118},[20086],[86,23120,23122,23468],{"className":23121},[1016,3836],[86,23123,23125,23465],{"className":23124},[1020],[86,23126,23129,23233,23337,23355],{"className":23127,"style":23128},[1024],"height:2.98em;",[86,23130,23132,23135],{"style":23131},"top:-5.8275em;",[86,23133],{"className":23134,"style":20103},[1031],[86,23136,23138,23181,23184,23187,23190],{"className":23137},[1003],[86,23139,23141,23144],{"className":23140},[1003],[86,23142,22],{"className":23143},[1003,1007],[86,23145,23147],{"className":23146},[1012],[86,23148,23150,23173],{"className":23149},[1016,3836],[86,23151,23153,23170],{"className":23152},[1020],[86,23154,23156],{"className":23155,"style":6984},[1024],[86,23157,23158,23161],{"style":6987},[86,23159],{"className":23160,"style":1032},[1031],[86,23162,23164],{"className":23163},[1036,1037,1038,1039],[86,23165,23167],{"className":23166},[1003,1039],[86,23168,22729],{"className":23169},[1003,1039],[86,23171,3963],{"className":23172},[3962],[86,23174,23176],{"className":23175},[1020],[86,23177,23179],{"className":23178,"style":7006},[1024],[86,23180],{},[86,23182],{"className":23183,"style":5012},[3221],[86,23185,6565],{"className":23186},[5016],[86,23188],{"className":23189,"style":5012},[3221],[86,23191,23193,23196],{"className":23192},[1003],[86,23194,22736],{"className":23195},[1003,1007],[86,23197,23199],{"className":23198},[1012],[86,23200,23202,23225],{"className":23201},[1016,3836],[86,23203,23205,23222],{"className":23204},[1020],[86,23206,23208],{"className":23207,"style":6984},[1024],[86,23209,23210,23213],{"style":6987},[86,23211],{"className":23212,"style":1032},[1031],[86,23214,23216],{"className":23215},[1036,1037,1038,1039],[86,23217,23219],{"className":23218},[1003,1039],[86,23220,22729],{"className":23221},[1003,1039],[86,23223,3963],{"className":23224},[3962],[86,23226,23228],{"className":23227},[1020],[86,23229,23231],{"className":23230,"style":7006},[1024],[86,23232],{},[86,23234,23236,23239],{"style":23235},"top:-4.6275em;",[86,23237],{"className":23238,"style":20103},[1031],[86,23240,23242,23285,23288,23291,23294],{"className":23241},[1003],[86,23243,23245,23248],{"className":23244},[1003],[86,23246,22],{"className":23247},[1003,1007],[86,23249,23251],{"className":23250},[1012],[86,23252,23254,23277],{"className":23253},[1016,3836],[86,23255,23257,23274],{"className":23256},[1020],[86,23258,23260],{"className":23259,"style":6984},[1024],[86,23261,23262,23265],{"style":6987},[86,23263],{"className":23264,"style":1032},[1031],[86,23266,23268],{"className":23267},[1036,1037,1038,1039],[86,23269,23271],{"className":23270},[1003,1039],[86,23272,22809],{"className":23273},[1003,1039],[86,23275,3963],{"className":23276},[3962],[86,23278,23280],{"className":23279},[1020],[86,23281,23283],{"className":23282,"style":7006},[1024],[86,23284],{},[86,23286],{"className":23287,"style":5012},[3221],[86,23289,6565],{"className":23290},[5016],[86,23292],{"className":23293,"style":5012},[3221],[86,23295,23297,23300],{"className":23296},[1003],[86,23298,22736],{"className":23299},[1003,1007],[86,23301,23303],{"className":23302},[1012],[86,23304,23306,23329],{"className":23305},[1016,3836],[86,23307,23309,23326],{"className":23308},[1020],[86,23310,23312],{"className":23311,"style":6984},[1024],[86,23313,23314,23317],{"style":6987},[86,23315],{"className":23316,"style":1032},[1031],[86,23318,23320],{"className":23319},[1036,1037,1038,1039],[86,23321,23323],{"className":23322},[1003,1039],[86,23324,22809],{"className":23325},[1003,1039],[86,23327,3963],{"className":23328},[3962],[86,23330,23332],{"className":23331},[1020],[86,23333,23335],{"className":23334,"style":7006},[1024],[86,23336],{},[86,23338,23340,23343],{"style":23339},"top:-2.7675em;",[86,23341],{"className":23342,"style":20103},[1031],[86,23344,23346],{"className":23345},[1003],[86,23347,23349,23352],{"className":23348},[1003],[86,23350,19959],{"className":23351},[1003],[86,23353],{"className":23354,"style":20141},[1003,20140],[86,23356,23358,23361],{"style":23357},"top:-1.5675em;",[86,23359],{"className":23360,"style":20103},[1031],[86,23362,23364,23410,23413,23416,23419],{"className":23363},[1003],[86,23365,23367,23370],{"className":23366},[1003],[86,23368,22],{"className":23369},[1003,1007],[86,23371,23373],{"className":23372},[1012],[86,23374,23376,23402],{"className":23375},[1016,3836],[86,23377,23379,23399],{"className":23378},[1020],[86,23380,23382],{"className":23381,"style":6984},[1024],[86,23383,23384,23387],{"style":6987},[86,23385],{"className":23386,"style":1032},[1031],[86,23388,23390],{"className":23389},[1036,1037,1038,1039],[86,23391,23393,23396],{"className":23392},[1003,1039],[86,23394,5940],{"className":23395},[1003,1007,1039],[86,23397,802],{"className":23398},[1003,1039],[86,23400,3963],{"className":23401},[3962],[86,23403,23405],{"className":23404},[1020],[86,23406,23408],{"className":23407,"style":7006},[1024],[86,23409],{},[86,23411],{"className":23412,"style":5012},[3221],[86,23414,6565],{"className":23415},[5016],[86,23417],{"className":23418,"style":5012},[3221],[86,23420,23422,23425],{"className":23421},[1003],[86,23423,22736],{"className":23424},[1003,1007],[86,23426,23428],{"className":23427},[1012],[86,23429,23431,23457],{"className":23430},[1016,3836],[86,23432,23434,23454],{"className":23433},[1020],[86,23435,23437],{"className":23436,"style":6984},[1024],[86,23438,23439,23442],{"style":6987},[86,23440],{"className":23441,"style":1032},[1031],[86,23443,23445],{"className":23444},[1036,1037,1038,1039],[86,23446,23448,23451],{"className":23447},[1003,1039],[86,23449,5940],{"className":23450},[1003,1007,1039],[86,23452,802],{"className":23453},[1003,1039],[86,23455,3963],{"className":23456},[3962],[86,23458,23460],{"className":23459},[1020],[86,23461,23463],{"className":23462,"style":7006},[1024],[86,23464],{},[86,23466,3963],{"className":23467},[3962],[86,23469,23471],{"className":23470},[1020],[86,23472,23475],{"className":23473,"style":23474},[1024],"height:2.48em;",[86,23476],{},[86,23478],{"className":23479,"style":20158},[20157],[86,23481],{"className":23482,"style":20158},[20157],[86,23484,23486],{"className":23485},[20086],[86,23487,23489,23830],{"className":23488},[1016,3836],[86,23490,23492,23827],{"className":23491},[1020],[86,23493,23495,23598,23701,23718],{"className":23494,"style":23128},[1024],[86,23496,23497,23500],{"style":23131},[86,23498],{"className":23499,"style":20103},[1031],[86,23501,23503,23546,23549,23552,23555],{"className":23502},[1003],[86,23504,23506,23509],{"className":23505},[1003],[86,23507,22],{"className":23508},[1003,1007],[86,23510,23512],{"className":23511},[1012],[86,23513,23515,23538],{"className":23514},[1016,3836],[86,23516,23518,23535],{"className":23517},[1020],[86,23519,23521],{"className":23520,"style":6984},[1024],[86,23522,23523,23526],{"style":6987},[86,23524],{"className":23525,"style":1032},[1031],[86,23527,23529],{"className":23528},[1036,1037,1038,1039],[86,23530,23532],{"className":23531},[1003,1039],[86,23533,22751],{"className":23534},[1003,1039],[86,23536,3963],{"className":23537},[3962],[86,23539,23541],{"className":23540},[1020],[86,23542,23544],{"className":23543,"style":7006},[1024],[86,23545],{},[86,23547],{"className":23548,"style":5012},[3221],[86,23550,6565],{"className":23551},[5016],[86,23553],{"className":23554,"style":5012},[3221],[86,23556,23558,23561],{"className":23557},[1003],[86,23559,22736],{"className":23560},[1003,1007],[86,23562,23564],{"className":23563},[1012],[86,23565,23567,23590],{"className":23566},[1016,3836],[86,23568,23570,23587],{"className":23569},[1020],[86,23571,23573],{"className":23572,"style":6984},[1024],[86,23574,23575,23578],{"style":6987},[86,23576],{"className":23577,"style":1032},[1031],[86,23579,23581],{"className":23580},[1036,1037,1038,1039],[86,23582,23584],{"className":23583},[1003,1039],[86,23585,22751],{"className":23586},[1003,1039],[86,23588,3963],{"className":23589},[3962],[86,23591,23593],{"className":23592},[1020],[86,23594,23596],{"className":23595,"style":7006},[1024],[86,23597],{},[86,23599,23600,23603],{"style":23235},[86,23601],{"className":23602,"style":20103},[1031],[86,23604,23606,23649,23652,23655,23658],{"className":23605},[1003],[86,23607,23609,23612],{"className":23608},[1003],[86,23610,22],{"className":23611},[1003,1007],[86,23613,23615],{"className":23614},[1012],[86,23616,23618,23641],{"className":23617},[1016,3836],[86,23619,23621,23638],{"className":23620},[1020],[86,23622,23624],{"className":23623,"style":6984},[1024],[86,23625,23626,23629],{"style":6987},[86,23627],{"className":23628,"style":1032},[1031],[86,23630,23632],{"className":23631},[1036,1037,1038,1039],[86,23633,23635],{"className":23634},[1003,1039],[86,23636,22830],{"className":23637},[1003,1039],[86,23639,3963],{"className":23640},[3962],[86,23642,23644],{"className":23643},[1020],[86,23645,23647],{"className":23646,"style":7006},[1024],[86,23648],{},[86,23650],{"className":23651,"style":5012},[3221],[86,23653,6565],{"className":23654},[5016],[86,23656],{"className":23657,"style":5012},[3221],[86,23659,23661,23664],{"className":23660},[1003],[86,23662,22736],{"className":23663},[1003,1007],[86,23665,23667],{"className":23666},[1012],[86,23668,23670,23693],{"className":23669},[1016,3836],[86,23671,23673,23690],{"className":23672},[1020],[86,23674,23676],{"className":23675,"style":6984},[1024],[86,23677,23678,23681],{"style":6987},[86,23679],{"className":23680,"style":1032},[1031],[86,23682,23684],{"className":23683},[1036,1037,1038,1039],[86,23685,23687],{"className":23686},[1003,1039],[86,23688,22830],{"className":23689},[1003,1039],[86,23691,3963],{"className":23692},[3962],[86,23694,23696],{"className":23695},[1020],[86,23697,23699],{"className":23698,"style":7006},[1024],[86,23700],{},[86,23702,23703,23706],{"style":23339},[86,23704],{"className":23705,"style":20103},[1031],[86,23707,23709],{"className":23708},[1003],[86,23710,23712,23715],{"className":23711},[1003],[86,23713,19959],{"className":23714},[1003],[86,23716],{"className":23717,"style":20141},[1003,20140],[86,23719,23720,23723],{"style":23357},[86,23721],{"className":23722,"style":20103},[1031],[86,23724,23726,23772,23775,23778,23781],{"className":23725},[1003],[86,23727,23729,23732],{"className":23728},[1003],[86,23730,22],{"className":23731},[1003,1007],[86,23733,23735],{"className":23734},[1012],[86,23736,23738,23764],{"className":23737},[1016,3836],[86,23739,23741,23761],{"className":23740},[1020],[86,23742,23744],{"className":23743,"style":6984},[1024],[86,23745,23746,23749],{"style":6987},[86,23747],{"className":23748,"style":1032},[1031],[86,23750,23752],{"className":23751},[1036,1037,1038,1039],[86,23753,23755,23758],{"className":23754},[1003,1039],[86,23756,5940],{"className":23757},[1003,1007,1039],[86,23759,980],{"className":23760},[1003,1039],[86,23762,3963],{"className":23763},[3962],[86,23765,23767],{"className":23766},[1020],[86,23768,23770],{"className":23769,"style":7006},[1024],[86,23771],{},[86,23773],{"className":23774,"style":5012},[3221],[86,23776,6565],{"className":23777},[5016],[86,23779],{"className":23780,"style":5012},[3221],[86,23782,23784,23787],{"className":23783},[1003],[86,23785,22736],{"className":23786},[1003,1007],[86,23788,23790],{"className":23789},[1012],[86,23791,23793,23819],{"className":23792},[1016,3836],[86,23794,23796,23816],{"className":23795},[1020],[86,23797,23799],{"className":23798,"style":6984},[1024],[86,23800,23801,23804],{"style":6987},[86,23802],{"className":23803,"style":1032},[1031],[86,23805,23807],{"className":23806},[1036,1037,1038,1039],[86,23808,23810,23813],{"className":23809},[1003,1039],[86,23811,5940],{"className":23812},[1003,1007,1039],[86,23814,980],{"className":23815},[1003,1039],[86,23817,3963],{"className":23818},[3962],[86,23820,23822],{"className":23821},[1020],[86,23823,23825],{"className":23824,"style":7006},[1024],[86,23826],{},[86,23828,3963],{"className":23829},[3962],[86,23831,23833],{"className":23832},[1020],[86,23834,23836],{"className":23835,"style":23474},[1024],[86,23837],{},[86,23839],{"className":23840,"style":20158},[20157],[86,23842],{"className":23843,"style":20158},[20157],[86,23845,23847],{"className":23846},[20086],[86,23848,23850,23908],{"className":23849},[1016,3836],[86,23851,23853,23905],{"className":23852},[1020],[86,23854,23856,23869,23881,23893],{"className":23855,"style":23128},[1024],[86,23857,23859,23863],{"style":23858},"top:-5.64em;",[86,23860],{"className":23861,"style":23862},[1031],"height:3.5em;",[86,23864,23866],{"className":23865},[1003],[86,23867,22766],{"className":23868},[7131],[86,23870,23872,23875],{"style":23871},"top:-4.44em;",[86,23873],{"className":23874,"style":23862},[1031],[86,23876,23878],{"className":23877},[1003],[86,23879,22766],{"className":23880},[7131],[86,23882,23884,23887],{"style":23883},"top:-2.58em;",[86,23885],{"className":23886,"style":23862},[1031],[86,23888,23890],{"className":23889},[1003],[86,23891,22905],{"className":23892},[7131],[86,23894,23896,23899],{"style":23895},"top:-1.38em;",[86,23897],{"className":23898,"style":23862},[1031],[86,23900,23902],{"className":23901},[1003],[86,23903,22766],{"className":23904},[7131],[86,23906,3963],{"className":23907},[3962],[86,23909,23911],{"className":23910},[1020],[86,23912,23914],{"className":23913,"style":23474},[1024],[86,23915],{},[86,23917],{"className":23918,"style":20158},[20157],[86,23920],{"className":23921,"style":20158},[20157],[86,23923,23925],{"className":23924},[20086],[86,23926,23928,24275],{"className":23927},[1016,3836],[86,23929,23931,24272],{"className":23930},[1020],[86,23932,23934,24043,24152,24169],{"className":23933,"style":23128},[1024],[86,23935,23936,23939],{"style":23131},[86,23937],{"className":23938,"style":20103},[1031],[86,23940,23942,23988,23991,23994,23997],{"className":23941},[1003],[86,23943,23945,23948],{"className":23944},[1003],[86,23946,22],{"className":23947},[1003,1007],[86,23949,23951],{"className":23950},[1012],[86,23952,23954,23980],{"className":23953},[1016,3836],[86,23955,23957,23977],{"className":23956},[1020],[86,23958,23960],{"className":23959,"style":6984},[1024],[86,23961,23962,23965],{"style":6987},[86,23963],{"className":23964,"style":1032},[1031],[86,23966,23968],{"className":23967},[1036,1037,1038,1039],[86,23969,23971,23974],{"className":23970},[1003,1039],[86,23972,802],{"className":23973},[1003,1039],[86,23975,6896],{"className":23976},[1003,1007,1039],[86,23978,3963],{"className":23979},[3962],[86,23981,23983],{"className":23982},[1020],[86,23984,23986],{"className":23985,"style":7006},[1024],[86,23987],{},[86,23989],{"className":23990,"style":5012},[3221],[86,23992,6565],{"className":23993},[5016],[86,23995],{"className":23996,"style":5012},[3221],[86,23998,24000,24003],{"className":23999},[1003],[86,24001,22736],{"className":24002},[1003,1007],[86,24004,24006],{"className":24005},[1012],[86,24007,24009,24035],{"className":24008},[1016,3836],[86,24010,24012,24032],{"className":24011},[1020],[86,24013,24015],{"className":24014,"style":6984},[1024],[86,24016,24017,24020],{"style":6987},[86,24018],{"className":24019,"style":1032},[1031],[86,24021,24023],{"className":24022},[1036,1037,1038,1039],[86,24024,24026,24029],{"className":24025},[1003,1039],[86,24027,802],{"className":24028},[1003,1039],[86,24030,6896],{"className":24031},[1003,1007,1039],[86,24033,3963],{"className":24034},[3962],[86,24036,24038],{"className":24037},[1020],[86,24039,24041],{"className":24040,"style":7006},[1024],[86,24042],{},[86,24044,24045,24048],{"style":23235},[86,24046],{"className":24047,"style":20103},[1031],[86,24049,24051,24097,24100,24103,24106],{"className":24050},[1003],[86,24052,24054,24057],{"className":24053},[1003],[86,24055,22],{"className":24056},[1003,1007],[86,24058,24060],{"className":24059},[1012],[86,24061,24063,24089],{"className":24062},[1016,3836],[86,24064,24066,24086],{"className":24065},[1020],[86,24067,24069],{"className":24068,"style":6984},[1024],[86,24070,24071,24074],{"style":6987},[86,24072],{"className":24073,"style":1032},[1031],[86,24075,24077],{"className":24076},[1036,1037,1038,1039],[86,24078,24080,24083],{"className":24079},[1003,1039],[86,24081,980],{"className":24082},[1003,1039],[86,24084,6896],{"className":24085},[1003,1007,1039],[86,24087,3963],{"className":24088},[3962],[86,24090,24092],{"className":24091},[1020],[86,24093,24095],{"className":24094,"style":7006},[1024],[86,24096],{},[86,24098],{"className":24099,"style":5012},[3221],[86,24101,6565],{"className":24102},[5016],[86,24104],{"className":24105,"style":5012},[3221],[86,24107,24109,24112],{"className":24108},[1003],[86,24110,22736],{"className":24111},[1003,1007],[86,24113,24115],{"className":24114},[1012],[86,24116,24118,24144],{"className":24117},[1016,3836],[86,24119,24121,24141],{"className":24120},[1020],[86,24122,24124],{"className":24123,"style":6984},[1024],[86,24125,24126,24129],{"style":6987},[86,24127],{"className":24128,"style":1032},[1031],[86,24130,24132],{"className":24131},[1036,1037,1038,1039],[86,24133,24135,24138],{"className":24134},[1003,1039],[86,24136,980],{"className":24137},[1003,1039],[86,24139,6896],{"className":24140},[1003,1007,1039],[86,24142,3963],{"className":24143},[3962],[86,24145,24147],{"className":24146},[1020],[86,24148,24150],{"className":24149,"style":7006},[1024],[86,24151],{},[86,24153,24154,24157],{"style":23339},[86,24155],{"className":24156,"style":20103},[1031],[86,24158,24160],{"className":24159},[1003],[86,24161,24163,24166],{"className":24162},[1003],[86,24164,19959],{"className":24165},[1003],[86,24167],{"className":24168,"style":20141},[1003,20140],[86,24170,24171,24174],{"style":23357},[86,24172],{"className":24173,"style":20103},[1031],[86,24175,24177,24220,24223,24226,24229],{"className":24176},[1003],[86,24178,24180,24183],{"className":24179},[1003],[86,24181,22],{"className":24182},[1003,1007],[86,24184,24186],{"className":24185},[1012],[86,24187,24189,24212],{"className":24188},[1016,3836],[86,24190,24192,24209],{"className":24191},[1020],[86,24193,24195],{"className":24194,"style":7171},[1024],[86,24196,24197,24200],{"style":6987},[86,24198],{"className":24199,"style":1032},[1031],[86,24201,24203],{"className":24202},[1036,1037,1038,1039],[86,24204,24206],{"className":24205},[1003,1039],[86,24207,978],{"className":24208},[1003,1007,1039],[86,24210,3963],{"className":24211},[3962],[86,24213,24215],{"className":24214},[1020],[86,24216,24218],{"className":24217,"style":7006},[1024],[86,24219],{},[86,24221],{"className":24222,"style":5012},[3221],[86,24224,6565],{"className":24225},[5016],[86,24227],{"className":24228,"style":5012},[3221],[86,24230,24232,24235],{"className":24231},[1003],[86,24233,22736],{"className":24234},[1003,1007],[86,24236,24238],{"className":24237},[1012],[86,24239,24241,24264],{"className":24240},[1016,3836],[86,24242,24244,24261],{"className":24243},[1020],[86,24245,24247],{"className":24246,"style":7171},[1024],[86,24248,24249,24252],{"style":6987},[86,24250],{"className":24251,"style":1032},[1031],[86,24253,24255],{"className":24254},[1036,1037,1038,1039],[86,24256,24258],{"className":24257},[1003,1039],[86,24259,978],{"className":24260},[1003,1007,1039],[86,24262,3963],{"className":24263},[3962],[86,24265,24267],{"className":24266},[1020],[86,24268,24270],{"className":24269,"style":7006},[1024],[86,24271],{},[86,24273,3963],{"className":24274},[3962],[86,24276,24278],{"className":24277},[1020],[86,24279,24281],{"className":24280,"style":23474},[1024],[86,24282],{},[86,24284,24286],{"className":24285},[3356],[86,24287,24289],{"className":24288},[10232,20036],[86,24290,24292,24313],{"className":24291},[1016,3836],[86,24293,24295,24310],{"className":24294},[1020],[86,24296,24298],{"className":24297,"style":23080},[1024],[86,24299,24300,24303],{"style":23083},[86,24301],{"className":24302,"style":23087},[1031],[86,24304,24305],{"style":23090},[10150,24306,24307],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,24308],{"d":24309},"M347 1759 V0 H0 V84 H263 V1759 v1800 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v1800 v1759 h84z",[86,24311,3963],{"className":24312},[3962],[86,24314,24316],{"className":24315},[1020],[86,24317,24319],{"className":24318,"style":23107},[1024],[86,24320],{},[30,24322,24323],{},[33,24324,24325,24328],{},[122,24326,24327],{},"Multiplicación de matrices",": Se multiplican dos matrices siguiendo la regla de multiplicación de filas por columnas.",[86,24330,24332],{"className":24331},[3173],[86,24333,24335,25001],{"className":24334},[955],[86,24336,24338],{"className":24337},[959],[961,24339,24340],{"xmlns":963,"display":3182},[965,24341,24342,24998],{},[968,24343,24344,24346,24348,24350,24352],{},[974,24345,3743],{"mathvariant":19893},[3191,24347,4975],{},[974,24349,4807],{"mathvariant":19893},[3191,24351,258],{},[968,24353,24354,24356,24996],{},[3191,24355,572],{"fence":990},[19901,24357,24358,24548,24738,24782],{"rowspacing":19903,"columnalign":22714,"columnspacing":19905},[19907,24359,24360,24418,24476,24482],{},[19910,24361,24362],{},[19913,24363,24364],{"scriptlevel":2553,"displaystyle":3295},[968,24365,24366,24372,24378,24380,24386,24392,24394,24396,24398,24408],{},[6849,24367,24368,24370],{},[974,24369,22],{},[978,24371,22729],{},[6849,24373,24374,24376],{},[974,24375,22736],{},[978,24377,22729],{},[3191,24379,6565],{},[6849,24381,24382,24384],{},[974,24383,22],{},[978,24385,22751],{},[6849,24387,24388,24390],{},[974,24389,22736],{},[978,24391,22809],{},[3191,24393,6565],{},[3191,24395,22766],{},[3191,24397,6565],{},[6849,24399,24400,24402],{},[974,24401,22],{},[968,24403,24404,24406],{},[978,24405,802],{},[974,24407,6896],{},[6849,24409,24410,24412],{},[974,24411,22736],{},[968,24413,24414,24416],{},[974,24415,6896],{},[978,24417,802],{},[19910,24419,24420],{},[19913,24421,24422],{"scriptlevel":2553,"displaystyle":3295},[968,24423,24424,24430,24436,24438,24444,24450,24452,24454,24456,24466],{},[6849,24425,24426,24428],{},[974,24427,22],{},[978,24429,22729],{},[6849,24431,24432,24434],{},[974,24433,22736],{},[978,24435,22751],{},[3191,24437,6565],{},[6849,24439,24440,24442],{},[974,24441,22],{},[978,24443,22751],{},[6849,24445,24446,24448],{},[974,24447,22736],{},[978,24449,22830],{},[3191,24451,6565],{},[3191,24453,22766],{},[3191,24455,6565],{},[6849,24457,24458,24460],{},[974,24459,22],{},[968,24461,24462,24464],{},[978,24463,802],{},[974,24465,6896],{},[6849,24467,24468,24470],{},[974,24469,22736],{},[968,24471,24472,24474],{},[974,24473,6896],{},[978,24475,980],{},[19910,24477,24478],{},[19913,24479,24480],{"scriptlevel":2553,"displaystyle":3295},[3191,24481,22766],{"lspace":19963,"rspace":19963},[19910,24483,24484],{},[19913,24485,24486],{"scriptlevel":2553,"displaystyle":3295},[968,24487,24488,24494,24504,24506,24512,24522,24524,24526,24528,24538],{},[6849,24489,24490,24492],{},[974,24491,22],{},[978,24493,22729],{},[6849,24495,24496,24498],{},[974,24497,22736],{},[968,24499,24500,24502],{},[978,24501,802],{},[974,24503,12],{},[3191,24505,6565],{},[6849,24507,24508,24510],{},[974,24509,22],{},[978,24511,22751],{},[6849,24513,24514,24516],{},[974,24515,22736],{},[968,24517,24518,24520],{},[978,24519,980],{},[974,24521,12],{},[3191,24523,6565],{},[3191,24525,22766],{},[3191,24527,6565],{},[6849,24529,24530,24532],{},[974,24531,22],{},[968,24533,24534,24536],{},[978,24535,802],{},[974,24537,6896],{},[6849,24539,24540,24542],{},[974,24541,22736],{},[968,24543,24544,24546],{},[974,24545,6896],{},[974,24547,12],{},[19907,24549,24550,24608,24666,24672],{},[19910,24551,24552],{},[19913,24553,24554],{"scriptlevel":2553,"displaystyle":3295},[968,24555,24556,24562,24568,24570,24576,24582,24584,24586,24588,24598],{},[6849,24557,24558,24560],{},[974,24559,22],{},[978,24561,22809],{},[6849,24563,24564,24566],{},[974,24565,22736],{},[978,24567,22729],{},[3191,24569,6565],{},[6849,24571,24572,24574],{},[974,24573,22],{},[978,24575,22830],{},[6849,24577,24578,24580],{},[974,24579,22736],{},[978,24581,22809],{},[3191,24583,6565],{},[3191,24585,22766],{},[3191,24587,6565],{},[6849,24589,24590,24592],{},[974,24591,22],{},[968,24593,24594,24596],{},[978,24595,980],{},[974,24597,6896],{},[6849,24599,24600,24602],{},[974,24601,22736],{},[968,24603,24604,24606],{},[974,24605,6896],{},[978,24607,802],{},[19910,24609,24610],{},[19913,24611,24612],{"scriptlevel":2553,"displaystyle":3295},[968,24613,24614,24620,24626,24628,24634,24640,24642,24644,24646,24656],{},[6849,24615,24616,24618],{},[974,24617,22],{},[978,24619,22809],{},[6849,24621,24622,24624],{},[974,24623,22736],{},[978,24625,22751],{},[3191,24627,6565],{},[6849,24629,24630,24632],{},[974,24631,22],{},[978,24633,22830],{},[6849,24635,24636,24638],{},[974,24637,22736],{},[978,24639,22830],{},[3191,24641,6565],{},[3191,24643,22766],{},[3191,24645,6565],{},[6849,24647,24648,24650],{},[974,24649,22],{},[968,24651,24652,24654],{},[978,24653,980],{},[974,24655,6896],{},[6849,24657,24658,24660],{},[974,24659,22736],{},[968,24661,24662,24664],{},[974,24663,6896],{},[978,24665,980],{},[19910,24667,24668],{},[19913,24669,24670],{"scriptlevel":2553,"displaystyle":3295},[3191,24671,22766],{"lspace":19963,"rspace":19963},[19910,24673,24674],{},[19913,24675,24676],{"scriptlevel":2553,"displaystyle":3295},[968,24677,24678,24684,24694,24696,24702,24712,24714,24716,24718,24728],{},[6849,24679,24680,24682],{},[974,24681,22],{},[978,24683,22809],{},[6849,24685,24686,24688],{},[974,24687,22736],{},[968,24689,24690,24692],{},[978,24691,802],{},[974,24693,12],{},[3191,24695,6565],{},[6849,24697,24698,24700],{},[974,24699,22],{},[978,24701,22830],{},[6849,24703,24704,24706],{},[974,24705,22736],{},[968,24707,24708,24710],{},[978,24709,980],{},[974,24711,12],{},[3191,24713,6565],{},[3191,24715,22766],{},[3191,24717,6565],{},[6849,24719,24720,24722],{},[974,24721,22],{},[968,24723,24724,24726],{},[978,24725,980],{},[974,24727,6896],{},[6849,24729,24730,24732],{},[974,24731,22736],{},[968,24733,24734,24736],{},[974,24735,6896],{},[974,24737,12],{},[19907,24739,24740,24752,24764,24770],{},[19910,24741,24742],{},[19913,24743,24744],{"scriptlevel":2553,"displaystyle":3295},[968,24745,24746,24748],{},[974,24747,19959],{"mathvariant":4327},[19961,24749,24750],{"height":19963,"voffset":19963},[3221,24751],{"mathbackground":19966,"width":19963,"height":19967},[19910,24753,24754],{},[19913,24755,24756],{"scriptlevel":2553,"displaystyle":3295},[968,24757,24758,24760],{},[974,24759,19959],{"mathvariant":4327},[19961,24761,24762],{"height":19963,"voffset":19963},[3221,24763],{"mathbackground":19966,"width":19963,"height":19967},[19910,24765,24766],{},[19913,24767,24768],{"scriptlevel":2553,"displaystyle":3295},[3191,24769,22905],{"lspace":19963,"rspace":19963},[19910,24771,24772],{},[19913,24773,24774],{"scriptlevel":2553,"displaystyle":3295},[968,24775,24776,24778],{},[974,24777,19959],{"mathvariant":4327},[19961,24779,24780],{"height":19963,"voffset":19963},[3221,24781],{"mathbackground":19966,"width":19963,"height":19967},[19907,24783,24784,24850,24916,24922],{},[19910,24785,24786],{},[19913,24787,24788],{"scriptlevel":2553,"displaystyle":3295},[968,24789,24790,24800,24806,24808,24818,24824,24826,24828,24830,24840],{},[6849,24791,24792,24794],{},[974,24793,22],{},[968,24795,24796,24798],{},[974,24797,5940],{},[978,24799,802],{},[6849,24801,24802,24804],{},[974,24803,22736],{},[978,24805,22729],{},[3191,24807,6565],{},[6849,24809,24810,24812],{},[974,24811,22],{},[968,24813,24814,24816],{},[974,24815,5940],{},[978,24817,980],{},[6849,24819,24820,24822],{},[974,24821,22736],{},[978,24823,22809],{},[3191,24825,6565],{},[3191,24827,22766],{},[3191,24829,6565],{},[6849,24831,24832,24834],{},[974,24833,22],{},[968,24835,24836,24838],{},[974,24837,5940],{},[974,24839,6896],{},[6849,24841,24842,24844],{},[974,24843,22736],{},[968,24845,24846,24848],{},[974,24847,6896],{},[978,24849,802],{},[19910,24851,24852],{},[19913,24853,24854],{"scriptlevel":2553,"displaystyle":3295},[968,24855,24856,24866,24872,24874,24884,24890,24892,24894,24896,24906],{},[6849,24857,24858,24860],{},[974,24859,22],{},[968,24861,24862,24864],{},[974,24863,5940],{},[978,24865,802],{},[6849,24867,24868,24870],{},[974,24869,22736],{},[978,24871,22751],{},[3191,24873,6565],{},[6849,24875,24876,24878],{},[974,24877,22],{},[968,24879,24880,24882],{},[974,24881,5940],{},[978,24883,980],{},[6849,24885,24886,24888],{},[974,24887,22736],{},[978,24889,22830],{},[3191,24891,6565],{},[3191,24893,22766],{},[3191,24895,6565],{},[6849,24897,24898,24900],{},[974,24899,22],{},[968,24901,24902,24904],{},[974,24903,5940],{},[974,24905,6896],{},[6849,24907,24908,24910],{},[974,24909,22736],{},[968,24911,24912,24914],{},[974,24913,6896],{},[978,24915,980],{},[19910,24917,24918],{},[19913,24919,24920],{"scriptlevel":2553,"displaystyle":3295},[3191,24921,22766],{"lspace":19963,"rspace":19963},[19910,24923,24924],{},[19913,24925,24926],{"scriptlevel":2553,"displaystyle":3295},[968,24927,24928,24938,24948,24950,24960,24970,24972,24974,24976,24986],{},[6849,24929,24930,24932],{},[974,24931,22],{},[968,24933,24934,24936],{},[974,24935,5940],{},[978,24937,802],{},[6849,24939,24940,24942],{},[974,24941,22736],{},[968,24943,24944,24946],{},[978,24945,802],{},[974,24947,12],{},[3191,24949,6565],{},[6849,24951,24952,24954],{},[974,24953,22],{},[968,24955,24956,24958],{},[974,24957,5940],{},[978,24959,980],{},[6849,24961,24962,24964],{},[974,24963,22736],{},[968,24965,24966,24968],{},[978,24967,980],{},[974,24969,12],{},[3191,24971,6565],{},[3191,24973,22766],{},[3191,24975,6565],{},[6849,24977,24978,24980],{},[974,24979,22],{},[968,24981,24982,24984],{},[974,24983,5940],{},[974,24985,6896],{},[6849,24987,24988,24990],{},[974,24989,22736],{},[968,24991,24992,24994],{},[974,24993,6896],{},[974,24995,12],{},[3191,24997,585],{"fence":990},[982,24999,25000],{"encoding":984},"\\mathbf{A} \\cdot \\mathbf{B} =\n\\begin{bmatrix}\na_{11}b_{11} + a_{12}b_{21} + \\cdots + a_{1n}b_{n1} & a_{11}b_{12} + a_{12}b_{22} + \\cdots + a_{1n}b_{n2} & \\cdots & a_{11}b_{1p} + a_{12}b_{2p} + \\cdots + a_{1n}b_{np} \\\\\na_{21}b_{11} + a_{22}b_{21} + \\cdots + a_{2n}b_{n1} & a_{21}b_{12} + a_{22}b_{22} + \\cdots + a_{2n}b_{n2} & \\cdots & a_{21}b_{1p} + a_{22}b_{2p} + \\cdots + a_{2n}b_{np} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{m1}b_{11} + a_{m2}b_{21} + \\cdots + a_{mn}b_{n1} & a_{m1}b_{12} + a_{m2}b_{22} + \\cdots + a_{mn}b_{n2} & \\cdots & a_{m1}b_{1p} + a_{m2}b_{2p} + \\cdots + a_{mn}b_{np} \\\\\n\\end{bmatrix}",[86,25002,25004,25022,25040],{"className":25003,"ariaHidden":990},[989],[86,25005,25007,25010,25013,25016,25019],{"className":25006},[994],[86,25008],{"className":25009,"style":20006},[998],[86,25011,3743],{"className":25012},[1003,20010],[86,25014],{"className":25015,"style":5012},[3221],[86,25017,4975],{"className":25018},[5016],[86,25020],{"className":25021,"style":5012},[3221],[86,25023,25025,25028,25031,25034,25037],{"className":25024},[994],[86,25026],{"className":25027,"style":20006},[998],[86,25029,4807],{"className":25030},[1003,20010],[86,25032],{"className":25033,"style":3222},[3221],[86,25035,258],{"className":25036},[3226],[86,25038],{"className":25039,"style":3222},[3221],[86,25041,25043,25046],{"className":25042},[994],[86,25044],{"className":25045,"style":23061},[998],[86,25047,25049,25086,28042],{"className":25048},[7131],[86,25050,25052],{"className":25051},[3320],[86,25053,25055],{"className":25054},[10232,20036],[86,25056,25058,25078],{"className":25057},[1016,3836],[86,25059,25061,25075],{"className":25060},[1020],[86,25062,25064],{"className":25063,"style":23080},[1024],[86,25065,25066,25069],{"style":23083},[86,25067],{"className":25068,"style":23087},[1031],[86,25070,25071],{"style":23090},[10150,25072,25073],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,25074],{"d":23097},[86,25076,3963],{"className":25077},[3962],[86,25079,25081],{"className":25080},[1020],[86,25082,25084],{"className":25083,"style":23107},[1024],[86,25085],{},[86,25087,25089],{"className":25088},[1003],[86,25090,25092,26041,26044,26047,26996,26999,27002,27069,27072,27075],{"className":25091},[19901],[86,25093,25095],{"className":25094},[20086],[86,25096,25098,26033],{"className":25097},[1016,3836],[86,25099,25101,26030],{"className":25100},[1020],[86,25102,25104,25406,25708,25725],{"className":25103,"style":23128},[1024],[86,25105,25106,25109],{"style":23131},[86,25107],{"className":25108,"style":20103},[1031],[86,25110,25112,25155,25198,25201,25204,25207,25250,25293,25296,25299,25302,25305,25308,25311,25314,25360],{"className":25111},[1003],[86,25113,25115,25118],{"className":25114},[1003],[86,25116,22],{"className":25117},[1003,1007],[86,25119,25121],{"className":25120},[1012],[86,25122,25124,25147],{"className":25123},[1016,3836],[86,25125,25127,25144],{"className":25126},[1020],[86,25128,25130],{"className":25129,"style":6984},[1024],[86,25131,25132,25135],{"style":6987},[86,25133],{"className":25134,"style":1032},[1031],[86,25136,25138],{"className":25137},[1036,1037,1038,1039],[86,25139,25141],{"className":25140},[1003,1039],[86,25142,22729],{"className":25143},[1003,1039],[86,25145,3963],{"className":25146},[3962],[86,25148,25150],{"className":25149},[1020],[86,25151,25153],{"className":25152,"style":7006},[1024],[86,25154],{},[86,25156,25158,25161],{"className":25157},[1003],[86,25159,22736],{"className":25160},[1003,1007],[86,25162,25164],{"className":25163},[1012],[86,25165,25167,25190],{"className":25166},[1016,3836],[86,25168,25170,25187],{"className":25169},[1020],[86,25171,25173],{"className":25172,"style":6984},[1024],[86,25174,25175,25178],{"style":6987},[86,25176],{"className":25177,"style":1032},[1031],[86,25179,25181],{"className":25180},[1036,1037,1038,1039],[86,25182,25184],{"className":25183},[1003,1039],[86,25185,22729],{"className":25186},[1003,1039],[86,25188,3963],{"className":25189},[3962],[86,25191,25193],{"className":25192},[1020],[86,25194,25196],{"className":25195,"style":7006},[1024],[86,25197],{},[86,25199],{"className":25200,"style":5012},[3221],[86,25202,6565],{"className":25203},[5016],[86,25205],{"className":25206,"style":5012},[3221],[86,25208,25210,25213],{"className":25209},[1003],[86,25211,22],{"className":25212},[1003,1007],[86,25214,25216],{"className":25215},[1012],[86,25217,25219,25242],{"className":25218},[1016,3836],[86,25220,25222,25239],{"className":25221},[1020],[86,25223,25225],{"className":25224,"style":6984},[1024],[86,25226,25227,25230],{"style":6987},[86,25228],{"className":25229,"style":1032},[1031],[86,25231,25233],{"className":25232},[1036,1037,1038,1039],[86,25234,25236],{"className":25235},[1003,1039],[86,25237,22751],{"className":25238},[1003,1039],[86,25240,3963],{"className":25241},[3962],[86,25243,25245],{"className":25244},[1020],[86,25246,25248],{"className":25247,"style":7006},[1024],[86,25249],{},[86,25251,25253,25256],{"className":25252},[1003],[86,25254,22736],{"className":25255},[1003,1007],[86,25257,25259],{"className":25258},[1012],[86,25260,25262,25285],{"className":25261},[1016,3836],[86,25263,25265,25282],{"className":25264},[1020],[86,25266,25268],{"className":25267,"style":6984},[1024],[86,25269,25270,25273],{"style":6987},[86,25271],{"className":25272,"style":1032},[1031],[86,25274,25276],{"className":25275},[1036,1037,1038,1039],[86,25277,25279],{"className":25278},[1003,1039],[86,25280,22809],{"className":25281},[1003,1039],[86,25283,3963],{"className":25284},[3962],[86,25286,25288],{"className":25287},[1020],[86,25289,25291],{"className":25290,"style":7006},[1024],[86,25292],{},[86,25294],{"className":25295,"style":5012},[3221],[86,25297,6565],{"className":25298},[5016],[86,25300],{"className":25301,"style":5012},[3221],[86,25303,22766],{"className":25304},[7131],[86,25306],{"className":25307,"style":5012},[3221],[86,25309,6565],{"className":25310},[5016],[86,25312],{"className":25313,"style":5012},[3221],[86,25315,25317,25320],{"className":25316},[1003],[86,25318,22],{"className":25319},[1003,1007],[86,25321,25323],{"className":25322},[1012],[86,25324,25326,25352],{"className":25325},[1016,3836],[86,25327,25329,25349],{"className":25328},[1020],[86,25330,25332],{"className":25331,"style":6984},[1024],[86,25333,25334,25337],{"style":6987},[86,25335],{"className":25336,"style":1032},[1031],[86,25338,25340],{"className":25339},[1036,1037,1038,1039],[86,25341,25343,25346],{"className":25342},[1003,1039],[86,25344,802],{"className":25345},[1003,1039],[86,25347,6896],{"className":25348},[1003,1007,1039],[86,25350,3963],{"className":25351},[3962],[86,25353,25355],{"className":25354},[1020],[86,25356,25358],{"className":25357,"style":7006},[1024],[86,25359],{},[86,25361,25363,25366],{"className":25362},[1003],[86,25364,22736],{"className":25365},[1003,1007],[86,25367,25369],{"className":25368},[1012],[86,25370,25372,25398],{"className":25371},[1016,3836],[86,25373,25375,25395],{"className":25374},[1020],[86,25376,25378],{"className":25377,"style":6984},[1024],[86,25379,25380,25383],{"style":6987},[86,25381],{"className":25382,"style":1032},[1031],[86,25384,25386],{"className":25385},[1036,1037,1038,1039],[86,25387,25389,25392],{"className":25388},[1003,1039],[86,25390,6896],{"className":25391},[1003,1007,1039],[86,25393,802],{"className":25394},[1003,1039],[86,25396,3963],{"className":25397},[3962],[86,25399,25401],{"className":25400},[1020],[86,25402,25404],{"className":25403,"style":7006},[1024],[86,25405],{},[86,25407,25408,25411],{"style":23235},[86,25409],{"className":25410,"style":20103},[1031],[86,25412,25414,25457,25500,25503,25506,25509,25552,25595,25598,25601,25604,25607,25610,25613,25616,25662],{"className":25413},[1003],[86,25415,25417,25420],{"className":25416},[1003],[86,25418,22],{"className":25419},[1003,1007],[86,25421,25423],{"className":25422},[1012],[86,25424,25426,25449],{"className":25425},[1016,3836],[86,25427,25429,25446],{"className":25428},[1020],[86,25430,25432],{"className":25431,"style":6984},[1024],[86,25433,25434,25437],{"style":6987},[86,25435],{"className":25436,"style":1032},[1031],[86,25438,25440],{"className":25439},[1036,1037,1038,1039],[86,25441,25443],{"className":25442},[1003,1039],[86,25444,22809],{"className":25445},[1003,1039],[86,25447,3963],{"className":25448},[3962],[86,25450,25452],{"className":25451},[1020],[86,25453,25455],{"className":25454,"style":7006},[1024],[86,25456],{},[86,25458,25460,25463],{"className":25459},[1003],[86,25461,22736],{"className":25462},[1003,1007],[86,25464,25466],{"className":25465},[1012],[86,25467,25469,25492],{"className":25468},[1016,3836],[86,25470,25472,25489],{"className":25471},[1020],[86,25473,25475],{"className":25474,"style":6984},[1024],[86,25476,25477,25480],{"style":6987},[86,25478],{"className":25479,"style":1032},[1031],[86,25481,25483],{"className":25482},[1036,1037,1038,1039],[86,25484,25486],{"className":25485},[1003,1039],[86,25487,22729],{"className":25488},[1003,1039],[86,25490,3963],{"className":25491},[3962],[86,25493,25495],{"className":25494},[1020],[86,25496,25498],{"className":25497,"style":7006},[1024],[86,25499],{},[86,25501],{"className":25502,"style":5012},[3221],[86,25504,6565],{"className":25505},[5016],[86,25507],{"className":25508,"style":5012},[3221],[86,25510,25512,25515],{"className":25511},[1003],[86,25513,22],{"className":25514},[1003,1007],[86,25516,25518],{"className":25517},[1012],[86,25519,25521,25544],{"className":25520},[1016,3836],[86,25522,25524,25541],{"className":25523},[1020],[86,25525,25527],{"className":25526,"style":6984},[1024],[86,25528,25529,25532],{"style":6987},[86,25530],{"className":25531,"style":1032},[1031],[86,25533,25535],{"className":25534},[1036,1037,1038,1039],[86,25536,25538],{"className":25537},[1003,1039],[86,25539,22830],{"className":25540},[1003,1039],[86,25542,3963],{"className":25543},[3962],[86,25545,25547],{"className":25546},[1020],[86,25548,25550],{"className":25549,"style":7006},[1024],[86,25551],{},[86,25553,25555,25558],{"className":25554},[1003],[86,25556,22736],{"className":25557},[1003,1007],[86,25559,25561],{"className":25560},[1012],[86,25562,25564,25587],{"className":25563},[1016,3836],[86,25565,25567,25584],{"className":25566},[1020],[86,25568,25570],{"className":25569,"style":6984},[1024],[86,25571,25572,25575],{"style":6987},[86,25573],{"className":25574,"style":1032},[1031],[86,25576,25578],{"className":25577},[1036,1037,1038,1039],[86,25579,25581],{"className":25580},[1003,1039],[86,25582,22809],{"className":25583},[1003,1039],[86,25585,3963],{"className":25586},[3962],[86,25588,25590],{"className":25589},[1020],[86,25591,25593],{"className":25592,"style":7006},[1024],[86,25594],{},[86,25596],{"className":25597,"style":5012},[3221],[86,25599,6565],{"className":25600},[5016],[86,25602],{"className":25603,"style":5012},[3221],[86,25605,22766],{"className":25606},[7131],[86,25608],{"className":25609,"style":5012},[3221],[86,25611,6565],{"className":25612},[5016],[86,25614],{"className":25615,"style":5012},[3221],[86,25617,25619,25622],{"className":25618},[1003],[86,25620,22],{"className":25621},[1003,1007],[86,25623,25625],{"className":25624},[1012],[86,25626,25628,25654],{"className":25627},[1016,3836],[86,25629,25631,25651],{"className":25630},[1020],[86,25632,25634],{"className":25633,"style":6984},[1024],[86,25635,25636,25639],{"style":6987},[86,25637],{"className":25638,"style":1032},[1031],[86,25640,25642],{"className":25641},[1036,1037,1038,1039],[86,25643,25645,25648],{"className":25644},[1003,1039],[86,25646,980],{"className":25647},[1003,1039],[86,25649,6896],{"className":25650},[1003,1007,1039],[86,25652,3963],{"className":25653},[3962],[86,25655,25657],{"className":25656},[1020],[86,25658,25660],{"className":25659,"style":7006},[1024],[86,25661],{},[86,25663,25665,25668],{"className":25664},[1003],[86,25666,22736],{"className":25667},[1003,1007],[86,25669,25671],{"className":25670},[1012],[86,25672,25674,25700],{"className":25673},[1016,3836],[86,25675,25677,25697],{"className":25676},[1020],[86,25678,25680],{"className":25679,"style":6984},[1024],[86,25681,25682,25685],{"style":6987},[86,25683],{"className":25684,"style":1032},[1031],[86,25686,25688],{"className":25687},[1036,1037,1038,1039],[86,25689,25691,25694],{"className":25690},[1003,1039],[86,25692,6896],{"className":25693},[1003,1007,1039],[86,25695,802],{"className":25696},[1003,1039],[86,25698,3963],{"className":25699},[3962],[86,25701,25703],{"className":25702},[1020],[86,25704,25706],{"className":25705,"style":7006},[1024],[86,25707],{},[86,25709,25710,25713],{"style":23339},[86,25711],{"className":25712,"style":20103},[1031],[86,25714,25716],{"className":25715},[1003],[86,25717,25719,25722],{"className":25718},[1003],[86,25720,19959],{"className":25721},[1003],[86,25723],{"className":25724,"style":20141},[1003,20140],[86,25726,25727,25730],{"style":23357},[86,25728],{"className":25729,"style":20103},[1031],[86,25731,25733,25779,25822,25825,25828,25831,25877,25920,25923,25926,25929,25932,25935,25938,25941,25984],{"className":25732},[1003],[86,25734,25736,25739],{"className":25735},[1003],[86,25737,22],{"className":25738},[1003,1007],[86,25740,25742],{"className":25741},[1012],[86,25743,25745,25771],{"className":25744},[1016,3836],[86,25746,25748,25768],{"className":25747},[1020],[86,25749,25751],{"className":25750,"style":6984},[1024],[86,25752,25753,25756],{"style":6987},[86,25754],{"className":25755,"style":1032},[1031],[86,25757,25759],{"className":25758},[1036,1037,1038,1039],[86,25760,25762,25765],{"className":25761},[1003,1039],[86,25763,5940],{"className":25764},[1003,1007,1039],[86,25766,802],{"className":25767},[1003,1039],[86,25769,3963],{"className":25770},[3962],[86,25772,25774],{"className":25773},[1020],[86,25775,25777],{"className":25776,"style":7006},[1024],[86,25778],{},[86,25780,25782,25785],{"className":25781},[1003],[86,25783,22736],{"className":25784},[1003,1007],[86,25786,25788],{"className":25787},[1012],[86,25789,25791,25814],{"className":25790},[1016,3836],[86,25792,25794,25811],{"className":25793},[1020],[86,25795,25797],{"className":25796,"style":6984},[1024],[86,25798,25799,25802],{"style":6987},[86,25800],{"className":25801,"style":1032},[1031],[86,25803,25805],{"className":25804},[1036,1037,1038,1039],[86,25806,25808],{"className":25807},[1003,1039],[86,25809,22729],{"className":25810},[1003,1039],[86,25812,3963],{"className":25813},[3962],[86,25815,25817],{"className":25816},[1020],[86,25818,25820],{"className":25819,"style":7006},[1024],[86,25821],{},[86,25823],{"className":25824,"style":5012},[3221],[86,25826,6565],{"className":25827},[5016],[86,25829],{"className":25830,"style":5012},[3221],[86,25832,25834,25837],{"className":25833},[1003],[86,25835,22],{"className":25836},[1003,1007],[86,25838,25840],{"className":25839},[1012],[86,25841,25843,25869],{"className":25842},[1016,3836],[86,25844,25846,25866],{"className":25845},[1020],[86,25847,25849],{"className":25848,"style":6984},[1024],[86,25850,25851,25854],{"style":6987},[86,25852],{"className":25853,"style":1032},[1031],[86,25855,25857],{"className":25856},[1036,1037,1038,1039],[86,25858,25860,25863],{"className":25859},[1003,1039],[86,25861,5940],{"className":25862},[1003,1007,1039],[86,25864,980],{"className":25865},[1003,1039],[86,25867,3963],{"className":25868},[3962],[86,25870,25872],{"className":25871},[1020],[86,25873,25875],{"className":25874,"style":7006},[1024],[86,25876],{},[86,25878,25880,25883],{"className":25879},[1003],[86,25881,22736],{"className":25882},[1003,1007],[86,25884,25886],{"className":25885},[1012],[86,25887,25889,25912],{"className":25888},[1016,3836],[86,25890,25892,25909],{"className":25891},[1020],[86,25893,25895],{"className":25894,"style":6984},[1024],[86,25896,25897,25900],{"style":6987},[86,25898],{"className":25899,"style":1032},[1031],[86,25901,25903],{"className":25902},[1036,1037,1038,1039],[86,25904,25906],{"className":25905},[1003,1039],[86,25907,22809],{"className":25908},[1003,1039],[86,25910,3963],{"className":25911},[3962],[86,25913,25915],{"className":25914},[1020],[86,25916,25918],{"className":25917,"style":7006},[1024],[86,25919],{},[86,25921],{"className":25922,"style":5012},[3221],[86,25924,6565],{"className":25925},[5016],[86,25927],{"className":25928,"style":5012},[3221],[86,25930,22766],{"className":25931},[7131],[86,25933],{"className":25934,"style":5012},[3221],[86,25936,6565],{"className":25937},[5016],[86,25939],{"className":25940,"style":5012},[3221],[86,25942,25944,25947],{"className":25943},[1003],[86,25945,22],{"className":25946},[1003,1007],[86,25948,25950],{"className":25949},[1012],[86,25951,25953,25976],{"className":25952},[1016,3836],[86,25954,25956,25973],{"className":25955},[1020],[86,25957,25959],{"className":25958,"style":7171},[1024],[86,25960,25961,25964],{"style":6987},[86,25962],{"className":25963,"style":1032},[1031],[86,25965,25967],{"className":25966},[1036,1037,1038,1039],[86,25968,25970],{"className":25969},[1003,1039],[86,25971,978],{"className":25972},[1003,1007,1039],[86,25974,3963],{"className":25975},[3962],[86,25977,25979],{"className":25978},[1020],[86,25980,25982],{"className":25981,"style":7006},[1024],[86,25983],{},[86,25985,25987,25990],{"className":25986},[1003],[86,25988,22736],{"className":25989},[1003,1007],[86,25991,25993],{"className":25992},[1012],[86,25994,25996,26022],{"className":25995},[1016,3836],[86,25997,25999,26019],{"className":25998},[1020],[86,26000,26002],{"className":26001,"style":6984},[1024],[86,26003,26004,26007],{"style":6987},[86,26005],{"className":26006,"style":1032},[1031],[86,26008,26010],{"className":26009},[1036,1037,1038,1039],[86,26011,26013,26016],{"className":26012},[1003,1039],[86,26014,6896],{"className":26015},[1003,1007,1039],[86,26017,802],{"className":26018},[1003,1039],[86,26020,3963],{"className":26021},[3962],[86,26023,26025],{"className":26024},[1020],[86,26026,26028],{"className":26027,"style":7006},[1024],[86,26029],{},[86,26031,3963],{"className":26032},[3962],[86,26034,26036],{"className":26035},[1020],[86,26037,26039],{"className":26038,"style":23474},[1024],[86,26040],{},[86,26042],{"className":26043,"style":20158},[20157],[86,26045],{"className":26046,"style":20158},[20157],[86,26048,26050],{"className":26049},[20086],[86,26051,26053,26988],{"className":26052},[1016,3836],[86,26054,26056,26985],{"className":26055},[1020],[86,26057,26059,26361,26663,26680],{"className":26058,"style":23128},[1024],[86,26060,26061,26064],{"style":23131},[86,26062],{"className":26063,"style":20103},[1031],[86,26065,26067,26110,26153,26156,26159,26162,26205,26248,26251,26254,26257,26260,26263,26266,26269,26315],{"className":26066},[1003],[86,26068,26070,26073],{"className":26069},[1003],[86,26071,22],{"className":26072},[1003,1007],[86,26074,26076],{"className":26075},[1012],[86,26077,26079,26102],{"className":26078},[1016,3836],[86,26080,26082,26099],{"className":26081},[1020],[86,26083,26085],{"className":26084,"style":6984},[1024],[86,26086,26087,26090],{"style":6987},[86,26088],{"className":26089,"style":1032},[1031],[86,26091,26093],{"className":26092},[1036,1037,1038,1039],[86,26094,26096],{"className":26095},[1003,1039],[86,26097,22729],{"className":26098},[1003,1039],[86,26100,3963],{"className":26101},[3962],[86,26103,26105],{"className":26104},[1020],[86,26106,26108],{"className":26107,"style":7006},[1024],[86,26109],{},[86,26111,26113,26116],{"className":26112},[1003],[86,26114,22736],{"className":26115},[1003,1007],[86,26117,26119],{"className":26118},[1012],[86,26120,26122,26145],{"className":26121},[1016,3836],[86,26123,26125,26142],{"className":26124},[1020],[86,26126,26128],{"className":26127,"style":6984},[1024],[86,26129,26130,26133],{"style":6987},[86,26131],{"className":26132,"style":1032},[1031],[86,26134,26136],{"className":26135},[1036,1037,1038,1039],[86,26137,26139],{"className":26138},[1003,1039],[86,26140,22751],{"className":26141},[1003,1039],[86,26143,3963],{"className":26144},[3962],[86,26146,26148],{"className":26147},[1020],[86,26149,26151],{"className":26150,"style":7006},[1024],[86,26152],{},[86,26154],{"className":26155,"style":5012},[3221],[86,26157,6565],{"className":26158},[5016],[86,26160],{"className":26161,"style":5012},[3221],[86,26163,26165,26168],{"className":26164},[1003],[86,26166,22],{"className":26167},[1003,1007],[86,26169,26171],{"className":26170},[1012],[86,26172,26174,26197],{"className":26173},[1016,3836],[86,26175,26177,26194],{"className":26176},[1020],[86,26178,26180],{"className":26179,"style":6984},[1024],[86,26181,26182,26185],{"style":6987},[86,26183],{"className":26184,"style":1032},[1031],[86,26186,26188],{"className":26187},[1036,1037,1038,1039],[86,26189,26191],{"className":26190},[1003,1039],[86,26192,22751],{"className":26193},[1003,1039],[86,26195,3963],{"className":26196},[3962],[86,26198,26200],{"className":26199},[1020],[86,26201,26203],{"className":26202,"style":7006},[1024],[86,26204],{},[86,26206,26208,26211],{"className":26207},[1003],[86,26209,22736],{"className":26210},[1003,1007],[86,26212,26214],{"className":26213},[1012],[86,26215,26217,26240],{"className":26216},[1016,3836],[86,26218,26220,26237],{"className":26219},[1020],[86,26221,26223],{"className":26222,"style":6984},[1024],[86,26224,26225,26228],{"style":6987},[86,26226],{"className":26227,"style":1032},[1031],[86,26229,26231],{"className":26230},[1036,1037,1038,1039],[86,26232,26234],{"className":26233},[1003,1039],[86,26235,22830],{"className":26236},[1003,1039],[86,26238,3963],{"className":26239},[3962],[86,26241,26243],{"className":26242},[1020],[86,26244,26246],{"className":26245,"style":7006},[1024],[86,26247],{},[86,26249],{"className":26250,"style":5012},[3221],[86,26252,6565],{"className":26253},[5016],[86,26255],{"className":26256,"style":5012},[3221],[86,26258,22766],{"className":26259},[7131],[86,26261],{"className":26262,"style":5012},[3221],[86,26264,6565],{"className":26265},[5016],[86,26267],{"className":26268,"style":5012},[3221],[86,26270,26272,26275],{"className":26271},[1003],[86,26273,22],{"className":26274},[1003,1007],[86,26276,26278],{"className":26277},[1012],[86,26279,26281,26307],{"className":26280},[1016,3836],[86,26282,26284,26304],{"className":26283},[1020],[86,26285,26287],{"className":26286,"style":6984},[1024],[86,26288,26289,26292],{"style":6987},[86,26290],{"className":26291,"style":1032},[1031],[86,26293,26295],{"className":26294},[1036,1037,1038,1039],[86,26296,26298,26301],{"className":26297},[1003,1039],[86,26299,802],{"className":26300},[1003,1039],[86,26302,6896],{"className":26303},[1003,1007,1039],[86,26305,3963],{"className":26306},[3962],[86,26308,26310],{"className":26309},[1020],[86,26311,26313],{"className":26312,"style":7006},[1024],[86,26314],{},[86,26316,26318,26321],{"className":26317},[1003],[86,26319,22736],{"className":26320},[1003,1007],[86,26322,26324],{"className":26323},[1012],[86,26325,26327,26353],{"className":26326},[1016,3836],[86,26328,26330,26350],{"className":26329},[1020],[86,26331,26333],{"className":26332,"style":6984},[1024],[86,26334,26335,26338],{"style":6987},[86,26336],{"className":26337,"style":1032},[1031],[86,26339,26341],{"className":26340},[1036,1037,1038,1039],[86,26342,26344,26347],{"className":26343},[1003,1039],[86,26345,6896],{"className":26346},[1003,1007,1039],[86,26348,980],{"className":26349},[1003,1039],[86,26351,3963],{"className":26352},[3962],[86,26354,26356],{"className":26355},[1020],[86,26357,26359],{"className":26358,"style":7006},[1024],[86,26360],{},[86,26362,26363,26366],{"style":23235},[86,26364],{"className":26365,"style":20103},[1031],[86,26367,26369,26412,26455,26458,26461,26464,26507,26550,26553,26556,26559,26562,26565,26568,26571,26617],{"className":26368},[1003],[86,26370,26372,26375],{"className":26371},[1003],[86,26373,22],{"className":26374},[1003,1007],[86,26376,26378],{"className":26377},[1012],[86,26379,26381,26404],{"className":26380},[1016,3836],[86,26382,26384,26401],{"className":26383},[1020],[86,26385,26387],{"className":26386,"style":6984},[1024],[86,26388,26389,26392],{"style":6987},[86,26390],{"className":26391,"style":1032},[1031],[86,26393,26395],{"className":26394},[1036,1037,1038,1039],[86,26396,26398],{"className":26397},[1003,1039],[86,26399,22809],{"className":26400},[1003,1039],[86,26402,3963],{"className":26403},[3962],[86,26405,26407],{"className":26406},[1020],[86,26408,26410],{"className":26409,"style":7006},[1024],[86,26411],{},[86,26413,26415,26418],{"className":26414},[1003],[86,26416,22736],{"className":26417},[1003,1007],[86,26419,26421],{"className":26420},[1012],[86,26422,26424,26447],{"className":26423},[1016,3836],[86,26425,26427,26444],{"className":26426},[1020],[86,26428,26430],{"className":26429,"style":6984},[1024],[86,26431,26432,26435],{"style":6987},[86,26433],{"className":26434,"style":1032},[1031],[86,26436,26438],{"className":26437},[1036,1037,1038,1039],[86,26439,26441],{"className":26440},[1003,1039],[86,26442,22751],{"className":26443},[1003,1039],[86,26445,3963],{"className":26446},[3962],[86,26448,26450],{"className":26449},[1020],[86,26451,26453],{"className":26452,"style":7006},[1024],[86,26454],{},[86,26456],{"className":26457,"style":5012},[3221],[86,26459,6565],{"className":26460},[5016],[86,26462],{"className":26463,"style":5012},[3221],[86,26465,26467,26470],{"className":26466},[1003],[86,26468,22],{"className":26469},[1003,1007],[86,26471,26473],{"className":26472},[1012],[86,26474,26476,26499],{"className":26475},[1016,3836],[86,26477,26479,26496],{"className":26478},[1020],[86,26480,26482],{"className":26481,"style":6984},[1024],[86,26483,26484,26487],{"style":6987},[86,26485],{"className":26486,"style":1032},[1031],[86,26488,26490],{"className":26489},[1036,1037,1038,1039],[86,26491,26493],{"className":26492},[1003,1039],[86,26494,22830],{"className":26495},[1003,1039],[86,26497,3963],{"className":26498},[3962],[86,26500,26502],{"className":26501},[1020],[86,26503,26505],{"className":26504,"style":7006},[1024],[86,26506],{},[86,26508,26510,26513],{"className":26509},[1003],[86,26511,22736],{"className":26512},[1003,1007],[86,26514,26516],{"className":26515},[1012],[86,26517,26519,26542],{"className":26518},[1016,3836],[86,26520,26522,26539],{"className":26521},[1020],[86,26523,26525],{"className":26524,"style":6984},[1024],[86,26526,26527,26530],{"style":6987},[86,26528],{"className":26529,"style":1032},[1031],[86,26531,26533],{"className":26532},[1036,1037,1038,1039],[86,26534,26536],{"className":26535},[1003,1039],[86,26537,22830],{"className":26538},[1003,1039],[86,26540,3963],{"className":26541},[3962],[86,26543,26545],{"className":26544},[1020],[86,26546,26548],{"className":26547,"style":7006},[1024],[86,26549],{},[86,26551],{"className":26552,"style":5012},[3221],[86,26554,6565],{"className":26555},[5016],[86,26557],{"className":26558,"style":5012},[3221],[86,26560,22766],{"className":26561},[7131],[86,26563],{"className":26564,"style":5012},[3221],[86,26566,6565],{"className":26567},[5016],[86,26569],{"className":26570,"style":5012},[3221],[86,26572,26574,26577],{"className":26573},[1003],[86,26575,22],{"className":26576},[1003,1007],[86,26578,26580],{"className":26579},[1012],[86,26581,26583,26609],{"className":26582},[1016,3836],[86,26584,26586,26606],{"className":26585},[1020],[86,26587,26589],{"className":26588,"style":6984},[1024],[86,26590,26591,26594],{"style":6987},[86,26592],{"className":26593,"style":1032},[1031],[86,26595,26597],{"className":26596},[1036,1037,1038,1039],[86,26598,26600,26603],{"className":26599},[1003,1039],[86,26601,980],{"className":26602},[1003,1039],[86,26604,6896],{"className":26605},[1003,1007,1039],[86,26607,3963],{"className":26608},[3962],[86,26610,26612],{"className":26611},[1020],[86,26613,26615],{"className":26614,"style":7006},[1024],[86,26616],{},[86,26618,26620,26623],{"className":26619},[1003],[86,26621,22736],{"className":26622},[1003,1007],[86,26624,26626],{"className":26625},[1012],[86,26627,26629,26655],{"className":26628},[1016,3836],[86,26630,26632,26652],{"className":26631},[1020],[86,26633,26635],{"className":26634,"style":6984},[1024],[86,26636,26637,26640],{"style":6987},[86,26638],{"className":26639,"style":1032},[1031],[86,26641,26643],{"className":26642},[1036,1037,1038,1039],[86,26644,26646,26649],{"className":26645},[1003,1039],[86,26647,6896],{"className":26648},[1003,1007,1039],[86,26650,980],{"className":26651},[1003,1039],[86,26653,3963],{"className":26654},[3962],[86,26656,26658],{"className":26657},[1020],[86,26659,26661],{"className":26660,"style":7006},[1024],[86,26662],{},[86,26664,26665,26668],{"style":23339},[86,26666],{"className":26667,"style":20103},[1031],[86,26669,26671],{"className":26670},[1003],[86,26672,26674,26677],{"className":26673},[1003],[86,26675,19959],{"className":26676},[1003],[86,26678],{"className":26679,"style":20141},[1003,20140],[86,26681,26682,26685],{"style":23357},[86,26683],{"className":26684,"style":20103},[1031],[86,26686,26688,26734,26777,26780,26783,26786,26832,26875,26878,26881,26884,26887,26890,26893,26896,26939],{"className":26687},[1003],[86,26689,26691,26694],{"className":26690},[1003],[86,26692,22],{"className":26693},[1003,1007],[86,26695,26697],{"className":26696},[1012],[86,26698,26700,26726],{"className":26699},[1016,3836],[86,26701,26703,26723],{"className":26702},[1020],[86,26704,26706],{"className":26705,"style":6984},[1024],[86,26707,26708,26711],{"style":6987},[86,26709],{"className":26710,"style":1032},[1031],[86,26712,26714],{"className":26713},[1036,1037,1038,1039],[86,26715,26717,26720],{"className":26716},[1003,1039],[86,26718,5940],{"className":26719},[1003,1007,1039],[86,26721,802],{"className":26722},[1003,1039],[86,26724,3963],{"className":26725},[3962],[86,26727,26729],{"className":26728},[1020],[86,26730,26732],{"className":26731,"style":7006},[1024],[86,26733],{},[86,26735,26737,26740],{"className":26736},[1003],[86,26738,22736],{"className":26739},[1003,1007],[86,26741,26743],{"className":26742},[1012],[86,26744,26746,26769],{"className":26745},[1016,3836],[86,26747,26749,26766],{"className":26748},[1020],[86,26750,26752],{"className":26751,"style":6984},[1024],[86,26753,26754,26757],{"style":6987},[86,26755],{"className":26756,"style":1032},[1031],[86,26758,26760],{"className":26759},[1036,1037,1038,1039],[86,26761,26763],{"className":26762},[1003,1039],[86,26764,22751],{"className":26765},[1003,1039],[86,26767,3963],{"className":26768},[3962],[86,26770,26772],{"className":26771},[1020],[86,26773,26775],{"className":26774,"style":7006},[1024],[86,26776],{},[86,26778],{"className":26779,"style":5012},[3221],[86,26781,6565],{"className":26782},[5016],[86,26784],{"className":26785,"style":5012},[3221],[86,26787,26789,26792],{"className":26788},[1003],[86,26790,22],{"className":26791},[1003,1007],[86,26793,26795],{"className":26794},[1012],[86,26796,26798,26824],{"className":26797},[1016,3836],[86,26799,26801,26821],{"className":26800},[1020],[86,26802,26804],{"className":26803,"style":6984},[1024],[86,26805,26806,26809],{"style":6987},[86,26807],{"className":26808,"style":1032},[1031],[86,26810,26812],{"className":26811},[1036,1037,1038,1039],[86,26813,26815,26818],{"className":26814},[1003,1039],[86,26816,5940],{"className":26817},[1003,1007,1039],[86,26819,980],{"className":26820},[1003,1039],[86,26822,3963],{"className":26823},[3962],[86,26825,26827],{"className":26826},[1020],[86,26828,26830],{"className":26829,"style":7006},[1024],[86,26831],{},[86,26833,26835,26838],{"className":26834},[1003],[86,26836,22736],{"className":26837},[1003,1007],[86,26839,26841],{"className":26840},[1012],[86,26842,26844,26867],{"className":26843},[1016,3836],[86,26845,26847,26864],{"className":26846},[1020],[86,26848,26850],{"className":26849,"style":6984},[1024],[86,26851,26852,26855],{"style":6987},[86,26853],{"className":26854,"style":1032},[1031],[86,26856,26858],{"className":26857},[1036,1037,1038,1039],[86,26859,26861],{"className":26860},[1003,1039],[86,26862,22830],{"className":26863},[1003,1039],[86,26865,3963],{"className":26866},[3962],[86,26868,26870],{"className":26869},[1020],[86,26871,26873],{"className":26872,"style":7006},[1024],[86,26874],{},[86,26876],{"className":26877,"style":5012},[3221],[86,26879,6565],{"className":26880},[5016],[86,26882],{"className":26883,"style":5012},[3221],[86,26885,22766],{"className":26886},[7131],[86,26888],{"className":26889,"style":5012},[3221],[86,26891,6565],{"className":26892},[5016],[86,26894],{"className":26895,"style":5012},[3221],[86,26897,26899,26902],{"className":26898},[1003],[86,26900,22],{"className":26901},[1003,1007],[86,26903,26905],{"className":26904},[1012],[86,26906,26908,26931],{"className":26907},[1016,3836],[86,26909,26911,26928],{"className":26910},[1020],[86,26912,26914],{"className":26913,"style":7171},[1024],[86,26915,26916,26919],{"style":6987},[86,26917],{"className":26918,"style":1032},[1031],[86,26920,26922],{"className":26921},[1036,1037,1038,1039],[86,26923,26925],{"className":26924},[1003,1039],[86,26926,978],{"className":26927},[1003,1007,1039],[86,26929,3963],{"className":26930},[3962],[86,26932,26934],{"className":26933},[1020],[86,26935,26937],{"className":26936,"style":7006},[1024],[86,26938],{},[86,26940,26942,26945],{"className":26941},[1003],[86,26943,22736],{"className":26944},[1003,1007],[86,26946,26948],{"className":26947},[1012],[86,26949,26951,26977],{"className":26950},[1016,3836],[86,26952,26954,26974],{"className":26953},[1020],[86,26955,26957],{"className":26956,"style":6984},[1024],[86,26958,26959,26962],{"style":6987},[86,26960],{"className":26961,"style":1032},[1031],[86,26963,26965],{"className":26964},[1036,1037,1038,1039],[86,26966,26968,26971],{"className":26967},[1003,1039],[86,26969,6896],{"className":26970},[1003,1007,1039],[86,26972,980],{"className":26973},[1003,1039],[86,26975,3963],{"className":26976},[3962],[86,26978,26980],{"className":26979},[1020],[86,26981,26983],{"className":26982,"style":7006},[1024],[86,26984],{},[86,26986,3963],{"className":26987},[3962],[86,26989,26991],{"className":26990},[1020],[86,26992,26994],{"className":26993,"style":23474},[1024],[86,26995],{},[86,26997],{"className":26998,"style":20158},[20157],[86,27000],{"className":27001,"style":20158},[20157],[86,27003,27005],{"className":27004},[20086],[86,27006,27008,27061],{"className":27007},[1016,3836],[86,27009,27011,27058],{"className":27010},[1020],[86,27012,27014,27025,27036,27047],{"className":27013,"style":23128},[1024],[86,27015,27016,27019],{"style":23858},[86,27017],{"className":27018,"style":23862},[1031],[86,27020,27022],{"className":27021},[1003],[86,27023,22766],{"className":27024},[7131],[86,27026,27027,27030],{"style":23871},[86,27028],{"className":27029,"style":23862},[1031],[86,27031,27033],{"className":27032},[1003],[86,27034,22766],{"className":27035},[7131],[86,27037,27038,27041],{"style":23883},[86,27039],{"className":27040,"style":23862},[1031],[86,27042,27044],{"className":27043},[1003],[86,27045,22905],{"className":27046},[7131],[86,27048,27049,27052],{"style":23895},[86,27050],{"className":27051,"style":23862},[1031],[86,27053,27055],{"className":27054},[1003],[86,27056,22766],{"className":27057},[7131],[86,27059,3963],{"className":27060},[3962],[86,27062,27064],{"className":27063},[1020],[86,27065,27067],{"className":27066,"style":23474},[1024],[86,27068],{},[86,27070],{"className":27071,"style":20158},[20157],[86,27073],{"className":27074,"style":20158},[20157],[86,27076,27078],{"className":27077},[20086],[86,27079,27081,28034],{"className":27080},[1016,3836],[86,27082,27084,28031],{"className":27083},[1020],[86,27085,27087,27395,27703,27720],{"className":27086,"style":23128},[1024],[86,27088,27089,27092],{"style":23131},[86,27090],{"className":27091,"style":20103},[1031],[86,27093,27095,27138,27184,27187,27190,27193,27236,27282,27285,27288,27291,27294,27297,27300,27303,27349],{"className":27094},[1003],[86,27096,27098,27101],{"className":27097},[1003],[86,27099,22],{"className":27100},[1003,1007],[86,27102,27104],{"className":27103},[1012],[86,27105,27107,27130],{"className":27106},[1016,3836],[86,27108,27110,27127],{"className":27109},[1020],[86,27111,27113],{"className":27112,"style":6984},[1024],[86,27114,27115,27118],{"style":6987},[86,27116],{"className":27117,"style":1032},[1031],[86,27119,27121],{"className":27120},[1036,1037,1038,1039],[86,27122,27124],{"className":27123},[1003,1039],[86,27125,22729],{"className":27126},[1003,1039],[86,27128,3963],{"className":27129},[3962],[86,27131,27133],{"className":27132},[1020],[86,27134,27136],{"className":27135,"style":7006},[1024],[86,27137],{},[86,27139,27141,27144],{"className":27140},[1003],[86,27142,22736],{"className":27143},[1003,1007],[86,27145,27147],{"className":27146},[1012],[86,27148,27150,27176],{"className":27149},[1016,3836],[86,27151,27153,27173],{"className":27152},[1020],[86,27154,27156],{"className":27155,"style":6984},[1024],[86,27157,27158,27161],{"style":6987},[86,27159],{"className":27160,"style":1032},[1031],[86,27162,27164],{"className":27163},[1036,1037,1038,1039],[86,27165,27167,27170],{"className":27166},[1003,1039],[86,27168,802],{"className":27169},[1003,1039],[86,27171,12],{"className":27172},[1003,1007,1039],[86,27174,3963],{"className":27175},[3962],[86,27177,27179],{"className":27178},[1020],[86,27180,27182],{"className":27181,"style":10443},[1024],[86,27183],{},[86,27185],{"className":27186,"style":5012},[3221],[86,27188,6565],{"className":27189},[5016],[86,27191],{"className":27192,"style":5012},[3221],[86,27194,27196,27199],{"className":27195},[1003],[86,27197,22],{"className":27198},[1003,1007],[86,27200,27202],{"className":27201},[1012],[86,27203,27205,27228],{"className":27204},[1016,3836],[86,27206,27208,27225],{"className":27207},[1020],[86,27209,27211],{"className":27210,"style":6984},[1024],[86,27212,27213,27216],{"style":6987},[86,27214],{"className":27215,"style":1032},[1031],[86,27217,27219],{"className":27218},[1036,1037,1038,1039],[86,27220,27222],{"className":27221},[1003,1039],[86,27223,22751],{"className":27224},[1003,1039],[86,27226,3963],{"className":27227},[3962],[86,27229,27231],{"className":27230},[1020],[86,27232,27234],{"className":27233,"style":7006},[1024],[86,27235],{},[86,27237,27239,27242],{"className":27238},[1003],[86,27240,22736],{"className":27241},[1003,1007],[86,27243,27245],{"className":27244},[1012],[86,27246,27248,27274],{"className":27247},[1016,3836],[86,27249,27251,27271],{"className":27250},[1020],[86,27252,27254],{"className":27253,"style":6984},[1024],[86,27255,27256,27259],{"style":6987},[86,27257],{"className":27258,"style":1032},[1031],[86,27260,27262],{"className":27261},[1036,1037,1038,1039],[86,27263,27265,27268],{"className":27264},[1003,1039],[86,27266,980],{"className":27267},[1003,1039],[86,27269,12],{"className":27270},[1003,1007,1039],[86,27272,3963],{"className":27273},[3962],[86,27275,27277],{"className":27276},[1020],[86,27278,27280],{"className":27279,"style":10443},[1024],[86,27281],{},[86,27283],{"className":27284,"style":5012},[3221],[86,27286,6565],{"className":27287},[5016],[86,27289],{"className":27290,"style":5012},[3221],[86,27292,22766],{"className":27293},[7131],[86,27295],{"className":27296,"style":5012},[3221],[86,27298,6565],{"className":27299},[5016],[86,27301],{"className":27302,"style":5012},[3221],[86,27304,27306,27309],{"className":27305},[1003],[86,27307,22],{"className":27308},[1003,1007],[86,27310,27312],{"className":27311},[1012],[86,27313,27315,27341],{"className":27314},[1016,3836],[86,27316,27318,27338],{"className":27317},[1020],[86,27319,27321],{"className":27320,"style":6984},[1024],[86,27322,27323,27326],{"style":6987},[86,27324],{"className":27325,"style":1032},[1031],[86,27327,27329],{"className":27328},[1036,1037,1038,1039],[86,27330,27332,27335],{"className":27331},[1003,1039],[86,27333,802],{"className":27334},[1003,1039],[86,27336,6896],{"className":27337},[1003,1007,1039],[86,27339,3963],{"className":27340},[3962],[86,27342,27344],{"className":27343},[1020],[86,27345,27347],{"className":27346,"style":7006},[1024],[86,27348],{},[86,27350,27352,27355],{"className":27351},[1003],[86,27353,22736],{"className":27354},[1003,1007],[86,27356,27358],{"className":27357},[1012],[86,27359,27361,27387],{"className":27360},[1016,3836],[86,27362,27364,27384],{"className":27363},[1020],[86,27365,27367],{"className":27366,"style":7171},[1024],[86,27368,27369,27372],{"style":6987},[86,27370],{"className":27371,"style":1032},[1031],[86,27373,27375],{"className":27374},[1036,1037,1038,1039],[86,27376,27378,27381],{"className":27377},[1003,1039],[86,27379,6896],{"className":27380},[1003,1007,1039],[86,27382,12],{"className":27383},[1003,1007,1039],[86,27385,3963],{"className":27386},[3962],[86,27388,27390],{"className":27389},[1020],[86,27391,27393],{"className":27392,"style":10443},[1024],[86,27394],{},[86,27396,27397,27400],{"style":23235},[86,27398],{"className":27399,"style":20103},[1031],[86,27401,27403,27446,27492,27495,27498,27501,27544,27590,27593,27596,27599,27602,27605,27608,27611,27657],{"className":27402},[1003],[86,27404,27406,27409],{"className":27405},[1003],[86,27407,22],{"className":27408},[1003,1007],[86,27410,27412],{"className":27411},[1012],[86,27413,27415,27438],{"className":27414},[1016,3836],[86,27416,27418,27435],{"className":27417},[1020],[86,27419,27421],{"className":27420,"style":6984},[1024],[86,27422,27423,27426],{"style":6987},[86,27424],{"className":27425,"style":1032},[1031],[86,27427,27429],{"className":27428},[1036,1037,1038,1039],[86,27430,27432],{"className":27431},[1003,1039],[86,27433,22809],{"className":27434},[1003,1039],[86,27436,3963],{"className":27437},[3962],[86,27439,27441],{"className":27440},[1020],[86,27442,27444],{"className":27443,"style":7006},[1024],[86,27445],{},[86,27447,27449,27452],{"className":27448},[1003],[86,27450,22736],{"className":27451},[1003,1007],[86,27453,27455],{"className":27454},[1012],[86,27456,27458,27484],{"className":27457},[1016,3836],[86,27459,27461,27481],{"className":27460},[1020],[86,27462,27464],{"className":27463,"style":6984},[1024],[86,27465,27466,27469],{"style":6987},[86,27467],{"className":27468,"style":1032},[1031],[86,27470,27472],{"className":27471},[1036,1037,1038,1039],[86,27473,27475,27478],{"className":27474},[1003,1039],[86,27476,802],{"className":27477},[1003,1039],[86,27479,12],{"className":27480},[1003,1007,1039],[86,27482,3963],{"className":27483},[3962],[86,27485,27487],{"className":27486},[1020],[86,27488,27490],{"className":27489,"style":10443},[1024],[86,27491],{},[86,27493],{"className":27494,"style":5012},[3221],[86,27496,6565],{"className":27497},[5016],[86,27499],{"className":27500,"style":5012},[3221],[86,27502,27504,27507],{"className":27503},[1003],[86,27505,22],{"className":27506},[1003,1007],[86,27508,27510],{"className":27509},[1012],[86,27511,27513,27536],{"className":27512},[1016,3836],[86,27514,27516,27533],{"className":27515},[1020],[86,27517,27519],{"className":27518,"style":6984},[1024],[86,27520,27521,27524],{"style":6987},[86,27522],{"className":27523,"style":1032},[1031],[86,27525,27527],{"className":27526},[1036,1037,1038,1039],[86,27528,27530],{"className":27529},[1003,1039],[86,27531,22830],{"className":27532},[1003,1039],[86,27534,3963],{"className":27535},[3962],[86,27537,27539],{"className":27538},[1020],[86,27540,27542],{"className":27541,"style":7006},[1024],[86,27543],{},[86,27545,27547,27550],{"className":27546},[1003],[86,27548,22736],{"className":27549},[1003,1007],[86,27551,27553],{"className":27552},[1012],[86,27554,27556,27582],{"className":27555},[1016,3836],[86,27557,27559,27579],{"className":27558},[1020],[86,27560,27562],{"className":27561,"style":6984},[1024],[86,27563,27564,27567],{"style":6987},[86,27565],{"className":27566,"style":1032},[1031],[86,27568,27570],{"className":27569},[1036,1037,1038,1039],[86,27571,27573,27576],{"className":27572},[1003,1039],[86,27574,980],{"className":27575},[1003,1039],[86,27577,12],{"className":27578},[1003,1007,1039],[86,27580,3963],{"className":27581},[3962],[86,27583,27585],{"className":27584},[1020],[86,27586,27588],{"className":27587,"style":10443},[1024],[86,27589],{},[86,27591],{"className":27592,"style":5012},[3221],[86,27594,6565],{"className":27595},[5016],[86,27597],{"className":27598,"style":5012},[3221],[86,27600,22766],{"className":27601},[7131],[86,27603],{"className":27604,"style":5012},[3221],[86,27606,6565],{"className":27607},[5016],[86,27609],{"className":27610,"style":5012},[3221],[86,27612,27614,27617],{"className":27613},[1003],[86,27615,22],{"className":27616},[1003,1007],[86,27618,27620],{"className":27619},[1012],[86,27621,27623,27649],{"className":27622},[1016,3836],[86,27624,27626,27646],{"className":27625},[1020],[86,27627,27629],{"className":27628,"style":6984},[1024],[86,27630,27631,27634],{"style":6987},[86,27632],{"className":27633,"style":1032},[1031],[86,27635,27637],{"className":27636},[1036,1037,1038,1039],[86,27638,27640,27643],{"className":27639},[1003,1039],[86,27641,980],{"className":27642},[1003,1039],[86,27644,6896],{"className":27645},[1003,1007,1039],[86,27647,3963],{"className":27648},[3962],[86,27650,27652],{"className":27651},[1020],[86,27653,27655],{"className":27654,"style":7006},[1024],[86,27656],{},[86,27658,27660,27663],{"className":27659},[1003],[86,27661,22736],{"className":27662},[1003,1007],[86,27664,27666],{"className":27665},[1012],[86,27667,27669,27695],{"className":27668},[1016,3836],[86,27670,27672,27692],{"className":27671},[1020],[86,27673,27675],{"className":27674,"style":7171},[1024],[86,27676,27677,27680],{"style":6987},[86,27678],{"className":27679,"style":1032},[1031],[86,27681,27683],{"className":27682},[1036,1037,1038,1039],[86,27684,27686,27689],{"className":27685},[1003,1039],[86,27687,6896],{"className":27688},[1003,1007,1039],[86,27690,12],{"className":27691},[1003,1007,1039],[86,27693,3963],{"className":27694},[3962],[86,27696,27698],{"className":27697},[1020],[86,27699,27701],{"className":27700,"style":10443},[1024],[86,27702],{},[86,27704,27705,27708],{"style":23339},[86,27706],{"className":27707,"style":20103},[1031],[86,27709,27711],{"className":27710},[1003],[86,27712,27714,27717],{"className":27713},[1003],[86,27715,19959],{"className":27716},[1003],[86,27718],{"className":27719,"style":20141},[1003,20140],[86,27721,27722,27725],{"style":23357},[86,27723],{"className":27724,"style":20103},[1031],[86,27726,27728,27774,27820,27823,27826,27829,27875,27921,27924,27927,27930,27933,27936,27939,27942,27985],{"className":27727},[1003],[86,27729,27731,27734],{"className":27730},[1003],[86,27732,22],{"className":27733},[1003,1007],[86,27735,27737],{"className":27736},[1012],[86,27738,27740,27766],{"className":27739},[1016,3836],[86,27741,27743,27763],{"className":27742},[1020],[86,27744,27746],{"className":27745,"style":6984},[1024],[86,27747,27748,27751],{"style":6987},[86,27749],{"className":27750,"style":1032},[1031],[86,27752,27754],{"className":27753},[1036,1037,1038,1039],[86,27755,27757,27760],{"className":27756},[1003,1039],[86,27758,5940],{"className":27759},[1003,1007,1039],[86,27761,802],{"className":27762},[1003,1039],[86,27764,3963],{"className":27765},[3962],[86,27767,27769],{"className":27768},[1020],[86,27770,27772],{"className":27771,"style":7006},[1024],[86,27773],{},[86,27775,27777,27780],{"className":27776},[1003],[86,27778,22736],{"className":27779},[1003,1007],[86,27781,27783],{"className":27782},[1012],[86,27784,27786,27812],{"className":27785},[1016,3836],[86,27787,27789,27809],{"className":27788},[1020],[86,27790,27792],{"className":27791,"style":6984},[1024],[86,27793,27794,27797],{"style":6987},[86,27795],{"className":27796,"style":1032},[1031],[86,27798,27800],{"className":27799},[1036,1037,1038,1039],[86,27801,27803,27806],{"className":27802},[1003,1039],[86,27804,802],{"className":27805},[1003,1039],[86,27807,12],{"className":27808},[1003,1007,1039],[86,27810,3963],{"className":27811},[3962],[86,27813,27815],{"className":27814},[1020],[86,27816,27818],{"className":27817,"style":10443},[1024],[86,27819],{},[86,27821],{"className":27822,"style":5012},[3221],[86,27824,6565],{"className":27825},[5016],[86,27827],{"className":27828,"style":5012},[3221],[86,27830,27832,27835],{"className":27831},[1003],[86,27833,22],{"className":27834},[1003,1007],[86,27836,27838],{"className":27837},[1012],[86,27839,27841,27867],{"className":27840},[1016,3836],[86,27842,27844,27864],{"className":27843},[1020],[86,27845,27847],{"className":27846,"style":6984},[1024],[86,27848,27849,27852],{"style":6987},[86,27850],{"className":27851,"style":1032},[1031],[86,27853,27855],{"className":27854},[1036,1037,1038,1039],[86,27856,27858,27861],{"className":27857},[1003,1039],[86,27859,5940],{"className":27860},[1003,1007,1039],[86,27862,980],{"className":27863},[1003,1039],[86,27865,3963],{"className":27866},[3962],[86,27868,27870],{"className":27869},[1020],[86,27871,27873],{"className":27872,"style":7006},[1024],[86,27874],{},[86,27876,27878,27881],{"className":27877},[1003],[86,27879,22736],{"className":27880},[1003,1007],[86,27882,27884],{"className":27883},[1012],[86,27885,27887,27913],{"className":27886},[1016,3836],[86,27888,27890,27910],{"className":27889},[1020],[86,27891,27893],{"className":27892,"style":6984},[1024],[86,27894,27895,27898],{"style":6987},[86,27896],{"className":27897,"style":1032},[1031],[86,27899,27901],{"className":27900},[1036,1037,1038,1039],[86,27902,27904,27907],{"className":27903},[1003,1039],[86,27905,980],{"className":27906},[1003,1039],[86,27908,12],{"className":27909},[1003,1007,1039],[86,27911,3963],{"className":27912},[3962],[86,27914,27916],{"className":27915},[1020],[86,27917,27919],{"className":27918,"style":10443},[1024],[86,27920],{},[86,27922],{"className":27923,"style":5012},[3221],[86,27925,6565],{"className":27926},[5016],[86,27928],{"className":27929,"style":5012},[3221],[86,27931,22766],{"className":27932},[7131],[86,27934],{"className":27935,"style":5012},[3221],[86,27937,6565],{"className":27938},[5016],[86,27940],{"className":27941,"style":5012},[3221],[86,27943,27945,27948],{"className":27944},[1003],[86,27946,22],{"className":27947},[1003,1007],[86,27949,27951],{"className":27950},[1012],[86,27952,27954,27977],{"className":27953},[1016,3836],[86,27955,27957,27974],{"className":27956},[1020],[86,27958,27960],{"className":27959,"style":7171},[1024],[86,27961,27962,27965],{"style":6987},[86,27963],{"className":27964,"style":1032},[1031],[86,27966,27968],{"className":27967},[1036,1037,1038,1039],[86,27969,27971],{"className":27970},[1003,1039],[86,27972,978],{"className":27973},[1003,1007,1039],[86,27975,3963],{"className":27976},[3962],[86,27978,27980],{"className":27979},[1020],[86,27981,27983],{"className":27982,"style":7006},[1024],[86,27984],{},[86,27986,27988,27991],{"className":27987},[1003],[86,27989,22736],{"className":27990},[1003,1007],[86,27992,27994],{"className":27993},[1012],[86,27995,27997,28023],{"className":27996},[1016,3836],[86,27998,28000,28020],{"className":27999},[1020],[86,28001,28003],{"className":28002,"style":7171},[1024],[86,28004,28005,28008],{"style":6987},[86,28006],{"className":28007,"style":1032},[1031],[86,28009,28011],{"className":28010},[1036,1037,1038,1039],[86,28012,28014,28017],{"className":28013},[1003,1039],[86,28015,6896],{"className":28016},[1003,1007,1039],[86,28018,12],{"className":28019},[1003,1007,1039],[86,28021,3963],{"className":28022},[3962],[86,28024,28026],{"className":28025},[1020],[86,28027,28029],{"className":28028,"style":10443},[1024],[86,28030],{},[86,28032,3963],{"className":28033},[3962],[86,28035,28037],{"className":28036},[1020],[86,28038,28040],{"className":28039,"style":23474},[1024],[86,28041],{},[86,28043,28045],{"className":28044},[3356],[86,28046,28048],{"className":28047},[10232,20036],[86,28049,28051,28071],{"className":28050},[1016,3836],[86,28052,28054,28068],{"className":28053},[1020],[86,28055,28057],{"className":28056,"style":23080},[1024],[86,28058,28059,28062],{"style":23083},[86,28060],{"className":28061,"style":23087},[1031],[86,28063,28064],{"style":23090},[10150,28065,28066],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,28067],{"d":24309},[86,28069,3963],{"className":28070},[3962],[86,28072,28074],{"className":28073},[1020],[86,28075,28077],{"className":28076,"style":23107},[1024],[86,28078],{},[30,28080,28081],{},[33,28082,28083,28086],{},[122,28084,28085],{},"Transposición",": Se intercambian las filas por las columnas de una matriz.",[86,28088,28090],{"className":28089},[3173],[86,28091,28093,28299],{"className":28092},[955],[86,28094,28096],{"className":28095},[959],[961,28097,28098],{"xmlns":963,"display":3182},[965,28099,28100,28296],{},[968,28101,28102,28108,28110],{},[971,28103,28104,28106],{},[974,28105,3743],{"mathvariant":19893},[974,28107,3489],{},[3191,28109,258],{},[968,28111,28112,28114,28294],{},[3191,28113,572],{"fence":990},[19901,28115,28116,28158,28200,28244],{"rowspacing":19903,"columnalign":22714,"columnspacing":19905},[19907,28117,28118,28128,28138,28144],{},[19910,28119,28120],{},[19913,28121,28122],{"scriptlevel":2553,"displaystyle":3295},[6849,28123,28124,28126],{},[974,28125,22],{},[978,28127,22729],{},[19910,28129,28130],{},[19913,28131,28132],{"scriptlevel":2553,"displaystyle":3295},[6849,28133,28134,28136],{},[974,28135,22],{},[978,28137,22809],{},[19910,28139,28140],{},[19913,28141,28142],{"scriptlevel":2553,"displaystyle":3295},[3191,28143,22766],{"lspace":19963,"rspace":19963},[19910,28145,28146],{},[19913,28147,28148],{"scriptlevel":2553,"displaystyle":3295},[6849,28149,28150,28152],{},[974,28151,22],{},[968,28153,28154,28156],{},[974,28155,5940],{},[978,28157,802],{},[19907,28159,28160,28170,28180,28186],{},[19910,28161,28162],{},[19913,28163,28164],{"scriptlevel":2553,"displaystyle":3295},[6849,28165,28166,28168],{},[974,28167,22],{},[978,28169,22751],{},[19910,28171,28172],{},[19913,28173,28174],{"scriptlevel":2553,"displaystyle":3295},[6849,28175,28176,28178],{},[974,28177,22],{},[978,28179,22830],{},[19910,28181,28182],{},[19913,28183,28184],{"scriptlevel":2553,"displaystyle":3295},[3191,28185,22766],{"lspace":19963,"rspace":19963},[19910,28187,28188],{},[19913,28189,28190],{"scriptlevel":2553,"displaystyle":3295},[6849,28191,28192,28194],{},[974,28193,22],{},[968,28195,28196,28198],{},[974,28197,5940],{},[978,28199,980],{},[19907,28201,28202,28214,28226,28232],{},[19910,28203,28204],{},[19913,28205,28206],{"scriptlevel":2553,"displaystyle":3295},[968,28207,28208,28210],{},[974,28209,19959],{"mathvariant":4327},[19961,28211,28212],{"height":19963,"voffset":19963},[3221,28213],{"mathbackground":19966,"width":19963,"height":19967},[19910,28215,28216],{},[19913,28217,28218],{"scriptlevel":2553,"displaystyle":3295},[968,28219,28220,28222],{},[974,28221,19959],{"mathvariant":4327},[19961,28223,28224],{"height":19963,"voffset":19963},[3221,28225],{"mathbackground":19966,"width":19963,"height":19967},[19910,28227,28228],{},[19913,28229,28230],{"scriptlevel":2553,"displaystyle":3295},[3191,28231,22905],{"lspace":19963,"rspace":19963},[19910,28233,28234],{},[19913,28235,28236],{"scriptlevel":2553,"displaystyle":3295},[968,28237,28238,28240],{},[974,28239,19959],{"mathvariant":4327},[19961,28241,28242],{"height":19963,"voffset":19963},[3221,28243],{"mathbackground":19966,"width":19963,"height":19967},[19907,28245,28246,28260,28274,28280],{},[19910,28247,28248],{},[19913,28249,28250],{"scriptlevel":2553,"displaystyle":3295},[6849,28251,28252,28254],{},[974,28253,22],{},[968,28255,28256,28258],{},[978,28257,802],{},[974,28259,12],{},[19910,28261,28262],{},[19913,28263,28264],{"scriptlevel":2553,"displaystyle":3295},[6849,28265,28266,28268],{},[974,28267,22],{},[968,28269,28270,28272],{},[978,28271,980],{},[974,28273,12],{},[19910,28275,28276],{},[19913,28277,28278],{"scriptlevel":2553,"displaystyle":3295},[3191,28279,22766],{"lspace":19963,"rspace":19963},[19910,28281,28282],{},[19913,28283,28284],{"scriptlevel":2553,"displaystyle":3295},[6849,28285,28286,28288],{},[974,28287,22],{},[968,28289,28290,28292],{},[974,28291,5940],{},[974,28293,12],{},[3191,28295,585],{"fence":990},[982,28297,28298],{"encoding":984},"\\mathbf{A}^T =\n\\begin{bmatrix}\na_{11} & a_{21} & \\cdots & a_{m1} \\\\\na_{12} & a_{22} & \\cdots & a_{m2} \\\\\n\\vdots & \\vdots & \\ddots & \\vdots \\\\\na_{1p} & a_{2p} & \\cdots & a_{mp} \\\\\n\\end{bmatrix}",[86,28300,28302,28346],{"className":28301,"ariaHidden":990},[989],[86,28303,28305,28308,28337,28340,28343],{"className":28304},[994],[86,28306],{"className":28307,"style":3525},[998],[86,28309,28311,28314],{"className":28310},[1003],[86,28312,3743],{"className":28313},[1003,20010],[86,28315,28317],{"className":28316},[1012],[86,28318,28320],{"className":28319},[1016],[86,28321,28323],{"className":28322},[1020],[86,28324,28326],{"className":28325,"style":3525},[1024],[86,28327,28328,28331],{"style":3258},[86,28329],{"className":28330,"style":1032},[1031],[86,28332,28334],{"className":28333},[1036,1037,1038,1039],[86,28335,3489],{"className":28336,"style":3537},[1003,1007,1039],[86,28338],{"className":28339,"style":3222},[3221],[86,28341,258],{"className":28342},[3226],[86,28344],{"className":28345,"style":3222},[3221],[86,28347,28349,28352],{"className":28348},[994],[86,28350],{"className":28351,"style":23061},[998],[86,28353,28355,28392,29077],{"className":28354},[7131],[86,28356,28358],{"className":28357},[3320],[86,28359,28361],{"className":28360},[10232,20036],[86,28362,28364,28384],{"className":28363},[1016,3836],[86,28365,28367,28381],{"className":28366},[1020],[86,28368,28370],{"className":28369,"style":23080},[1024],[86,28371,28372,28375],{"style":23083},[86,28373],{"className":28374,"style":23087},[1031],[86,28376,28377],{"style":23090},[10150,28378,28379],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,28380],{"d":23097},[86,28382,3963],{"className":28383},[3962],[86,28385,28387],{"className":28386},[1020],[86,28388,28390],{"className":28389,"style":23107},[1024],[86,28391],{},[86,28393,28395],{"className":28394},[1003],[86,28396,28398,28594,28597,28600,28796,28799,28802,28869,28872,28875],{"className":28397},[19901],[86,28399,28401],{"className":28400},[20086],[86,28402,28404,28586],{"className":28403},[1016,3836],[86,28405,28407,28583],{"className":28406},[1020],[86,28408,28410,28461,28512,28529],{"className":28409,"style":23128},[1024],[86,28411,28412,28415],{"style":23131},[86,28413],{"className":28414,"style":20103},[1031],[86,28416,28418],{"className":28417},[1003],[86,28419,28421,28424],{"className":28420},[1003],[86,28422,22],{"className":28423},[1003,1007],[86,28425,28427],{"className":28426},[1012],[86,28428,28430,28453],{"className":28429},[1016,3836],[86,28431,28433,28450],{"className":28432},[1020],[86,28434,28436],{"className":28435,"style":6984},[1024],[86,28437,28438,28441],{"style":6987},[86,28439],{"className":28440,"style":1032},[1031],[86,28442,28444],{"className":28443},[1036,1037,1038,1039],[86,28445,28447],{"className":28446},[1003,1039],[86,28448,22729],{"className":28449},[1003,1039],[86,28451,3963],{"className":28452},[3962],[86,28454,28456],{"className":28455},[1020],[86,28457,28459],{"className":28458,"style":7006},[1024],[86,28460],{},[86,28462,28463,28466],{"style":23235},[86,28464],{"className":28465,"style":20103},[1031],[86,28467,28469],{"className":28468},[1003],[86,28470,28472,28475],{"className":28471},[1003],[86,28473,22],{"className":28474},[1003,1007],[86,28476,28478],{"className":28477},[1012],[86,28479,28481,28504],{"className":28480},[1016,3836],[86,28482,28484,28501],{"className":28483},[1020],[86,28485,28487],{"className":28486,"style":6984},[1024],[86,28488,28489,28492],{"style":6987},[86,28490],{"className":28491,"style":1032},[1031],[86,28493,28495],{"className":28494},[1036,1037,1038,1039],[86,28496,28498],{"className":28497},[1003,1039],[86,28499,22751],{"className":28500},[1003,1039],[86,28502,3963],{"className":28503},[3962],[86,28505,28507],{"className":28506},[1020],[86,28508,28510],{"className":28509,"style":7006},[1024],[86,28511],{},[86,28513,28514,28517],{"style":23339},[86,28515],{"className":28516,"style":20103},[1031],[86,28518,28520],{"className":28519},[1003],[86,28521,28523,28526],{"className":28522},[1003],[86,28524,19959],{"className":28525},[1003],[86,28527],{"className":28528,"style":20141},[1003,20140],[86,28530,28531,28534],{"style":23357},[86,28532],{"className":28533,"style":20103},[1031],[86,28535,28537],{"className":28536},[1003],[86,28538,28540,28543],{"className":28539},[1003],[86,28541,22],{"className":28542},[1003,1007],[86,28544,28546],{"className":28545},[1012],[86,28547,28549,28575],{"className":28548},[1016,3836],[86,28550,28552,28572],{"className":28551},[1020],[86,28553,28555],{"className":28554,"style":6984},[1024],[86,28556,28557,28560],{"style":6987},[86,28558],{"className":28559,"style":1032},[1031],[86,28561,28563],{"className":28562},[1036,1037,1038,1039],[86,28564,28566,28569],{"className":28565},[1003,1039],[86,28567,802],{"className":28568},[1003,1039],[86,28570,12],{"className":28571},[1003,1007,1039],[86,28573,3963],{"className":28574},[3962],[86,28576,28578],{"className":28577},[1020],[86,28579,28581],{"className":28580,"style":10443},[1024],[86,28582],{},[86,28584,3963],{"className":28585},[3962],[86,28587,28589],{"className":28588},[1020],[86,28590,28592],{"className":28591,"style":23474},[1024],[86,28593],{},[86,28595],{"className":28596,"style":20158},[20157],[86,28598],{"className":28599,"style":20158},[20157],[86,28601,28603],{"className":28602},[20086],[86,28604,28606,28788],{"className":28605},[1016,3836],[86,28607,28609,28785],{"className":28608},[1020],[86,28610,28612,28663,28714,28731],{"className":28611,"style":23128},[1024],[86,28613,28614,28617],{"style":23131},[86,28615],{"className":28616,"style":20103},[1031],[86,28618,28620],{"className":28619},[1003],[86,28621,28623,28626],{"className":28622},[1003],[86,28624,22],{"className":28625},[1003,1007],[86,28627,28629],{"className":28628},[1012],[86,28630,28632,28655],{"className":28631},[1016,3836],[86,28633,28635,28652],{"className":28634},[1020],[86,28636,28638],{"className":28637,"style":6984},[1024],[86,28639,28640,28643],{"style":6987},[86,28641],{"className":28642,"style":1032},[1031],[86,28644,28646],{"className":28645},[1036,1037,1038,1039],[86,28647,28649],{"className":28648},[1003,1039],[86,28650,22809],{"className":28651},[1003,1039],[86,28653,3963],{"className":28654},[3962],[86,28656,28658],{"className":28657},[1020],[86,28659,28661],{"className":28660,"style":7006},[1024],[86,28662],{},[86,28664,28665,28668],{"style":23235},[86,28666],{"className":28667,"style":20103},[1031],[86,28669,28671],{"className":28670},[1003],[86,28672,28674,28677],{"className":28673},[1003],[86,28675,22],{"className":28676},[1003,1007],[86,28678,28680],{"className":28679},[1012],[86,28681,28683,28706],{"className":28682},[1016,3836],[86,28684,28686,28703],{"className":28685},[1020],[86,28687,28689],{"className":28688,"style":6984},[1024],[86,28690,28691,28694],{"style":6987},[86,28692],{"className":28693,"style":1032},[1031],[86,28695,28697],{"className":28696},[1036,1037,1038,1039],[86,28698,28700],{"className":28699},[1003,1039],[86,28701,22830],{"className":28702},[1003,1039],[86,28704,3963],{"className":28705},[3962],[86,28707,28709],{"className":28708},[1020],[86,28710,28712],{"className":28711,"style":7006},[1024],[86,28713],{},[86,28715,28716,28719],{"style":23339},[86,28717],{"className":28718,"style":20103},[1031],[86,28720,28722],{"className":28721},[1003],[86,28723,28725,28728],{"className":28724},[1003],[86,28726,19959],{"className":28727},[1003],[86,28729],{"className":28730,"style":20141},[1003,20140],[86,28732,28733,28736],{"style":23357},[86,28734],{"className":28735,"style":20103},[1031],[86,28737,28739],{"className":28738},[1003],[86,28740,28742,28745],{"className":28741},[1003],[86,28743,22],{"className":28744},[1003,1007],[86,28746,28748],{"className":28747},[1012],[86,28749,28751,28777],{"className":28750},[1016,3836],[86,28752,28754,28774],{"className":28753},[1020],[86,28755,28757],{"className":28756,"style":6984},[1024],[86,28758,28759,28762],{"style":6987},[86,28760],{"className":28761,"style":1032},[1031],[86,28763,28765],{"className":28764},[1036,1037,1038,1039],[86,28766,28768,28771],{"className":28767},[1003,1039],[86,28769,980],{"className":28770},[1003,1039],[86,28772,12],{"className":28773},[1003,1007,1039],[86,28775,3963],{"className":28776},[3962],[86,28778,28780],{"className":28779},[1020],[86,28781,28783],{"className":28782,"style":10443},[1024],[86,28784],{},[86,28786,3963],{"className":28787},[3962],[86,28789,28791],{"className":28790},[1020],[86,28792,28794],{"className":28793,"style":23474},[1024],[86,28795],{},[86,28797],{"className":28798,"style":20158},[20157],[86,28800],{"className":28801,"style":20158},[20157],[86,28803,28805],{"className":28804},[20086],[86,28806,28808,28861],{"className":28807},[1016,3836],[86,28809,28811,28858],{"className":28810},[1020],[86,28812,28814,28825,28836,28847],{"className":28813,"style":23128},[1024],[86,28815,28816,28819],{"style":23858},[86,28817],{"className":28818,"style":23862},[1031],[86,28820,28822],{"className":28821},[1003],[86,28823,22766],{"className":28824},[7131],[86,28826,28827,28830],{"style":23871},[86,28828],{"className":28829,"style":23862},[1031],[86,28831,28833],{"className":28832},[1003],[86,28834,22766],{"className":28835},[7131],[86,28837,28838,28841],{"style":23883},[86,28839],{"className":28840,"style":23862},[1031],[86,28842,28844],{"className":28843},[1003],[86,28845,22905],{"className":28846},[7131],[86,28848,28849,28852],{"style":23895},[86,28850],{"className":28851,"style":23862},[1031],[86,28853,28855],{"className":28854},[1003],[86,28856,22766],{"className":28857},[7131],[86,28859,3963],{"className":28860},[3962],[86,28862,28864],{"className":28863},[1020],[86,28865,28867],{"className":28866,"style":23474},[1024],[86,28868],{},[86,28870],{"className":28871,"style":20158},[20157],[86,28873],{"className":28874,"style":20158},[20157],[86,28876,28878],{"className":28877},[20086],[86,28879,28881,29069],{"className":28880},[1016,3836],[86,28882,28884,29066],{"className":28883},[1020],[86,28885,28887,28941,28995,29012],{"className":28886,"style":23128},[1024],[86,28888,28889,28892],{"style":23131},[86,28890],{"className":28891,"style":20103},[1031],[86,28893,28895],{"className":28894},[1003],[86,28896,28898,28901],{"className":28897},[1003],[86,28899,22],{"className":28900},[1003,1007],[86,28902,28904],{"className":28903},[1012],[86,28905,28907,28933],{"className":28906},[1016,3836],[86,28908,28910,28930],{"className":28909},[1020],[86,28911,28913],{"className":28912,"style":6984},[1024],[86,28914,28915,28918],{"style":6987},[86,28916],{"className":28917,"style":1032},[1031],[86,28919,28921],{"className":28920},[1036,1037,1038,1039],[86,28922,28924,28927],{"className":28923},[1003,1039],[86,28925,5940],{"className":28926},[1003,1007,1039],[86,28928,802],{"className":28929},[1003,1039],[86,28931,3963],{"className":28932},[3962],[86,28934,28936],{"className":28935},[1020],[86,28937,28939],{"className":28938,"style":7006},[1024],[86,28940],{},[86,28942,28943,28946],{"style":23235},[86,28944],{"className":28945,"style":20103},[1031],[86,28947,28949],{"className":28948},[1003],[86,28950,28952,28955],{"className":28951},[1003],[86,28953,22],{"className":28954},[1003,1007],[86,28956,28958],{"className":28957},[1012],[86,28959,28961,28987],{"className":28960},[1016,3836],[86,28962,28964,28984],{"className":28963},[1020],[86,28965,28967],{"className":28966,"style":6984},[1024],[86,28968,28969,28972],{"style":6987},[86,28970],{"className":28971,"style":1032},[1031],[86,28973,28975],{"className":28974},[1036,1037,1038,1039],[86,28976,28978,28981],{"className":28977},[1003,1039],[86,28979,5940],{"className":28980},[1003,1007,1039],[86,28982,980],{"className":28983},[1003,1039],[86,28985,3963],{"className":28986},[3962],[86,28988,28990],{"className":28989},[1020],[86,28991,28993],{"className":28992,"style":7006},[1024],[86,28994],{},[86,28996,28997,29000],{"style":23339},[86,28998],{"className":28999,"style":20103},[1031],[86,29001,29003],{"className":29002},[1003],[86,29004,29006,29009],{"className":29005},[1003],[86,29007,19959],{"className":29008},[1003],[86,29010],{"className":29011,"style":20141},[1003,20140],[86,29013,29014,29017],{"style":23357},[86,29015],{"className":29016,"style":20103},[1031],[86,29018,29020],{"className":29019},[1003],[86,29021,29023,29026],{"className":29022},[1003],[86,29024,22],{"className":29025},[1003,1007],[86,29027,29029],{"className":29028},[1012],[86,29030,29032,29058],{"className":29031},[1016,3836],[86,29033,29035,29055],{"className":29034},[1020],[86,29036,29038],{"className":29037,"style":7171},[1024],[86,29039,29040,29043],{"style":6987},[86,29041],{"className":29042,"style":1032},[1031],[86,29044,29046],{"className":29045},[1036,1037,1038,1039],[86,29047,29049,29052],{"className":29048},[1003,1039],[86,29050,5940],{"className":29051},[1003,1007,1039],[86,29053,12],{"className":29054},[1003,1007,1039],[86,29056,3963],{"className":29057},[3962],[86,29059,29061],{"className":29060},[1020],[86,29062,29064],{"className":29063,"style":10443},[1024],[86,29065],{},[86,29067,3963],{"className":29068},[3962],[86,29070,29072],{"className":29071},[1020],[86,29073,29075],{"className":29074,"style":23474},[1024],[86,29076],{},[86,29078,29080],{"className":29079},[3356],[86,29081,29083],{"className":29082},[10232,20036],[86,29084,29086,29106],{"className":29085},[1016,3836],[86,29087,29089,29103],{"className":29088},[1020],[86,29090,29092],{"className":29091,"style":23080},[1024],[86,29093,29094,29097],{"style":23083},[86,29095],{"className":29096,"style":23087},[1031],[86,29098,29099],{"style":23090},[10150,29100,29101],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,29102],{"d":24309},[86,29104,3963],{"className":29105},[3962],[86,29107,29109],{"className":29108},[1020],[86,29110,29112],{"className":29111,"style":23107},[1024],[86,29113],{},[30,29115,29116],{},[33,29117,29118,29121],{},[122,29119,29120],{},"Inversa",": Se calcula la matriz inversa, que es útil para resolver sistemas de ecuaciones lineales.",[86,29123,29125],{"className":29124},[3173],[86,29126,29128,29158],{"className":29127},[955],[86,29129,29131],{"className":29130},[959],[961,29132,29133],{"xmlns":963,"display":3182},[965,29134,29135,29155],{},[968,29136,29137,29147,29149,29151,29153],{},[971,29138,29139,29141],{},[974,29140,3743],{"mathvariant":19893},[968,29142,29143,29145],{},[3191,29144,9864],{},[978,29146,802],{},[3191,29148,4975],{},[974,29150,3743],{"mathvariant":19893},[3191,29152,258],{},[974,29154,14076],{"mathvariant":19893},[982,29156,29157],{"encoding":984},"\\mathbf{A}^{-1} \\cdot \\mathbf{A} = \\mathbf{I}",[86,29159,29161,29211,29229],{"className":29160,"ariaHidden":990},[989],[86,29162,29164,29167,29202,29205,29208],{"className":29163},[994],[86,29165],{"className":29166,"style":3236},[998],[86,29168,29170,29173],{"className":29169},[1003],[86,29171,3743],{"className":29172},[1003,20010],[86,29174,29176],{"className":29175},[1012],[86,29177,29179],{"className":29178},[1016],[86,29180,29182],{"className":29181},[1020],[86,29183,29185],{"className":29184,"style":3236},[1024],[86,29186,29187,29190],{"style":3258},[86,29188],{"className":29189,"style":1032},[1031],[86,29191,29193],{"className":29192},[1036,1037,1038,1039],[86,29194,29196,29199],{"className":29195},[1003,1039],[86,29197,9864],{"className":29198},[1003,1039],[86,29200,802],{"className":29201},[1003,1039],[86,29203],{"className":29204,"style":5012},[3221],[86,29206,4975],{"className":29207},[5016],[86,29209],{"className":29210,"style":5012},[3221],[86,29212,29214,29217,29220,29223,29226],{"className":29213},[994],[86,29215],{"className":29216,"style":20006},[998],[86,29218,3743],{"className":29219},[1003,20010],[86,29221],{"className":29222,"style":3222},[3221],[86,29224,258],{"className":29225},[3226],[86,29227],{"className":29228,"style":3222},[3221],[86,29230,29232,29235],{"className":29231},[994],[86,29233],{"className":29234,"style":20006},[998],[86,29236,14076],{"className":29237},[1003,20010],[30,29239,29240],{},[33,29241,29242,29245],{},[122,29243,29244],{},"Descomposición",": Se descompone una matriz en factores más simples, como la descomposición en valores singulares (SVD) o la descomposición LU, lo que es útil para la reducción de dimensionalidad y la optimización de modelos.",[86,29247,29249],{"className":29248},[3173],[86,29250,29252,29280],{"className":29251},[955],[86,29253,29255],{"className":29254},[959],[961,29256,29257],{"xmlns":963,"display":3182},[965,29258,29259,29277],{},[968,29260,29261,29263,29265,29268,29271],{},[974,29262,3743],{"mathvariant":19893},[3191,29264,258],{},[974,29266,29267],{"mathvariant":19893},"U",[974,29269,29270],{"mathvariant":4327},"Σ",[971,29272,29273,29275],{},[974,29274,10593],{"mathvariant":19893},[974,29276,3489],{},[982,29278,29279],{"encoding":984},"\\mathbf{A} = \\mathbf{U} \\Sigma \\mathbf{V}^T",[86,29281,29283,29301],{"className":29282,"ariaHidden":990},[989],[86,29284,29286,29289,29292,29295,29298],{"className":29285},[994],[86,29287],{"className":29288,"style":20006},[998],[86,29290,3743],{"className":29291},[1003,20010],[86,29293],{"className":29294,"style":3222},[3221],[86,29296,258],{"className":29297},[3226],[86,29299],{"className":29300,"style":3222},[3221],[86,29302,29304,29307,29310,29313],{"className":29303},[994],[86,29305],{"className":29306,"style":3525},[998],[86,29308,29267],{"className":29309},[1003,20010],[86,29311,29270],{"className":29312},[1003],[86,29314,29316,29319],{"className":29315},[1003],[86,29317,10593],{"className":29318,"style":20401},[1003,20010],[86,29320,29322],{"className":29321},[1012],[86,29323,29325],{"className":29324},[1016],[86,29326,29328],{"className":29327},[1020],[86,29329,29331],{"className":29330,"style":3525},[1024],[86,29332,29333,29336],{"style":3258},[86,29334],{"className":29335,"style":1032},[1031],[86,29337,29339],{"className":29338},[1036,1037,1038,1039],[86,29340,3489],{"className":29341,"style":3537},[1003,1007,1039],[30,29343,29344],{},[33,29345,29346,29349],{},[122,29347,29348],{},"Producto matriz-vector",": Se multiplica una matriz por un vector, lo que es común en la aplicación de modelos lineales.",[86,29351,29353],{"className":29352},[3173],[86,29354,29356,29575],{"className":29355},[955],[86,29357,29359],{"className":29358},[959],[961,29360,29361],{"xmlns":963,"display":3182},[965,29362,29363,29572],{},[968,29364,29365,29367,29369,29371,29373],{},[974,29366,3743],{"mathvariant":19893},[3191,29368,4975],{},[974,29370,7912],{"mathvariant":19893},[3191,29372,258],{},[968,29374,29375,29377,29570],{},[3191,29376,572],{"fence":990},[19901,29378,29380,29436,29492,29506],{"rowspacing":19903,"columnalign":29379,"columnspacing":19905},"center",[19907,29381,29382],{},[19910,29383,29384],{},[19913,29385,29386],{"scriptlevel":2553,"displaystyle":3295},[968,29387,29388,29394,29400,29402,29408,29414,29416,29418,29420,29430],{},[6849,29389,29390,29392],{},[974,29391,22],{},[978,29393,22729],{},[6849,29395,29396,29398],{},[974,29397,7912],{},[978,29399,802],{},[3191,29401,6565],{},[6849,29403,29404,29406],{},[974,29405,22],{},[978,29407,22751],{},[6849,29409,29410,29412],{},[974,29411,7912],{},[978,29413,980],{},[3191,29415,6565],{},[3191,29417,22766],{},[3191,29419,6565],{},[6849,29421,29422,29424],{},[974,29423,22],{},[968,29425,29426,29428],{},[978,29427,802],{},[974,29429,6896],{},[6849,29431,29432,29434],{},[974,29433,7912],{},[974,29435,6896],{},[19907,29437,29438],{},[19910,29439,29440],{},[19913,29441,29442],{"scriptlevel":2553,"displaystyle":3295},[968,29443,29444,29450,29456,29458,29464,29470,29472,29474,29476,29486],{},[6849,29445,29446,29448],{},[974,29447,22],{},[978,29449,22809],{},[6849,29451,29452,29454],{},[974,29453,7912],{},[978,29455,802],{},[3191,29457,6565],{},[6849,29459,29460,29462],{},[974,29461,22],{},[978,29463,22830],{},[6849,29465,29466,29468],{},[974,29467,7912],{},[978,29469,980],{},[3191,29471,6565],{},[3191,29473,22766],{},[3191,29475,6565],{},[6849,29477,29478,29480],{},[974,29479,22],{},[968,29481,29482,29484],{},[978,29483,980],{},[974,29485,6896],{},[6849,29487,29488,29490],{},[974,29489,7912],{},[974,29491,6896],{},[19907,29493,29494],{},[19910,29495,29496],{},[19913,29497,29498],{"scriptlevel":2553,"displaystyle":3295},[968,29499,29500,29502],{},[974,29501,19959],{"mathvariant":4327},[19961,29503,29504],{"height":19963,"voffset":19963},[3221,29505],{"mathbackground":19966,"width":19963,"height":19967},[19907,29507,29508],{},[19910,29509,29510],{},[19913,29511,29512],{"scriptlevel":2553,"displaystyle":3295},[968,29513,29514,29524,29530,29532,29542,29548,29550,29552,29554,29564],{},[6849,29515,29516,29518],{},[974,29517,22],{},[968,29519,29520,29522],{},[974,29521,5940],{},[978,29523,802],{},[6849,29525,29526,29528],{},[974,29527,7912],{},[978,29529,802],{},[3191,29531,6565],{},[6849,29533,29534,29536],{},[974,29535,22],{},[968,29537,29538,29540],{},[974,29539,5940],{},[978,29541,980],{},[6849,29543,29544,29546],{},[974,29545,7912],{},[978,29547,980],{},[3191,29549,6565],{},[3191,29551,22766],{},[3191,29553,6565],{},[6849,29555,29556,29558],{},[974,29557,22],{},[968,29559,29560,29562],{},[974,29561,5940],{},[974,29563,6896],{},[6849,29565,29566,29568],{},[974,29567,7912],{},[974,29569,6896],{},[3191,29571,585],{"fence":990},[982,29573,29574],{"encoding":984},"\\mathbf{A} \\cdot \\mathbf{v} =\n\\begin{bmatrix}\na_{11}v_1 + a_{12}v_2 + \\cdots + a_{1n}v_n \\\\\na_{21}v_1 + a_{22}v_2 + \\cdots + a_{2n}v_n \\\\\n\\vdots \\\\\na_{m1}v_1 + a_{m2}v_2 + \\cdots + a_{mn}v_n \\\\\n\\end{bmatrix}",[86,29576,29578,29596,29614],{"className":29577,"ariaHidden":990},[989],[86,29579,29581,29584,29587,29590,29593],{"className":29580},[994],[86,29582],{"className":29583,"style":20006},[998],[86,29585,3743],{"className":29586},[1003,20010],[86,29588],{"className":29589,"style":5012},[3221],[86,29591,4975],{"className":29592},[5016],[86,29594],{"className":29595,"style":5012},[3221],[86,29597,29599,29602,29605,29608,29611],{"className":29598},[994],[86,29600],{"className":29601,"style":20397},[998],[86,29603,7912],{"className":29604,"style":20401},[1003,20010],[86,29606],{"className":29607,"style":3222},[3221],[86,29609,258],{"className":29610},[3226],[86,29612],{"className":29613,"style":3222},[3221],[86,29615,29617,29620],{"className":29616},[994],[86,29618],{"className":29619,"style":23061},[998],[86,29621,29623,29660,30579],{"className":29622},[7131],[86,29624,29626],{"className":29625},[3320],[86,29627,29629],{"className":29628},[10232,20036],[86,29630,29632,29652],{"className":29631},[1016,3836],[86,29633,29635,29649],{"className":29634},[1020],[86,29636,29638],{"className":29637,"style":23080},[1024],[86,29639,29640,29643],{"style":23083},[86,29641],{"className":29642,"style":23087},[1031],[86,29644,29645],{"style":23090},[10150,29646,29647],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,29648],{"d":23097},[86,29650,3963],{"className":29651},[3962],[86,29653,29655],{"className":29654},[1020],[86,29656,29658],{"className":29657,"style":23107},[1024],[86,29659],{},[86,29661,29663],{"className":29662},[1003],[86,29664,29666],{"className":29665},[19901],[86,29667,29669],{"className":29668},[20086],[86,29670,29672,30571],{"className":29671},[1016,3836],[86,29673,29675,30568],{"className":29674},[1020],[86,29676,29678,29968,30258,30275],{"className":29677,"style":23128},[1024],[86,29679,29680,29683],{"style":23131},[86,29681],{"className":29682,"style":20103},[1031],[86,29684,29686,29729,29769,29772,29775,29778,29821,29861,29864,29867,29870,29873,29876,29879,29882,29928],{"className":29685},[1003],[86,29687,29689,29692],{"className":29688},[1003],[86,29690,22],{"className":29691},[1003,1007],[86,29693,29695],{"className":29694},[1012],[86,29696,29698,29721],{"className":29697},[1016,3836],[86,29699,29701,29718],{"className":29700},[1020],[86,29702,29704],{"className":29703,"style":6984},[1024],[86,29705,29706,29709],{"style":6987},[86,29707],{"className":29708,"style":1032},[1031],[86,29710,29712],{"className":29711},[1036,1037,1038,1039],[86,29713,29715],{"className":29714},[1003,1039],[86,29716,22729],{"className":29717},[1003,1039],[86,29719,3963],{"className":29720},[3962],[86,29722,29724],{"className":29723},[1020],[86,29725,29727],{"className":29726,"style":7006},[1024],[86,29728],{},[86,29730,29732,29735],{"className":29731},[1003],[86,29733,7912],{"className":29734,"style":8109},[1003,1007],[86,29736,29738],{"className":29737},[1012],[86,29739,29741,29761],{"className":29740},[1016,3836],[86,29742,29744,29758],{"className":29743},[1020],[86,29745,29747],{"className":29746,"style":6984},[1024],[86,29748,29749,29752],{"style":20440},[86,29750],{"className":29751,"style":1032},[1031],[86,29753,29755],{"className":29754},[1036,1037,1038,1039],[86,29756,802],{"className":29757},[1003,1039],[86,29759,3963],{"className":29760},[3962],[86,29762,29764],{"className":29763},[1020],[86,29765,29767],{"className":29766,"style":7006},[1024],[86,29768],{},[86,29770],{"className":29771,"style":5012},[3221],[86,29773,6565],{"className":29774},[5016],[86,29776],{"className":29777,"style":5012},[3221],[86,29779,29781,29784],{"className":29780},[1003],[86,29782,22],{"className":29783},[1003,1007],[86,29785,29787],{"className":29786},[1012],[86,29788,29790,29813],{"className":29789},[1016,3836],[86,29791,29793,29810],{"className":29792},[1020],[86,29794,29796],{"className":29795,"style":6984},[1024],[86,29797,29798,29801],{"style":6987},[86,29799],{"className":29800,"style":1032},[1031],[86,29802,29804],{"className":29803},[1036,1037,1038,1039],[86,29805,29807],{"className":29806},[1003,1039],[86,29808,22751],{"className":29809},[1003,1039],[86,29811,3963],{"className":29812},[3962],[86,29814,29816],{"className":29815},[1020],[86,29817,29819],{"className":29818,"style":7006},[1024],[86,29820],{},[86,29822,29824,29827],{"className":29823},[1003],[86,29825,7912],{"className":29826,"style":8109},[1003,1007],[86,29828,29830],{"className":29829},[1012],[86,29831,29833,29853],{"className":29832},[1016,3836],[86,29834,29836,29850],{"className":29835},[1020],[86,29837,29839],{"className":29838,"style":6984},[1024],[86,29840,29841,29844],{"style":20440},[86,29842],{"className":29843,"style":1032},[1031],[86,29845,29847],{"className":29846},[1036,1037,1038,1039],[86,29848,980],{"className":29849},[1003,1039],[86,29851,3963],{"className":29852},[3962],[86,29854,29856],{"className":29855},[1020],[86,29857,29859],{"className":29858,"style":7006},[1024],[86,29860],{},[86,29862],{"className":29863,"style":5012},[3221],[86,29865,6565],{"className":29866},[5016],[86,29868],{"className":29869,"style":5012},[3221],[86,29871,22766],{"className":29872},[7131],[86,29874],{"className":29875,"style":5012},[3221],[86,29877,6565],{"className":29878},[5016],[86,29880],{"className":29881,"style":5012},[3221],[86,29883,29885,29888],{"className":29884},[1003],[86,29886,22],{"className":29887},[1003,1007],[86,29889,29891],{"className":29890},[1012],[86,29892,29894,29920],{"className":29893},[1016,3836],[86,29895,29897,29917],{"className":29896},[1020],[86,29898,29900],{"className":29899,"style":6984},[1024],[86,29901,29902,29905],{"style":6987},[86,29903],{"className":29904,"style":1032},[1031],[86,29906,29908],{"className":29907},[1036,1037,1038,1039],[86,29909,29911,29914],{"className":29910},[1003,1039],[86,29912,802],{"className":29913},[1003,1039],[86,29915,6896],{"className":29916},[1003,1007,1039],[86,29918,3963],{"className":29919},[3962],[86,29921,29923],{"className":29922},[1020],[86,29924,29926],{"className":29925,"style":7006},[1024],[86,29927],{},[86,29929,29931,29934],{"className":29930},[1003],[86,29932,7912],{"className":29933,"style":8109},[1003,1007],[86,29935,29937],{"className":29936},[1012],[86,29938,29940,29960],{"className":29939},[1016,3836],[86,29941,29943,29957],{"className":29942},[1020],[86,29944,29946],{"className":29945,"style":7171},[1024],[86,29947,29948,29951],{"style":20440},[86,29949],{"className":29950,"style":1032},[1031],[86,29952,29954],{"className":29953},[1036,1037,1038,1039],[86,29955,6896],{"className":29956},[1003,1007,1039],[86,29958,3963],{"className":29959},[3962],[86,29961,29963],{"className":29962},[1020],[86,29964,29966],{"className":29965,"style":7006},[1024],[86,29967],{},[86,29969,29970,29973],{"style":23235},[86,29971],{"className":29972,"style":20103},[1031],[86,29974,29976,30019,30059,30062,30065,30068,30111,30151,30154,30157,30160,30163,30166,30169,30172,30218],{"className":29975},[1003],[86,29977,29979,29982],{"className":29978},[1003],[86,29980,22],{"className":29981},[1003,1007],[86,29983,29985],{"className":29984},[1012],[86,29986,29988,30011],{"className":29987},[1016,3836],[86,29989,29991,30008],{"className":29990},[1020],[86,29992,29994],{"className":29993,"style":6984},[1024],[86,29995,29996,29999],{"style":6987},[86,29997],{"className":29998,"style":1032},[1031],[86,30000,30002],{"className":30001},[1036,1037,1038,1039],[86,30003,30005],{"className":30004},[1003,1039],[86,30006,22809],{"className":30007},[1003,1039],[86,30009,3963],{"className":30010},[3962],[86,30012,30014],{"className":30013},[1020],[86,30015,30017],{"className":30016,"style":7006},[1024],[86,30018],{},[86,30020,30022,30025],{"className":30021},[1003],[86,30023,7912],{"className":30024,"style":8109},[1003,1007],[86,30026,30028],{"className":30027},[1012],[86,30029,30031,30051],{"className":30030},[1016,3836],[86,30032,30034,30048],{"className":30033},[1020],[86,30035,30037],{"className":30036,"style":6984},[1024],[86,30038,30039,30042],{"style":20440},[86,30040],{"className":30041,"style":1032},[1031],[86,30043,30045],{"className":30044},[1036,1037,1038,1039],[86,30046,802],{"className":30047},[1003,1039],[86,30049,3963],{"className":30050},[3962],[86,30052,30054],{"className":30053},[1020],[86,30055,30057],{"className":30056,"style":7006},[1024],[86,30058],{},[86,30060],{"className":30061,"style":5012},[3221],[86,30063,6565],{"className":30064},[5016],[86,30066],{"className":30067,"style":5012},[3221],[86,30069,30071,30074],{"className":30070},[1003],[86,30072,22],{"className":30073},[1003,1007],[86,30075,30077],{"className":30076},[1012],[86,30078,30080,30103],{"className":30079},[1016,3836],[86,30081,30083,30100],{"className":30082},[1020],[86,30084,30086],{"className":30085,"style":6984},[1024],[86,30087,30088,30091],{"style":6987},[86,30089],{"className":30090,"style":1032},[1031],[86,30092,30094],{"className":30093},[1036,1037,1038,1039],[86,30095,30097],{"className":30096},[1003,1039],[86,30098,22830],{"className":30099},[1003,1039],[86,30101,3963],{"className":30102},[3962],[86,30104,30106],{"className":30105},[1020],[86,30107,30109],{"className":30108,"style":7006},[1024],[86,30110],{},[86,30112,30114,30117],{"className":30113},[1003],[86,30115,7912],{"className":30116,"style":8109},[1003,1007],[86,30118,30120],{"className":30119},[1012],[86,30121,30123,30143],{"className":30122},[1016,3836],[86,30124,30126,30140],{"className":30125},[1020],[86,30127,30129],{"className":30128,"style":6984},[1024],[86,30130,30131,30134],{"style":20440},[86,30132],{"className":30133,"style":1032},[1031],[86,30135,30137],{"className":30136},[1036,1037,1038,1039],[86,30138,980],{"className":30139},[1003,1039],[86,30141,3963],{"className":30142},[3962],[86,30144,30146],{"className":30145},[1020],[86,30147,30149],{"className":30148,"style":7006},[1024],[86,30150],{},[86,30152],{"className":30153,"style":5012},[3221],[86,30155,6565],{"className":30156},[5016],[86,30158],{"className":30159,"style":5012},[3221],[86,30161,22766],{"className":30162},[7131],[86,30164],{"className":30165,"style":5012},[3221],[86,30167,6565],{"className":30168},[5016],[86,30170],{"className":30171,"style":5012},[3221],[86,30173,30175,30178],{"className":30174},[1003],[86,30176,22],{"className":30177},[1003,1007],[86,30179,30181],{"className":30180},[1012],[86,30182,30184,30210],{"className":30183},[1016,3836],[86,30185,30187,30207],{"className":30186},[1020],[86,30188,30190],{"className":30189,"style":6984},[1024],[86,30191,30192,30195],{"style":6987},[86,30193],{"className":30194,"style":1032},[1031],[86,30196,30198],{"className":30197},[1036,1037,1038,1039],[86,30199,30201,30204],{"className":30200},[1003,1039],[86,30202,980],{"className":30203},[1003,1039],[86,30205,6896],{"className":30206},[1003,1007,1039],[86,30208,3963],{"className":30209},[3962],[86,30211,30213],{"className":30212},[1020],[86,30214,30216],{"className":30215,"style":7006},[1024],[86,30217],{},[86,30219,30221,30224],{"className":30220},[1003],[86,30222,7912],{"className":30223,"style":8109},[1003,1007],[86,30225,30227],{"className":30226},[1012],[86,30228,30230,30250],{"className":30229},[1016,3836],[86,30231,30233,30247],{"className":30232},[1020],[86,30234,30236],{"className":30235,"style":7171},[1024],[86,30237,30238,30241],{"style":20440},[86,30239],{"className":30240,"style":1032},[1031],[86,30242,30244],{"className":30243},[1036,1037,1038,1039],[86,30245,6896],{"className":30246},[1003,1007,1039],[86,30248,3963],{"className":30249},[3962],[86,30251,30253],{"className":30252},[1020],[86,30254,30256],{"className":30255,"style":7006},[1024],[86,30257],{},[86,30259,30260,30263],{"style":23339},[86,30261],{"className":30262,"style":20103},[1031],[86,30264,30266],{"className":30265},[1003],[86,30267,30269,30272],{"className":30268},[1003],[86,30270,19959],{"className":30271},[1003],[86,30273],{"className":30274,"style":20141},[1003,20140],[86,30276,30277,30280],{"style":23357},[86,30278],{"className":30279,"style":20103},[1031],[86,30281,30283,30329,30369,30372,30375,30378,30424,30464,30467,30470,30473,30476,30479,30482,30485,30528],{"className":30282},[1003],[86,30284,30286,30289],{"className":30285},[1003],[86,30287,22],{"className":30288},[1003,1007],[86,30290,30292],{"className":30291},[1012],[86,30293,30295,30321],{"className":30294},[1016,3836],[86,30296,30298,30318],{"className":30297},[1020],[86,30299,30301],{"className":30300,"style":6984},[1024],[86,30302,30303,30306],{"style":6987},[86,30304],{"className":30305,"style":1032},[1031],[86,30307,30309],{"className":30308},[1036,1037,1038,1039],[86,30310,30312,30315],{"className":30311},[1003,1039],[86,30313,5940],{"className":30314},[1003,1007,1039],[86,30316,802],{"className":30317},[1003,1039],[86,30319,3963],{"className":30320},[3962],[86,30322,30324],{"className":30323},[1020],[86,30325,30327],{"className":30326,"style":7006},[1024],[86,30328],{},[86,30330,30332,30335],{"className":30331},[1003],[86,30333,7912],{"className":30334,"style":8109},[1003,1007],[86,30336,30338],{"className":30337},[1012],[86,30339,30341,30361],{"className":30340},[1016,3836],[86,30342,30344,30358],{"className":30343},[1020],[86,30345,30347],{"className":30346,"style":6984},[1024],[86,30348,30349,30352],{"style":20440},[86,30350],{"className":30351,"style":1032},[1031],[86,30353,30355],{"className":30354},[1036,1037,1038,1039],[86,30356,802],{"className":30357},[1003,1039],[86,30359,3963],{"className":30360},[3962],[86,30362,30364],{"className":30363},[1020],[86,30365,30367],{"className":30366,"style":7006},[1024],[86,30368],{},[86,30370],{"className":30371,"style":5012},[3221],[86,30373,6565],{"className":30374},[5016],[86,30376],{"className":30377,"style":5012},[3221],[86,30379,30381,30384],{"className":30380},[1003],[86,30382,22],{"className":30383},[1003,1007],[86,30385,30387],{"className":30386},[1012],[86,30388,30390,30416],{"className":30389},[1016,3836],[86,30391,30393,30413],{"className":30392},[1020],[86,30394,30396],{"className":30395,"style":6984},[1024],[86,30397,30398,30401],{"style":6987},[86,30399],{"className":30400,"style":1032},[1031],[86,30402,30404],{"className":30403},[1036,1037,1038,1039],[86,30405,30407,30410],{"className":30406},[1003,1039],[86,30408,5940],{"className":30409},[1003,1007,1039],[86,30411,980],{"className":30412},[1003,1039],[86,30414,3963],{"className":30415},[3962],[86,30417,30419],{"className":30418},[1020],[86,30420,30422],{"className":30421,"style":7006},[1024],[86,30423],{},[86,30425,30427,30430],{"className":30426},[1003],[86,30428,7912],{"className":30429,"style":8109},[1003,1007],[86,30431,30433],{"className":30432},[1012],[86,30434,30436,30456],{"className":30435},[1016,3836],[86,30437,30439,30453],{"className":30438},[1020],[86,30440,30442],{"className":30441,"style":6984},[1024],[86,30443,30444,30447],{"style":20440},[86,30445],{"className":30446,"style":1032},[1031],[86,30448,30450],{"className":30449},[1036,1037,1038,1039],[86,30451,980],{"className":30452},[1003,1039],[86,30454,3963],{"className":30455},[3962],[86,30457,30459],{"className":30458},[1020],[86,30460,30462],{"className":30461,"style":7006},[1024],[86,30463],{},[86,30465],{"className":30466,"style":5012},[3221],[86,30468,6565],{"className":30469},[5016],[86,30471],{"className":30472,"style":5012},[3221],[86,30474,22766],{"className":30475},[7131],[86,30477],{"className":30478,"style":5012},[3221],[86,30480,6565],{"className":30481},[5016],[86,30483],{"className":30484,"style":5012},[3221],[86,30486,30488,30491],{"className":30487},[1003],[86,30489,22],{"className":30490},[1003,1007],[86,30492,30494],{"className":30493},[1012],[86,30495,30497,30520],{"className":30496},[1016,3836],[86,30498,30500,30517],{"className":30499},[1020],[86,30501,30503],{"className":30502,"style":7171},[1024],[86,30504,30505,30508],{"style":6987},[86,30506],{"className":30507,"style":1032},[1031],[86,30509,30511],{"className":30510},[1036,1037,1038,1039],[86,30512,30514],{"className":30513},[1003,1039],[86,30515,978],{"className":30516},[1003,1007,1039],[86,30518,3963],{"className":30519},[3962],[86,30521,30523],{"className":30522},[1020],[86,30524,30526],{"className":30525,"style":7006},[1024],[86,30527],{},[86,30529,30531,30534],{"className":30530},[1003],[86,30532,7912],{"className":30533,"style":8109},[1003,1007],[86,30535,30537],{"className":30536},[1012],[86,30538,30540,30560],{"className":30539},[1016,3836],[86,30541,30543,30557],{"className":30542},[1020],[86,30544,30546],{"className":30545,"style":7171},[1024],[86,30547,30548,30551],{"style":20440},[86,30549],{"className":30550,"style":1032},[1031],[86,30552,30554],{"className":30553},[1036,1037,1038,1039],[86,30555,6896],{"className":30556},[1003,1007,1039],[86,30558,3963],{"className":30559},[3962],[86,30561,30563],{"className":30562},[1020],[86,30564,30566],{"className":30565,"style":7006},[1024],[86,30567],{},[86,30569,3963],{"className":30570},[3962],[86,30572,30574],{"className":30573},[1020],[86,30575,30577],{"className":30576,"style":23474},[1024],[86,30578],{},[86,30580,30582],{"className":30581},[3356],[86,30583,30585],{"className":30584},[10232,20036],[86,30586,30588,30608],{"className":30587},[1016,3836],[86,30589,30591,30605],{"className":30590},[1020],[86,30592,30594],{"className":30593,"style":23080},[1024],[86,30595,30596,30599],{"style":23083},[86,30597],{"className":30598,"style":23087},[1031],[86,30600,30601],{"style":23090},[10150,30602,30603],{"xmlns":10152,"width":20059,"height":23093,"viewBox":23094},[246,30604],{"d":24309},[86,30606,3963],{"className":30607},[3962],[86,30609,30611],{"className":30610},[1020],[86,30612,30614],{"className":30613,"style":23107},[1024],[86,30615],{},[12,30617,30618],{},"Una de las operaciones más importantes en el aprendizaje automático es la multiplicación, ya sea de matrices o de matrices por vectores, ya que es fundamental para el entrenamiento de modelos y la realización de predicciones. Por ejemplo, en un modelo de regresión lineal, la predicción se realiza multiplicando la matriz de características por el vector de pesos del modelo:",[86,30620,30622],{"className":30621},[3173],[86,30623,30625,30651],{"className":30624},[955],[86,30626,30628],{"className":30627},[959],[961,30629,30630],{"xmlns":963,"display":3182},[965,30631,30632,30648],{},[968,30633,30634,30640,30642,30644,30646],{},[3758,30635,30636,30638],{"accent":990},[974,30637,5464],{"mathvariant":19893},[3191,30639,7242],{},[3191,30641,258],{},[974,30643,4624],{"mathvariant":19893},[3191,30645,4975],{},[974,30647,12059],{"mathvariant":19893},[982,30649,30650],{"encoding":984},"\\hat{\\mathbf{y}} = \\mathbf{X} \\cdot \\mathbf{w}",[86,30652,30654,30715,30733],{"className":30653,"ariaHidden":990},[989],[86,30655,30657,30661,30706,30709,30712],{"className":30656},[994],[86,30658],{"className":30659,"style":30660},[998],"height:0.9023em;vertical-align:-0.1944em;",[86,30662,30664],{"className":30663},[1003,3863],[86,30665,30667,30697],{"className":30666},[1016,3836],[86,30668,30670,30694],{"className":30669},[1020],[86,30671,30674,30682],{"className":30672,"style":30673},[1024],"height:0.7079em;",[86,30675,30676,30679],{"style":3876},[86,30677],{"className":30678,"style":3850},[1031],[86,30680,5464],{"className":30681,"style":20401},[1003,20010],[86,30683,30685,30688],{"style":30684},"top:-3.0134em;",[86,30686],{"className":30687,"style":3850},[1031],[86,30689,30691],{"className":30690,"style":3892},[3891],[86,30692,7242],{"className":30693},[1003],[86,30695,3963],{"className":30696},[3962],[86,30698,30700],{"className":30699},[1020],[86,30701,30704],{"className":30702,"style":30703},[1024],"height:0.1944em;",[86,30705],{},[86,30707],{"className":30708,"style":3222},[3221],[86,30710,258],{"className":30711},[3226],[86,30713],{"className":30714,"style":3222},[3221],[86,30716,30718,30721,30724,30727,30730],{"className":30717},[994],[86,30719],{"className":30720,"style":20006},[998],[86,30722,4624],{"className":30723},[1003,20010],[86,30725],{"className":30726,"style":5012},[3221],[86,30728,4975],{"className":30729},[5016],[86,30731],{"className":30732,"style":5012},[3221],[86,30734,30736,30739],{"className":30735},[994],[86,30737],{"className":30738,"style":20397},[998],[86,30740,12059],{"className":30741,"style":20401},[1003,20010],[12,30743,30744,30745,30747,30748,30750,30751,61],{},"Para generar predicciones, se multiplica la matriz de características ",[145,30746,4624],{}," por el vector de pesos ",[145,30749,12059],{},", lo que da como resultado un vector de predicciones ",[145,30752,30753],{},"ŷ",[12,30755,30756],{},"Veámos un ejemplo concreto:",[12,30758,30759],{},"Supongamos que tenemos un modelo de regresión lineal con dos características (altura y peso) y un conjunto de datos con tres instancias:",[461,30761,30762,30770],{},[464,30763,30764],{},[467,30765,30766,30768],{},[470,30767,19843],{},[470,30769,19846],{},[480,30771,30772,30778,30784],{},[467,30773,30774,30776],{},[485,30775,19856],{},[485,30777,19859],{},[467,30779,30780,30782],{},[485,30781,19866],{},[485,30783,19869],{},[467,30785,30786,30789],{},[485,30787,30788],{},"160",[485,30790,30791],{},"55",[12,30793,30794,30795,162],{},"Podemos representar este conjunto de datos como una matriz ",[145,30796,4624],{},[86,30798,30800],{"className":30799},[3173],[86,30801,30803,30870],{"className":30802},[955],[86,30804,30806],{"className":30805},[959],[961,30807,30808],{"xmlns":963,"display":3182},[965,30809,30810,30867],{},[968,30811,30812,30814,30816],{},[974,30813,4624],{"mathvariant":19893},[3191,30815,258],{},[968,30817,30818,30820,30865],{},[3191,30819,572],{"fence":990},[19901,30821,30823,30837,30851],{"rowspacing":19903,"columnalign":30822,"columnspacing":19905},"center center",[19907,30824,30825,30831],{},[19910,30826,30827],{},[19913,30828,30829],{"scriptlevel":2553,"displaystyle":3295},[978,30830,19856],{},[19910,30832,30833],{},[19913,30834,30835],{"scriptlevel":2553,"displaystyle":3295},[978,30836,19859],{},[19907,30838,30839,30845],{},[19910,30840,30841],{},[19913,30842,30843],{"scriptlevel":2553,"displaystyle":3295},[978,30844,19866],{},[19910,30846,30847],{},[19913,30848,30849],{"scriptlevel":2553,"displaystyle":3295},[978,30850,19869],{},[19907,30852,30853,30859],{},[19910,30854,30855],{},[19913,30856,30857],{"scriptlevel":2553,"displaystyle":3295},[978,30858,30788],{},[19910,30860,30861],{},[19913,30862,30863],{"scriptlevel":2553,"displaystyle":3295},[978,30864,30791],{},[3191,30866,585],{"fence":990},[982,30868,30869],{"encoding":984},"\\mathbf{X} =\n\\begin{bmatrix}\n170 & 65 \\\\\n182 & 75 \\\\\n160 & 55 \\\\\n\\end{bmatrix}",[86,30871,30873,30891],{"className":30872,"ariaHidden":990},[989],[86,30874,30876,30879,30882,30885,30888],{"className":30875},[994],[86,30877],{"className":30878,"style":20006},[998],[86,30880,4624],{"className":30881},[1003,20010],[86,30883],{"className":30884,"style":3222},[3221],[86,30886,258],{"className":30887},[3226],[86,30889],{"className":30890,"style":3222},[3221],[86,30892,30894,30898],{"className":30893},[994],[86,30895],{"className":30896,"style":30897},[998],"height:3.6em;vertical-align:-1.55em;",[86,30899,30901,30946,31073],{"className":30900},[7131],[86,30902,30904],{"className":30903},[3320],[86,30905,30907],{"className":30906},[10232,20036],[86,30908,30910,30937],{"className":30909},[1016,3836],[86,30911,30913,30934],{"className":30912},[1020],[86,30914,30917],{"className":30915,"style":30916},[1024],"height:2.05em;",[86,30918,30920,30924],{"style":30919},"top:-4.05em;",[86,30921],{"className":30922,"style":30923},[1031],"height:5.6em;",[86,30925,30927],{"style":30926},"width:0.667em;height:3.6em;",[10150,30928,30931],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},"3.6em","0 0 667 3600",[246,30932],{"d":30933},"M403 1759 V84 H666 V0 H319 V1759 v0 v1759 h347 v-84\nH403z M403 1759 V0 H319 V1759 v0 v1759 h84z",[86,30935,3963],{"className":30936},[3962],[86,30938,30940],{"className":30939},[1020],[86,30941,30944],{"className":30942,"style":30943},[1024],"height:1.55em;",[86,30945],{},[86,30947,30949],{"className":30948},[1003],[86,30950,30952,31011,31014,31017],{"className":30951},[19901],[86,30953,30955],{"className":30954},[20086],[86,30956,30958,31003],{"className":30957},[1016,3836],[86,30959,30961,31000],{"className":30960},[1020],[86,30962,30964,30976,30988],{"className":30963,"style":30916},[1024],[86,30965,30967,30970],{"style":30966},"top:-4.21em;",[86,30968],{"className":30969,"style":3850},[1031],[86,30971,30973],{"className":30972},[1003],[86,30974,19856],{"className":30975},[1003],[86,30977,30979,30982],{"style":30978},"top:-3.01em;",[86,30980],{"className":30981,"style":3850},[1031],[86,30983,30985],{"className":30984},[1003],[86,30986,19866],{"className":30987},[1003],[86,30989,30991,30994],{"style":30990},"top:-1.81em;",[86,30992],{"className":30993,"style":3850},[1031],[86,30995,30997],{"className":30996},[1003],[86,30998,30788],{"className":30999},[1003],[86,31001,3963],{"className":31002},[3962],[86,31004,31006],{"className":31005},[1020],[86,31007,31009],{"className":31008,"style":30943},[1024],[86,31010],{},[86,31012],{"className":31013,"style":20158},[20157],[86,31015],{"className":31016,"style":20158},[20157],[86,31018,31020],{"className":31019},[20086],[86,31021,31023,31065],{"className":31022},[1016,3836],[86,31024,31026,31062],{"className":31025},[1020],[86,31027,31029,31040,31051],{"className":31028,"style":30916},[1024],[86,31030,31031,31034],{"style":30966},[86,31032],{"className":31033,"style":3850},[1031],[86,31035,31037],{"className":31036},[1003],[86,31038,19859],{"className":31039},[1003],[86,31041,31042,31045],{"style":30978},[86,31043],{"className":31044,"style":3850},[1031],[86,31046,31048],{"className":31047},[1003],[86,31049,19869],{"className":31050},[1003],[86,31052,31053,31056],{"style":30990},[86,31054],{"className":31055,"style":3850},[1031],[86,31057,31059],{"className":31058},[1003],[86,31060,30791],{"className":31061},[1003],[86,31063,3963],{"className":31064},[3962],[86,31066,31068],{"className":31067},[1020],[86,31069,31071],{"className":31070,"style":30943},[1024],[86,31072],{},[86,31074,31076],{"className":31075},[3356],[86,31077,31079],{"className":31078},[10232,20036],[86,31080,31082,31103],{"className":31081},[1016,3836],[86,31083,31085,31100],{"className":31084},[1020],[86,31086,31088],{"className":31087,"style":30916},[1024],[86,31089,31090,31093],{"style":30919},[86,31091],{"className":31092,"style":30923},[1031],[86,31094,31095],{"style":30926},[10150,31096,31097],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,31098],{"d":31099},"M347 1759 V0 H0 V84 H263 V1759 v0 v1759 H0 v84 H347z\nM347 1759 V0 H263 V1759 v0 v1759 h84z",[86,31101,3963],{"className":31102},[3962],[86,31104,31106],{"className":31105},[1020],[86,31107,31109],{"className":31108,"style":30943},[1024],[86,31110],{},[12,31112,31113,31114,31116],{},"Si nuestro modelo tiene un vector de pesos ",[145,31115,12059],{}," que representa la importancia de cada característica, por ejemplo:",[86,31118,31120],{"className":31119},[3173],[86,31121,31123,31164],{"className":31122},[955],[86,31124,31126],{"className":31125},[959],[961,31127,31128],{"xmlns":963,"display":3182},[965,31129,31130,31161],{},[968,31131,31132,31134,31136],{},[974,31133,12059],{"mathvariant":19893},[3191,31135,258],{},[968,31137,31138,31140,31159],{},[3191,31139,572],{"fence":990},[19901,31141,31142,31151],{"rowspacing":19903,"columnalign":29379,"columnspacing":19905},[19907,31143,31144],{},[19910,31145,31146],{},[19913,31147,31148],{"scriptlevel":2553,"displaystyle":3295},[978,31149,31150],{},"0.5",[19907,31152,31153],{},[19910,31154,31155],{},[19913,31156,31157],{"scriptlevel":2553,"displaystyle":3295},[978,31158,9777],{},[3191,31160,585],{"fence":990},[982,31162,31163],{"encoding":984},"\\mathbf{w} =\n\\begin{bmatrix}\n0.5 \\\\\n0.3 \\\\\n\\end{bmatrix}",[86,31165,31167,31185],{"className":31166,"ariaHidden":990},[989],[86,31168,31170,31173,31176,31179,31182],{"className":31169},[994],[86,31171],{"className":31172,"style":20397},[998],[86,31174,12059],{"className":31175,"style":20401},[1003,20010],[86,31177],{"className":31178,"style":3222},[3221],[86,31180,258],{"className":31181},[3226],[86,31183],{"className":31184,"style":3222},[3221],[86,31186,31188,31191],{"className":31187},[994],[86,31189],{"className":31190,"style":14190},[998],[86,31192,31194,31200,31255],{"className":31193},[7131],[86,31195,31197],{"className":31196,"style":10228},[3320,10227],[86,31198,572],{"className":31199},[10232,1038],[86,31201,31203],{"className":31202},[1003],[86,31204,31206],{"className":31205},[19901],[86,31207,31209],{"className":31208},[20086],[86,31210,31212,31246],{"className":31211},[1016,3836],[86,31213,31215,31243],{"className":31214},[1020],[86,31216,31219,31231],{"className":31217,"style":31218},[1024],"height:1.45em;",[86,31220,31222,31225],{"style":31221},"top:-3.61em;",[86,31223],{"className":31224,"style":3850},[1031],[86,31226,31228],{"className":31227},[1003],[86,31229,31150],{"className":31230},[1003],[86,31232,31234,31237],{"style":31233},"top:-2.41em;",[86,31235],{"className":31236,"style":3850},[1031],[86,31238,31240],{"className":31239},[1003],[86,31241,9777],{"className":31242},[1003],[86,31244,3963],{"className":31245},[3962],[86,31247,31249],{"className":31248},[1020],[86,31250,31253],{"className":31251,"style":31252},[1024],"height:0.95em;",[86,31254],{},[86,31256,31258],{"className":31257,"style":10228},[3356,10227],[86,31259,585],{"className":31260},[10232,1038],[12,31262,31263,31264,31266,31267,162],{},"Podemos generar predicciones multiplicando la matriz ",[145,31265,4624],{}," por el vector ",[145,31268,12059],{},[86,31270,31272],{"className":31271},[3173],[86,31273,31275,31379],{"className":31274},[955],[86,31276,31278],{"className":31277},[959],[961,31279,31280],{"xmlns":963,"display":3182},[965,31281,31282,31376],{},[968,31283,31284,31290,31292,31294,31296,31298,31300,31350,31352],{},[3758,31285,31286,31288],{"accent":990},[974,31287,5464],{"mathvariant":19893},[3191,31289,7242],{},[3191,31291,258],{},[974,31293,4624],{"mathvariant":19893},[3191,31295,4975],{},[974,31297,12059],{"mathvariant":19893},[3191,31299,258],{},[968,31301,31302,31304,31348],{},[3191,31303,572],{"fence":990},[19901,31305,31306,31320,31334],{"rowspacing":19903,"columnalign":30822,"columnspacing":19905},[19907,31307,31308,31314],{},[19910,31309,31310],{},[19913,31311,31312],{"scriptlevel":2553,"displaystyle":3295},[978,31313,19856],{},[19910,31315,31316],{},[19913,31317,31318],{"scriptlevel":2553,"displaystyle":3295},[978,31319,19859],{},[19907,31321,31322,31328],{},[19910,31323,31324],{},[19913,31325,31326],{"scriptlevel":2553,"displaystyle":3295},[978,31327,19866],{},[19910,31329,31330],{},[19913,31331,31332],{"scriptlevel":2553,"displaystyle":3295},[978,31333,19869],{},[19907,31335,31336,31342],{},[19910,31337,31338],{},[19913,31339,31340],{"scriptlevel":2553,"displaystyle":3295},[978,31341,30788],{},[19910,31343,31344],{},[19913,31345,31346],{"scriptlevel":2553,"displaystyle":3295},[978,31347,30791],{},[3191,31349,585],{"fence":990},[3191,31351,4975],{},[968,31353,31354,31356,31374],{},[3191,31355,572],{"fence":990},[19901,31357,31358,31366],{"rowspacing":19903,"columnalign":29379,"columnspacing":19905},[19907,31359,31360],{},[19910,31361,31362],{},[19913,31363,31364],{"scriptlevel":2553,"displaystyle":3295},[978,31365,31150],{},[19907,31367,31368],{},[19910,31369,31370],{},[19913,31371,31372],{"scriptlevel":2553,"displaystyle":3295},[978,31373,9777],{},[3191,31375,585],{"fence":990},[982,31377,31378],{"encoding":984},"\\hat{\\mathbf{y}} = \\mathbf{X} \\cdot \\mathbf{w} =\n\\begin{bmatrix}\n170 & 65 \\\\\n182 & 75 \\\\\n160 & 55 \\\\\n\\end{bmatrix}\n\\cdot\n\\begin{bmatrix}\n0.5 \\\\\n0.3 \\\\\n\\end{bmatrix}",[86,31380,31382,31439,31457,31475,31691],{"className":31381,"ariaHidden":990},[989],[86,31383,31385,31388,31430,31433,31436],{"className":31384},[994],[86,31386],{"className":31387,"style":30660},[998],[86,31389,31391],{"className":31390},[1003,3863],[86,31392,31394,31422],{"className":31393},[1016,3836],[86,31395,31397,31419],{"className":31396},[1020],[86,31398,31400,31408],{"className":31399,"style":30673},[1024],[86,31401,31402,31405],{"style":3876},[86,31403],{"className":31404,"style":3850},[1031],[86,31406,5464],{"className":31407,"style":20401},[1003,20010],[86,31409,31410,31413],{"style":30684},[86,31411],{"className":31412,"style":3850},[1031],[86,31414,31416],{"className":31415,"style":3892},[3891],[86,31417,7242],{"className":31418},[1003],[86,31420,3963],{"className":31421},[3962],[86,31423,31425],{"className":31424},[1020],[86,31426,31428],{"className":31427,"style":30703},[1024],[86,31429],{},[86,31431],{"className":31432,"style":3222},[3221],[86,31434,258],{"className":31435},[3226],[86,31437],{"className":31438,"style":3222},[3221],[86,31440,31442,31445,31448,31451,31454],{"className":31441},[994],[86,31443],{"className":31444,"style":20006},[998],[86,31446,4624],{"className":31447},[1003,20010],[86,31449],{"className":31450,"style":5012},[3221],[86,31452,4975],{"className":31453},[5016],[86,31455],{"className":31456,"style":5012},[3221],[86,31458,31460,31463,31466,31469,31472],{"className":31459},[994],[86,31461],{"className":31462,"style":20397},[998],[86,31464,12059],{"className":31465,"style":20401},[1003,20010],[86,31467],{"className":31468,"style":3222},[3221],[86,31470,258],{"className":31471},[3226],[86,31473],{"className":31474,"style":3222},[3221],[86,31476,31478,31481,31682,31685,31688],{"className":31477},[994],[86,31479],{"className":31480,"style":30897},[998],[86,31482,31484,31521,31645],{"className":31483},[7131],[86,31485,31487],{"className":31486},[3320],[86,31488,31490],{"className":31489},[10232,20036],[86,31491,31493,31513],{"className":31492},[1016,3836],[86,31494,31496,31510],{"className":31495},[1020],[86,31497,31499],{"className":31498,"style":30916},[1024],[86,31500,31501,31504],{"style":30919},[86,31502],{"className":31503,"style":30923},[1031],[86,31505,31506],{"style":30926},[10150,31507,31508],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,31509],{"d":30933},[86,31511,3963],{"className":31512},[3962],[86,31514,31516],{"className":31515},[1020],[86,31517,31519],{"className":31518,"style":30943},[1024],[86,31520],{},[86,31522,31524],{"className":31523},[1003],[86,31525,31527,31583,31586,31589],{"className":31526},[19901],[86,31528,31530],{"className":31529},[20086],[86,31531,31533,31575],{"className":31532},[1016,3836],[86,31534,31536,31572],{"className":31535},[1020],[86,31537,31539,31550,31561],{"className":31538,"style":30916},[1024],[86,31540,31541,31544],{"style":30966},[86,31542],{"className":31543,"style":3850},[1031],[86,31545,31547],{"className":31546},[1003],[86,31548,19856],{"className":31549},[1003],[86,31551,31552,31555],{"style":30978},[86,31553],{"className":31554,"style":3850},[1031],[86,31556,31558],{"className":31557},[1003],[86,31559,19866],{"className":31560},[1003],[86,31562,31563,31566],{"style":30990},[86,31564],{"className":31565,"style":3850},[1031],[86,31567,31569],{"className":31568},[1003],[86,31570,30788],{"className":31571},[1003],[86,31573,3963],{"className":31574},[3962],[86,31576,31578],{"className":31577},[1020],[86,31579,31581],{"className":31580,"style":30943},[1024],[86,31582],{},[86,31584],{"className":31585,"style":20158},[20157],[86,31587],{"className":31588,"style":20158},[20157],[86,31590,31592],{"className":31591},[20086],[86,31593,31595,31637],{"className":31594},[1016,3836],[86,31596,31598,31634],{"className":31597},[1020],[86,31599,31601,31612,31623],{"className":31600,"style":30916},[1024],[86,31602,31603,31606],{"style":30966},[86,31604],{"className":31605,"style":3850},[1031],[86,31607,31609],{"className":31608},[1003],[86,31610,19859],{"className":31611},[1003],[86,31613,31614,31617],{"style":30978},[86,31615],{"className":31616,"style":3850},[1031],[86,31618,31620],{"className":31619},[1003],[86,31621,19869],{"className":31622},[1003],[86,31624,31625,31628],{"style":30990},[86,31626],{"className":31627,"style":3850},[1031],[86,31629,31631],{"className":31630},[1003],[86,31632,30791],{"className":31633},[1003],[86,31635,3963],{"className":31636},[3962],[86,31638,31640],{"className":31639},[1020],[86,31641,31643],{"className":31642,"style":30943},[1024],[86,31644],{},[86,31646,31648],{"className":31647},[3356],[86,31649,31651],{"className":31650},[10232,20036],[86,31652,31654,31674],{"className":31653},[1016,3836],[86,31655,31657,31671],{"className":31656},[1020],[86,31658,31660],{"className":31659,"style":30916},[1024],[86,31661,31662,31665],{"style":30919},[86,31663],{"className":31664,"style":30923},[1031],[86,31666,31667],{"style":30926},[10150,31668,31669],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,31670],{"d":31099},[86,31672,3963],{"className":31673},[3962],[86,31675,31677],{"className":31676},[1020],[86,31678,31680],{"className":31679,"style":30943},[1024],[86,31681],{},[86,31683],{"className":31684,"style":5012},[3221],[86,31686,4975],{"className":31687},[5016],[86,31689],{"className":31690,"style":5012},[3221],[86,31692,31694,31697],{"className":31693},[994],[86,31695],{"className":31696,"style":14190},[998],[86,31698,31700,31706,31757],{"className":31699},[7131],[86,31701,31703],{"className":31702,"style":10228},[3320,10227],[86,31704,572],{"className":31705},[10232,1038],[86,31707,31709],{"className":31708},[1003],[86,31710,31712],{"className":31711},[19901],[86,31713,31715],{"className":31714},[20086],[86,31716,31718,31749],{"className":31717},[1016,3836],[86,31719,31721,31746],{"className":31720},[1020],[86,31722,31724,31735],{"className":31723,"style":31218},[1024],[86,31725,31726,31729],{"style":31221},[86,31727],{"className":31728,"style":3850},[1031],[86,31730,31732],{"className":31731},[1003],[86,31733,31150],{"className":31734},[1003],[86,31736,31737,31740],{"style":31233},[86,31738],{"className":31739,"style":3850},[1031],[86,31741,31743],{"className":31742},[1003],[86,31744,9777],{"className":31745},[1003],[86,31747,3963],{"className":31748},[3962],[86,31750,31752],{"className":31751},[1020],[86,31753,31755],{"className":31754,"style":31252},[1024],[86,31756],{},[86,31758,31760],{"className":31759,"style":10228},[3356,10227],[86,31761,585],{"className":31762},[10232,1038],[16,31764,31765],{},[12,31766,31767,31768],{},"Hemos omitido el bias en este ejemplo para simplificar la explicación, pero en un modelo real, también se incluiría un término de sesgo (bias) que se sumaría a las predicciones: ",[86,31769,31771,31801],{"className":31770},[955],[86,31772,31774],{"className":31773},[959],[961,31775,31776],{"xmlns":963},[965,31777,31778,31798],{},[968,31779,31780,31786,31788,31790,31792,31794,31796],{},[3758,31781,31782,31784],{"accent":990},[974,31783,5464],{"mathvariant":19893},[3191,31785,7242],{},[3191,31787,258],{},[974,31789,4624],{"mathvariant":19893},[3191,31791,4975],{},[974,31793,12059],{"mathvariant":19893},[3191,31795,6565],{},[974,31797,22736],{"mathvariant":19893},[982,31799,31800],{"encoding":984},"\\hat{\\mathbf{y}} = \\mathbf{X} \\cdot \\mathbf{w} + \\mathbf{b} ",[86,31802,31804,31861,31879,31897],{"className":31803,"ariaHidden":990},[989],[86,31805,31807,31810,31852,31855,31858],{"className":31806},[994],[86,31808],{"className":31809,"style":30660},[998],[86,31811,31813],{"className":31812},[1003,3863],[86,31814,31816,31844],{"className":31815},[1016,3836],[86,31817,31819,31841],{"className":31818},[1020],[86,31820,31822,31830],{"className":31821,"style":30673},[1024],[86,31823,31824,31827],{"style":3876},[86,31825],{"className":31826,"style":3850},[1031],[86,31828,5464],{"className":31829,"style":20401},[1003,20010],[86,31831,31832,31835],{"style":30684},[86,31833],{"className":31834,"style":3850},[1031],[86,31836,31838],{"className":31837,"style":3892},[3891],[86,31839,7242],{"className":31840},[1003],[86,31842,3963],{"className":31843},[3962],[86,31845,31847],{"className":31846},[1020],[86,31848,31850],{"className":31849,"style":30703},[1024],[86,31851],{},[86,31853],{"className":31854,"style":3222},[3221],[86,31856,258],{"className":31857},[3226],[86,31859],{"className":31860,"style":3222},[3221],[86,31862,31864,31867,31870,31873,31876],{"className":31863},[994],[86,31865],{"className":31866,"style":20006},[998],[86,31868,4624],{"className":31869},[1003,20010],[86,31871],{"className":31872,"style":5012},[3221],[86,31874,4975],{"className":31875},[5016],[86,31877],{"className":31878,"style":5012},[3221],[86,31880,31882,31885,31888,31891,31894],{"className":31881},[994],[86,31883],{"className":31884,"style":14141},[998],[86,31886,12059],{"className":31887,"style":20401},[1003,20010],[86,31889],{"className":31890,"style":5012},[3221],[86,31892,6565],{"className":31893},[5016],[86,31895],{"className":31896,"style":5012},[3221],[86,31898,31900,31903],{"className":31899},[994],[86,31901],{"className":31902,"style":3873},[998],[86,31904,22736],{"className":31905},[1003,20010],[12,31907,31908],{},"Calculando el producto, obtenemos:",[86,31910,31912],{"className":31911},[3173],[86,31913,31915,32104],{"className":31914},[955],[86,31916,31918],{"className":31917},[959],[961,31919,31920],{"xmlns":963,"display":3182},[965,31921,31922,32101],{},[968,31923,31924,31930,31932,32006,32008,32064,32066],{},[3758,31925,31926,31928],{"accent":990},[974,31927,5464],{"mathvariant":19893},[3191,31929,7242],{},[3191,31931,258],{},[968,31933,31934,31936,32004],{},[3191,31935,572],{"fence":990},[19901,31937,31938,31960,31982],{"rowspacing":19903,"columnalign":29379,"columnspacing":19905},[19907,31939,31940],{},[19910,31941,31942],{},[19913,31943,31944],{"scriptlevel":2553,"displaystyle":3295},[968,31945,31946,31948,31950,31952,31954,31956,31958],{},[978,31947,19856],{},[3191,31949,4975],{},[978,31951,31150],{},[3191,31953,6565],{},[978,31955,19859],{},[3191,31957,4975],{},[978,31959,9777],{},[19907,31961,31962],{},[19910,31963,31964],{},[19913,31965,31966],{"scriptlevel":2553,"displaystyle":3295},[968,31967,31968,31970,31972,31974,31976,31978,31980],{},[978,31969,19866],{},[3191,31971,4975],{},[978,31973,31150],{},[3191,31975,6565],{},[978,31977,19869],{},[3191,31979,4975],{},[978,31981,9777],{},[19907,31983,31984],{},[19910,31985,31986],{},[19913,31987,31988],{"scriptlevel":2553,"displaystyle":3295},[968,31989,31990,31992,31994,31996,31998,32000,32002],{},[978,31991,30788],{},[3191,31993,4975],{},[978,31995,31150],{},[3191,31997,6565],{},[978,31999,30791],{},[3191,32001,4975],{},[978,32003,9777],{},[3191,32005,585],{"fence":990},[3191,32007,258],{},[968,32009,32010,32012,32062],{},[3191,32011,572],{"fence":990},[19901,32013,32014,32030,32046],{"rowspacing":19903,"columnalign":29379,"columnspacing":19905},[19907,32015,32016],{},[19910,32017,32018],{},[19913,32019,32020],{"scriptlevel":2553,"displaystyle":3295},[968,32021,32022,32025,32027],{},[978,32023,32024],{},"85",[3191,32026,6565],{},[978,32028,32029],{},"19.5",[19907,32031,32032],{},[19910,32033,32034],{},[19913,32035,32036],{"scriptlevel":2553,"displaystyle":3295},[968,32037,32038,32041,32043],{},[978,32039,32040],{},"91",[3191,32042,6565],{},[978,32044,32045],{},"22.5",[19907,32047,32048],{},[19910,32049,32050],{},[19913,32051,32052],{"scriptlevel":2553,"displaystyle":3295},[968,32053,32054,32057,32059],{},[978,32055,32056],{},"80",[3191,32058,6565],{},[978,32060,32061],{},"16.5",[3191,32063,585],{"fence":990},[3191,32065,258],{},[968,32067,32068,32070,32099],{},[3191,32069,572],{"fence":990},[19901,32071,32072,32081,32090],{"rowspacing":19903,"columnalign":29379,"columnspacing":19905},[19907,32073,32074],{},[19910,32075,32076],{},[19913,32077,32078],{"scriptlevel":2553,"displaystyle":3295},[978,32079,32080],{},"104.5",[19907,32082,32083],{},[19910,32084,32085],{},[19913,32086,32087],{"scriptlevel":2553,"displaystyle":3295},[978,32088,32089],{},"113.5",[19907,32091,32092],{},[19910,32093,32094],{},[19913,32095,32096],{"scriptlevel":2553,"displaystyle":3295},[978,32097,32098],{},"96.5",[3191,32100,585],{"fence":990},[982,32102,32103],{"encoding":984},"\\hat{\\mathbf{y}} =\n\\begin{bmatrix}\n170 \\cdot 0.5 + 65 \\cdot 0.3 \\\\\n182 \\cdot 0.5 + 75 \\cdot 0.3 \\\\\n160 \\cdot 0.5 + 55 \\cdot 0.3 \\\\\n\\end{bmatrix} =\n\\begin{bmatrix}85 + 19.5 \\\\91 + 22.5 \\\\80 + 16.5 \\end{bmatrix} =\n\\begin{bmatrix}104.5 \\\\113.5 \\\\96.5 \\end{bmatrix}",[86,32105,32107,32164,32426,32616],{"className":32106,"ariaHidden":990},[989],[86,32108,32110,32113,32155,32158,32161],{"className":32109},[994],[86,32111],{"className":32112,"style":30660},[998],[86,32114,32116],{"className":32115},[1003,3863],[86,32117,32119,32147],{"className":32118},[1016,3836],[86,32120,32122,32144],{"className":32121},[1020],[86,32123,32125,32133],{"className":32124,"style":30673},[1024],[86,32126,32127,32130],{"style":3876},[86,32128],{"className":32129,"style":3850},[1031],[86,32131,5464],{"className":32132,"style":20401},[1003,20010],[86,32134,32135,32138],{"style":30684},[86,32136],{"className":32137,"style":3850},[1031],[86,32139,32141],{"className":32140,"style":3892},[3891],[86,32142,7242],{"className":32143},[1003],[86,32145,3963],{"className":32146},[3962],[86,32148,32150],{"className":32149},[1020],[86,32151,32153],{"className":32152,"style":30703},[1024],[86,32154],{},[86,32156],{"className":32157,"style":3222},[3221],[86,32159,258],{"className":32160},[3226],[86,32162],{"className":32163,"style":3222},[3221],[86,32165,32167,32170,32417,32420,32423],{"className":32166},[994],[86,32168],{"className":32169,"style":30897},[998],[86,32171,32173,32210,32380],{"className":32172},[7131],[86,32174,32176],{"className":32175},[3320],[86,32177,32179],{"className":32178},[10232,20036],[86,32180,32182,32202],{"className":32181},[1016,3836],[86,32183,32185,32199],{"className":32184},[1020],[86,32186,32188],{"className":32187,"style":30916},[1024],[86,32189,32190,32193],{"style":30919},[86,32191],{"className":32192,"style":30923},[1031],[86,32194,32195],{"style":30926},[10150,32196,32197],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,32198],{"d":30933},[86,32200,3963],{"className":32201},[3962],[86,32203,32205],{"className":32204},[1020],[86,32206,32208],{"className":32207,"style":30943},[1024],[86,32209],{},[86,32211,32213],{"className":32212},[1003],[86,32214,32216],{"className":32215},[19901],[86,32217,32219],{"className":32218},[20086],[86,32220,32222,32372],{"className":32221},[1016,3836],[86,32223,32225,32369],{"className":32224},[1020],[86,32226,32228,32275,32322],{"className":32227,"style":30916},[1024],[86,32229,32230,32233],{"style":30966},[86,32231],{"className":32232,"style":3850},[1031],[86,32234,32236,32239,32242,32245,32248,32251,32254,32257,32260,32263,32266,32269,32272],{"className":32235},[1003],[86,32237,19856],{"className":32238},[1003],[86,32240],{"className":32241,"style":5012},[3221],[86,32243,4975],{"className":32244},[5016],[86,32246],{"className":32247,"style":5012},[3221],[86,32249,31150],{"className":32250},[1003],[86,32252],{"className":32253,"style":5012},[3221],[86,32255,6565],{"className":32256},[5016],[86,32258],{"className":32259,"style":5012},[3221],[86,32261,19859],{"className":32262},[1003],[86,32264],{"className":32265,"style":5012},[3221],[86,32267,4975],{"className":32268},[5016],[86,32270],{"className":32271,"style":5012},[3221],[86,32273,9777],{"className":32274},[1003],[86,32276,32277,32280],{"style":30978},[86,32278],{"className":32279,"style":3850},[1031],[86,32281,32283,32286,32289,32292,32295,32298,32301,32304,32307,32310,32313,32316,32319],{"className":32282},[1003],[86,32284,19866],{"className":32285},[1003],[86,32287],{"className":32288,"style":5012},[3221],[86,32290,4975],{"className":32291},[5016],[86,32293],{"className":32294,"style":5012},[3221],[86,32296,31150],{"className":32297},[1003],[86,32299],{"className":32300,"style":5012},[3221],[86,32302,6565],{"className":32303},[5016],[86,32305],{"className":32306,"style":5012},[3221],[86,32308,19869],{"className":32309},[1003],[86,32311],{"className":32312,"style":5012},[3221],[86,32314,4975],{"className":32315},[5016],[86,32317],{"className":32318,"style":5012},[3221],[86,32320,9777],{"className":32321},[1003],[86,32323,32324,32327],{"style":30990},[86,32325],{"className":32326,"style":3850},[1031],[86,32328,32330,32333,32336,32339,32342,32345,32348,32351,32354,32357,32360,32363,32366],{"className":32329},[1003],[86,32331,30788],{"className":32332},[1003],[86,32334],{"className":32335,"style":5012},[3221],[86,32337,4975],{"className":32338},[5016],[86,32340],{"className":32341,"style":5012},[3221],[86,32343,31150],{"className":32344},[1003],[86,32346],{"className":32347,"style":5012},[3221],[86,32349,6565],{"className":32350},[5016],[86,32352],{"className":32353,"style":5012},[3221],[86,32355,30791],{"className":32356},[1003],[86,32358],{"className":32359,"style":5012},[3221],[86,32361,4975],{"className":32362},[5016],[86,32364],{"className":32365,"style":5012},[3221],[86,32367,9777],{"className":32368},[1003],[86,32370,3963],{"className":32371},[3962],[86,32373,32375],{"className":32374},[1020],[86,32376,32378],{"className":32377,"style":30943},[1024],[86,32379],{},[86,32381,32383],{"className":32382},[3356],[86,32384,32386],{"className":32385},[10232,20036],[86,32387,32389,32409],{"className":32388},[1016,3836],[86,32390,32392,32406],{"className":32391},[1020],[86,32393,32395],{"className":32394,"style":30916},[1024],[86,32396,32397,32400],{"style":30919},[86,32398],{"className":32399,"style":30923},[1031],[86,32401,32402],{"style":30926},[10150,32403,32404],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,32405],{"d":31099},[86,32407,3963],{"className":32408},[3962],[86,32410,32412],{"className":32411},[1020],[86,32413,32415],{"className":32414,"style":30943},[1024],[86,32416],{},[86,32418],{"className":32419,"style":3222},[3221],[86,32421,258],{"className":32422},[3226],[86,32424],{"className":32425,"style":3222},[3221],[86,32427,32429,32432,32607,32610,32613],{"className":32428},[994],[86,32430],{"className":32431,"style":30897},[998],[86,32433,32435,32472,32570],{"className":32434},[7131],[86,32436,32438],{"className":32437},[3320],[86,32439,32441],{"className":32440},[10232,20036],[86,32442,32444,32464],{"className":32443},[1016,3836],[86,32445,32447,32461],{"className":32446},[1020],[86,32448,32450],{"className":32449,"style":30916},[1024],[86,32451,32452,32455],{"style":30919},[86,32453],{"className":32454,"style":30923},[1031],[86,32456,32457],{"style":30926},[10150,32458,32459],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,32460],{"d":30933},[86,32462,3963],{"className":32463},[3962],[86,32465,32467],{"className":32466},[1020],[86,32468,32470],{"className":32469,"style":30943},[1024],[86,32471],{},[86,32473,32475],{"className":32474},[1003],[86,32476,32478],{"className":32477},[19901],[86,32479,32481],{"className":32480},[20086],[86,32482,32484,32562],{"className":32483},[1016,3836],[86,32485,32487,32559],{"className":32486},[1020],[86,32488,32490,32513,32536],{"className":32489,"style":30916},[1024],[86,32491,32492,32495],{"style":30966},[86,32493],{"className":32494,"style":3850},[1031],[86,32496,32498,32501,32504,32507,32510],{"className":32497},[1003],[86,32499,32024],{"className":32500},[1003],[86,32502],{"className":32503,"style":5012},[3221],[86,32505,6565],{"className":32506},[5016],[86,32508],{"className":32509,"style":5012},[3221],[86,32511,32029],{"className":32512},[1003],[86,32514,32515,32518],{"style":30978},[86,32516],{"className":32517,"style":3850},[1031],[86,32519,32521,32524,32527,32530,32533],{"className":32520},[1003],[86,32522,32040],{"className":32523},[1003],[86,32525],{"className":32526,"style":5012},[3221],[86,32528,6565],{"className":32529},[5016],[86,32531],{"className":32532,"style":5012},[3221],[86,32534,32045],{"className":32535},[1003],[86,32537,32538,32541],{"style":30990},[86,32539],{"className":32540,"style":3850},[1031],[86,32542,32544,32547,32550,32553,32556],{"className":32543},[1003],[86,32545,32056],{"className":32546},[1003],[86,32548],{"className":32549,"style":5012},[3221],[86,32551,6565],{"className":32552},[5016],[86,32554],{"className":32555,"style":5012},[3221],[86,32557,32061],{"className":32558},[1003],[86,32560,3963],{"className":32561},[3962],[86,32563,32565],{"className":32564},[1020],[86,32566,32568],{"className":32567,"style":30943},[1024],[86,32569],{},[86,32571,32573],{"className":32572},[3356],[86,32574,32576],{"className":32575},[10232,20036],[86,32577,32579,32599],{"className":32578},[1016,3836],[86,32580,32582,32596],{"className":32581},[1020],[86,32583,32585],{"className":32584,"style":30916},[1024],[86,32586,32587,32590],{"style":30919},[86,32588],{"className":32589,"style":30923},[1031],[86,32591,32592],{"style":30926},[10150,32593,32594],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,32595],{"d":31099},[86,32597,3963],{"className":32598},[3962],[86,32600,32602],{"className":32601},[1020],[86,32603,32605],{"className":32604,"style":30943},[1024],[86,32606],{},[86,32608],{"className":32609,"style":3222},[3221],[86,32611,258],{"className":32612},[3226],[86,32614],{"className":32615,"style":3222},[3221],[86,32617,32619,32622],{"className":32618},[994],[86,32620],{"className":32621,"style":30897},[998],[86,32623,32625,32662,32724],{"className":32624},[7131],[86,32626,32628],{"className":32627},[3320],[86,32629,32631],{"className":32630},[10232,20036],[86,32632,32634,32654],{"className":32633},[1016,3836],[86,32635,32637,32651],{"className":32636},[1020],[86,32638,32640],{"className":32639,"style":30916},[1024],[86,32641,32642,32645],{"style":30919},[86,32643],{"className":32644,"style":30923},[1031],[86,32646,32647],{"style":30926},[10150,32648,32649],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,32650],{"d":30933},[86,32652,3963],{"className":32653},[3962],[86,32655,32657],{"className":32656},[1020],[86,32658,32660],{"className":32659,"style":30943},[1024],[86,32661],{},[86,32663,32665],{"className":32664},[1003],[86,32666,32668],{"className":32667},[19901],[86,32669,32671],{"className":32670},[20086],[86,32672,32674,32716],{"className":32673},[1016,3836],[86,32675,32677,32713],{"className":32676},[1020],[86,32678,32680,32691,32702],{"className":32679,"style":30916},[1024],[86,32681,32682,32685],{"style":30966},[86,32683],{"className":32684,"style":3850},[1031],[86,32686,32688],{"className":32687},[1003],[86,32689,32080],{"className":32690},[1003],[86,32692,32693,32696],{"style":30978},[86,32694],{"className":32695,"style":3850},[1031],[86,32697,32699],{"className":32698},[1003],[86,32700,32089],{"className":32701},[1003],[86,32703,32704,32707],{"style":30990},[86,32705],{"className":32706,"style":3850},[1031],[86,32708,32710],{"className":32709},[1003],[86,32711,32098],{"className":32712},[1003],[86,32714,3963],{"className":32715},[3962],[86,32717,32719],{"className":32718},[1020],[86,32720,32722],{"className":32721,"style":30943},[1024],[86,32723],{},[86,32725,32727],{"className":32726},[3356],[86,32728,32730],{"className":32729},[10232,20036],[86,32731,32733,32753],{"className":32732},[1016,3836],[86,32734,32736,32750],{"className":32735},[1020],[86,32737,32739],{"className":32738,"style":30916},[1024],[86,32740,32741,32744],{"style":30919},[86,32742],{"className":32743,"style":30923},[1031],[86,32745,32746],{"style":30926},[10150,32747,32748],{"xmlns":10152,"width":20059,"height":30929,"viewBox":30930},[246,32749],{"d":31099},[86,32751,3963],{"className":32752},[3962],[86,32754,32756],{"className":32755},[1020],[86,32757,32759],{"className":32758,"style":30943},[1024],[86,32760],{},[12,32762,32763,32764,32766],{},"En este ejemplo, las predicciones ",[145,32765,30753],{}," para cada instancia de datos se calculan como una combinación lineal de las características (altura y peso) ponderadas por los pesos del modelo.",[461,32768,32769,32780],{},[464,32770,32771],{},[467,32772,32773,32775,32777],{},[470,32774,19843],{},[470,32776,19846],{},[470,32778,32779],{},"Predicción (ŷ)",[480,32781,32782,32790,32798],{},[467,32783,32784,32786,32788],{},[485,32785,19856],{},[485,32787,19859],{},[485,32789,32080],{},[467,32791,32792,32794,32796],{},[485,32793,19866],{},[485,32795,19869],{},[485,32797,32089],{},[467,32799,32800,32802,32804],{},[485,32801,30788],{},[485,32803,30791],{},[485,32805,32098],{},[12,32807,32808],{},"Si el problema que estamos tratando es de clasificación, podríamos aplicar una función de activación (como la función sigmoide) a las predicciones para obtener probabilidades de clase, si es regresión podríamos usar las predicciones directamente para evaluar el rendimiento del modelo (el valor podría representar tal vez un índice de riesgo o X variable continua estimada a partir de las características).",[46,32810,32812],{"id":32811},"uso-en-algoritmos-y-librerias","Uso en Algoritmos y Librerias",[12,32814,32815],{},"Hablando de forma puntual, las operaciones matriciales son la base de muchos algoritmos de aprendizaje automático:",[30,32817,32818,32823,32829],{},[33,32819,32820,32822],{},[122,32821,927],{},": Utiliza la multiplicación de matrices para calcular las predicciones a partir de las características y los pesos del modelo, y en su forma cerrada emplea operaciones como transposición e inversa de matrices.",[33,32824,32825,32828],{},[122,32826,32827],{},"Redes Neuronales",": Utilizan operaciones matriciales para calcular las activaciones en cada capa de la red, así como para actualizar los pesos durante el entrenamiento.",[33,32830,32831,32833],{},[122,32832,1439],{},": Utiliza la multiplicación de matrices para calcular y luego poder obtener las probabilidades de clase a partir de las características y los pesos del modelo.",[12,32835,32836],{},"En cuánto a su uso, librerías como NumPy, TensorFlow y PyTorch, Scikit-learn proporcionan funciones optimizadas para realizar operaciones con vectores de manera eficiente:",[164,32838,32840],{"className":166,"code":32839,"language":168,"meta":169,"style":169},"import numpy as np\n# Crear una matriz de datos\nX = np.array([[170, 65], [182, 75], [160, 55]])\n# Crear un vector de pesos\nw = np.array([0.5, 0.3])\n# Generar predicciones\ny_hat = X.dot(w)\nprint(y_hat)\n",[145,32841,32842,32852,32857,32905,32910,32934,32939,32959],{"__ignoreMap":169},[86,32843,32844,32846,32848,32850],{"class":174,"line":175},[86,32845,179],{"class":178},[86,32847,183],{"class":182},[86,32849,186],{"class":178},[86,32851,189],{"class":182},[86,32853,32854],{"class":174,"line":192},[86,32855,32856],{"class":1360},"# Crear una matriz de datos\n",[86,32858,32859,32861,32863,32865,32867,32870,32873,32875,32877,32880,32882,32884,32886,32888,32891,32893,32895,32897,32899,32902],{"class":174,"line":205},[86,32860,12095],{"class":182},[86,32862,258],{"class":219},[86,32864,294],{"class":182},[86,32866,61],{"class":219},[86,32868,32869],{"class":182},"array",[86,32871,32872],{"class":219},"([[",[86,32874,19856],{"class":223},[86,32876,291],{"class":219},[86,32878,32879],{"class":223}," 65",[86,32881,9750],{"class":219},[86,32883,726],{"class":219},[86,32885,19866],{"class":223},[86,32887,291],{"class":219},[86,32889,32890],{"class":223}," 75",[86,32892,9750],{"class":219},[86,32894,726],{"class":219},[86,32896,30788],{"class":223},[86,32898,291],{"class":219},[86,32900,32901],{"class":223}," 55",[86,32903,32904],{"class":219},"]])\n",[86,32906,32907],{"class":174,"line":212},[86,32908,32909],{"class":1360},"# Crear un vector de pesos\n",[86,32911,32912,32914,32916,32918,32920,32922,32925,32927,32929,32932],{"class":174,"line":227},[86,32913,12007],{"class":182},[86,32915,258],{"class":219},[86,32917,294],{"class":182},[86,32919,61],{"class":219},[86,32921,32869],{"class":182},[86,32923,32924],{"class":219},"([",[86,32926,31150],{"class":223},[86,32928,291],{"class":219},[86,32930,32931],{"class":223}," 0.3",[86,32933,1417],{"class":219},[86,32935,32936],{"class":174,"line":232},[86,32937,32938],{"class":1360},"# Generar predicciones\n",[86,32940,32941,32944,32946,32948,32950,32953,32955,32957],{"class":174,"line":252},[86,32942,32943],{"class":182},"y_hat ",[86,32945,258],{"class":219},[86,32947,1093],{"class":182},[86,32949,61],{"class":219},[86,32951,32952],{"class":182},"dot",[86,32954,243],{"class":219},[86,32956,12059],{"class":182},[86,32958,273],{"class":219},[86,32960,32961,32963,32965,32968],{"class":174,"line":276},[86,32962,13294],{"class":812},[86,32964,243],{"class":219},[86,32966,32967],{"class":182},"y_hat",[86,32969,273],{"class":219},[46,32971,32973],{"id":32972},"recopilación-de-ejercicios","Recopilación de ejercicios",[12,32975,32976,32977],{},"En este Colab puedes practicar operaciones con vectores y matrices utilizando NumPy: ",[22,32978,32981],{"href":32979,"target":27,"rel":32980},"https:\u002F\u002Fcolab.research.google.com\u002Fdrive\u002F1P7gBDg7b6wVl1EMlCDf0UCWy5UBJ6b6N?usp=sharing",[7760,7761],"Ejercicios de Vectores y Matrices en Machine Learning",[43,32983],{},[12,32985,32986],{},"Eso sería todo por esta ocasión, en el próximo artículo comenzaremos a profundizar en el campo de la estadística y probabilidad. ¡Nos vemos!",[2218,32988,32989],{},"html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":169,"searchDepth":205,"depth":205,"links":32991},[32992,32996,32997],{"id":19798,"depth":192,"text":19799,"children":32993},[32994,32995],{"id":20335,"depth":205,"text":20336},{"id":22242,"depth":205,"text":22243},{"id":32811,"depth":192,"text":32812},{"id":32972,"depth":192,"text":32973},"2026-04-25","\u002Fblog\u002Fvectors-matrices-machine-learning\u002Fshared\u002Fvectors-matrices.webp",{},"\u002Fblog\u002Fblog\u002Fvectors-matrices-machine-learning",{"title":12750,"description":19783},{"loc":33004,"priority":2259,"lastmod":32998},"\u002Fes\u002Fblog\u002Fvectors-matrices-machine-learning","vectors-matrices-machine-learning","blog\u002Fblog\u002Fvectors-matrices-machine-learning","Los vectores son una parte esencial del aprendizaje automático, ya que permiten representar datos y parámetros de modelos de manera eficiente. En este artículo, exploraremos su definición y aplicación en algoritmos de machine learning.",[3625,33009,33010,33011,2264,33012],"vectores","matrices","álgebra lineal","linear algebra","AJQKTO0V_ucIcMhG3-aWvwQvNP__SlLyQGL_gcJqv3M",{"id":33015,"title":19791,"author":7,"body":33016,"date":40484,"description":33020,"extension":2250,"image":40485,"lastmod":40484,"meta":40486,"navigation":208,"order":232,"path":40487,"seo":40488,"sitemap":40489,"slug":40491,"stem":40492,"summary":40493,"tags":40494,"__hash__":40498},"content_es\u002Fblog\u002Fblog\u002Fexperimenting-with-titanic-dataset.md",{"type":9,"value":33017,"toc":40468},[33018,33021,33029,33031,33033,33037,33049,33052,33069,33077,33081,33084,33402,33421,33649,33653,33656,33667,33672,34087,34096,34101,34109,34119,34131,34134,34156,34159,34200,34211,34220,34223,34297,34435,34671,34677,34681,34684,34688,35090,35099,35105,35109,35505,35514,35517,35521,35682,35690,35695,35737,35740,35781,35784,35799,35809,36129,36137,36140,36143,36147,36157,36165,36168,36431,36438,36441,36668,36674,36677,37004,37008,37011,37343,37351,37357,38275,38278,38285,38292,38298,38305,38312,38315,38319,38326,38769,38773,38779,39060,39063,39069,39072,39086,39089,39097,39101,39108,40282,40285,40323,40330,40337,40343,40363,40369,40372,40386,40393,40401,40409,40411,40415,40418,40429,40432,40435,40465],[12,33019,33020],{},"Esta vez vamos a experimentar con el EDA (Análisis Exploratorio de Datos) usando el dataset de supervivencia del Titanic.",[12,33022,33023,33024],{},"En el artículo anterior de esta serie de Machine Learning realizamos un ejercicio similar para una tienda de café: ",[22,33025,33028],{"href":33026,"rel":33027},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis",[26],"Experimentando con el análisis exploratorio de datos",[40,33030],{},[43,33032],{},[46,33034,33036],{"id":33035},"un-ejercicio-práctico-el-dataset-del-titanic","Un Ejercicio Práctico: El Dataset del Titanic",[12,33038,33039,33040,33043,33044,33046,33047,789],{},"El dataset del Titanic es un clásico en aprendizaje automático. Incluye información de los pasajeros (edad, sexo, clase, tarifa, puerto de embarque, etc.) y la variable objetivo ",[145,33041,33042],{},"survived",", que indica si la persona sobrevivió (",[145,33045,802],{},") o no (",[145,33048,2553],{},[12,33050,33051],{},"Lo vamos a usar para practicar un flujo completo, pero esta vez con un enfoque más orientado a técnicas de limpieza y evaluación:",[117,33053,33054,33057,33060,33063,33066],{},[33,33055,33056],{},"Carga y revisión inicial.",[33,33058,33059],{},"Limpieza y transformación de variables.",[33,33061,33062],{},"EDA con visualizaciones.",[33,33064,33065],{},"Preparación para modelado.",[33,33067,33068],{},"Entrenamiento y evaluación con varias métricas.",[12,33070,33071,33072],{},"Puedes ver el notebook completo con el código y visualizaciones aquí: ",[22,33073,33076],{"href":33074,"target":27,"rel":33075},"https:\u002F\u002Fcolab.research.google.com\u002Fdrive\u002F1-yoNx_d1vY0TVCyx-1PLi1lGXQLbMMYC?usp=sharing",[7760,7761],"EDA with the Titanic dataset",[323,33078,33080],{"id":33079},"_1-carga-y-exploración-inicial","1. Carga y Exploración Inicial",[12,33082,33083],{},"Comenzamos importando librerías, cargando el dataset y revisando estructura\u002Ftipos para entender con qué estamos trabajando.",[164,33085,33087],{"className":166,"code":33086,"language":168,"meta":169,"style":169},"import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Estilo base de gráficas\nsns.set_style('whitegrid')\nplt.rcParams['figure.figsize'] = (12, 8)\n\n# Cargar dataset\ndf_raw = sns.load_dataset('titanic')\ndf = df_raw.copy()\n\nprint('Primeras 5 filas del dataset original:')\ndisplay(df.head())\n\nprint(f\"\\nDimensión del dataset: {df.shape[0]} filas x {df.shape[1]} columnas\")\nprint('\\nTipos de datos por columna:')\ndisplay(df.dtypes.to_frame(name='dtype'))\n",[145,33088,33089,33099,33109,33126,33138,33142,33147,33168,33202,33206,33211,33237,33253,33257,33272,33289,33293,33350,33367],{"__ignoreMap":169},[86,33090,33091,33093,33095,33097],{"class":174,"line":175},[86,33092,179],{"class":178},[86,33094,197],{"class":182},[86,33096,186],{"class":178},[86,33098,202],{"class":182},[86,33100,33101,33103,33105,33107],{"class":174,"line":192},[86,33102,179],{"class":178},[86,33104,183],{"class":182},[86,33106,186],{"class":178},[86,33108,189],{"class":182},[86,33110,33111,33113,33116,33118,33121,33123],{"class":174,"line":205},[86,33112,179],{"class":178},[86,33114,33115],{"class":182}," matplotlib",[86,33117,61],{"class":219},[86,33119,33120],{"class":182},"pyplot ",[86,33122,186],{"class":178},[86,33124,33125],{"class":182}," plt\n",[86,33127,33128,33130,33133,33135],{"class":174,"line":212},[86,33129,179],{"class":178},[86,33131,33132],{"class":182}," seaborn ",[86,33134,186],{"class":178},[86,33136,33137],{"class":182}," sns\n",[86,33139,33140],{"class":174,"line":227},[86,33141,209],{"emptyLinePlaceholder":208},[86,33143,33144],{"class":174,"line":232},[86,33145,33146],{"class":1360},"# Estilo base de gráficas\n",[86,33148,33149,33152,33154,33157,33159,33161,33164,33166],{"class":174,"line":252},[86,33150,33151],{"class":182},"sns",[86,33153,61],{"class":219},[86,33155,33156],{"class":182},"set_style",[86,33158,243],{"class":219},[86,33160,10971],{"class":575},[86,33162,33163],{"class":579},"whitegrid",[86,33165,10971],{"class":575},[86,33167,273],{"class":219},[86,33169,33170,33173,33175,33178,33180,33182,33185,33187,33189,33191,33193,33195,33197,33200],{"class":174,"line":276},[86,33171,33172],{"class":182},"plt",[86,33174,61],{"class":219},[86,33176,33177],{"class":182},"rcParams",[86,33179,572],{"class":219},[86,33181,10971],{"class":575},[86,33183,33184],{"class":579},"figure.figsize",[86,33186,10971],{"class":575},[86,33188,585],{"class":219},[86,33190,220],{"class":219},[86,33192,606],{"class":219},[86,33194,22751],{"class":223},[86,33196,291],{"class":219},[86,33198,33199],{"class":223}," 8",[86,33201,273],{"class":219},[86,33203,33204],{"class":174,"line":315},[86,33205,209],{"emptyLinePlaceholder":208},[86,33207,33208],{"class":174,"line":3665},[86,33209,33210],{"class":1360},"# Cargar dataset\n",[86,33212,33213,33216,33218,33221,33223,33226,33228,33230,33233,33235],{"class":174,"line":13256},[86,33214,33215],{"class":182},"df_raw ",[86,33217,258],{"class":219},[86,33219,33220],{"class":182}," sns",[86,33222,61],{"class":219},[86,33224,33225],{"class":182},"load_dataset",[86,33227,243],{"class":219},[86,33229,10971],{"class":575},[86,33231,33232],{"class":579},"titanic",[86,33234,10971],{"class":575},[86,33236,273],{"class":219},[86,33238,33239,33241,33243,33246,33248,33251],{"class":174,"line":13286},[86,33240,13168],{"class":182},[86,33242,258],{"class":219},[86,33244,33245],{"class":182}," df_raw",[86,33247,61],{"class":219},[86,33249,33250],{"class":182},"copy",[86,33252,11991],{"class":219},[86,33254,33255],{"class":174,"line":13291},[86,33256,209],{"emptyLinePlaceholder":208},[86,33258,33259,33261,33263,33265,33268,33270],{"class":174,"line":13308},[86,33260,13294],{"class":812},[86,33262,243],{"class":219},[86,33264,10971],{"class":575},[86,33266,33267],{"class":579},"Primeras 5 filas del dataset original:",[86,33269,10971],{"class":575},[86,33271,273],{"class":219},[86,33273,33274,33277,33279,33281,33283,33286],{"class":174,"line":13334},[86,33275,33276],{"class":182},"display",[86,33278,243],{"class":219},[86,33280,569],{"class":182},[86,33282,61],{"class":219},[86,33284,33285],{"class":182},"head",[86,33287,33288],{"class":219},"())\n",[86,33290,33291],{"class":174,"line":13359},[86,33292,209],{"emptyLinePlaceholder":208},[86,33294,33295,33297,33299,33301,33303,33306,33309,33311,33313,33315,33318,33320,33322,33324,33326,33329,33331,33333,33335,33337,33339,33341,33343,33345,33348],{"class":174,"line":13385},[86,33296,13294],{"class":812},[86,33298,243],{"class":219},[86,33300,6178],{"class":235},[86,33302,576],{"class":579},[86,33304,33305],{"class":215},"\\n",[86,33307,33308],{"class":579},"Dimensión del dataset: ",[86,33310,4089],{"class":215},[86,33312,569],{"class":182},[86,33314,61],{"class":219},[86,33316,33317],{"class":182},"shape",[86,33319,572],{"class":219},[86,33321,2553],{"class":223},[86,33323,585],{"class":219},[86,33325,4117],{"class":215},[86,33327,33328],{"class":579}," filas x ",[86,33330,4089],{"class":215},[86,33332,569],{"class":182},[86,33334,61],{"class":219},[86,33336,33317],{"class":182},[86,33338,572],{"class":219},[86,33340,802],{"class":223},[86,33342,585],{"class":219},[86,33344,4117],{"class":215},[86,33346,33347],{"class":579}," columnas\"",[86,33349,273],{"class":219},[86,33351,33352,33354,33356,33358,33360,33363,33365],{"class":174,"line":13390},[86,33353,13294],{"class":812},[86,33355,243],{"class":219},[86,33357,10971],{"class":575},[86,33359,33305],{"class":215},[86,33361,33362],{"class":579},"Tipos de datos por columna:",[86,33364,10971],{"class":575},[86,33366,273],{"class":219},[86,33368,33369,33371,33373,33375,33377,33380,33382,33385,33387,33390,33392,33394,33397,33399],{"class":174,"line":13396},[86,33370,33276],{"class":182},[86,33372,243],{"class":219},[86,33374,569],{"class":182},[86,33376,61],{"class":219},[86,33378,33379],{"class":182},"dtypes",[86,33381,61],{"class":219},[86,33383,33384],{"class":182},"to_frame",[86,33386,243],{"class":219},[86,33388,33389],{"class":304},"name",[86,33391,258],{"class":219},[86,33393,10971],{"class":575},[86,33395,33396],{"class":579},"dtype",[86,33398,10971],{"class":575},[86,33400,33401],{"class":219},"))\n",[12,33403,33404,33405,33408,33409,33412,33413,93,33415,33412,33418,789],{},"Aquí observamos una mezcla de variables numéricas y categóricas, además de columnas con nulos (por ejemplo ",[145,33406,33407],{},"deck",") y algunas variables redundantes (",[145,33410,33411],{},"alive"," vs ",[145,33414,33042],{},[145,33416,33417],{},"class",[145,33419,33420],{},"pclass",[461,33422,33423,33468],{},[464,33424,33425],{},[467,33426,33427,33430,33432,33435,33438,33441,33444,33447,33450,33452,33455,33458,33460,33463,33465],{},[470,33428,33042],{"align":33429},"left",[470,33431,33420],{"align":33429},[470,33433,33434],{"align":33429},"sex",[470,33436,33437],{"align":33429},"age",[470,33439,33440],{"align":33429},"sibsp",[470,33442,33443],{"align":33429},"parch",[470,33445,33446],{"align":33429},"fare",[470,33448,33449],{"align":33429},"embarked",[470,33451,33417],{"align":33429},[470,33453,33454],{"align":33429},"who",[470,33456,33457],{"align":33429},"adult_male",[470,33459,33407],{"align":33429},[470,33461,33462],{"align":33429},"embark_town",[470,33464,33411],{"align":33429},[470,33466,33467],{"align":33429},"alone",[480,33469,33470,33509,33548,33582,33616],{},[467,33471,33472,33474,33476,33479,33481,33483,33485,33488,33490,33493,33496,33498,33500,33503,33506],{},[485,33473,2553],{"align":33429},[485,33475,4100],{"align":33429},[485,33477,33478],{"align":33429},"male",[485,33480,22830],{"align":33429},[485,33482,802],{"align":33429},[485,33484,2553],{"align":33429},[485,33486,33487],{"align":33429},"7.25",[485,33489,4084],{"align":33429},[485,33491,33492],{"align":33429},"Third",[485,33494,33495],{"align":33429},"man",[485,33497,310],{"align":33429},[485,33499,161],{"align":33429},[485,33501,33502],{"align":33429},"Southampton",[485,33504,33505],{"align":33429},"no",[485,33507,33508],{"align":33429},"False",[467,33510,33511,33513,33515,33518,33521,33523,33525,33528,33530,33533,33536,33538,33540,33543,33546],{},[485,33512,802],{"align":33429},[485,33514,802],{"align":33429},[485,33516,33517],{"align":33429},"female",[485,33519,33520],{"align":33429},"38",[485,33522,802],{"align":33429},[485,33524,2553],{"align":33429},[485,33526,33527],{"align":33429},"71.2833",[485,33529,1514],{"align":33429},[485,33531,33532],{"align":33429},"First",[485,33534,33535],{"align":33429},"woman",[485,33537,33508],{"align":33429},[485,33539,1514],{"align":33429},[485,33541,33542],{"align":33429},"Cherbourg",[485,33544,33545],{"align":33429},"yes",[485,33547,33508],{"align":33429},[467,33549,33550,33552,33554,33556,33559,33561,33563,33566,33568,33570,33572,33574,33576,33578,33580],{},[485,33551,802],{"align":33429},[485,33553,4100],{"align":33429},[485,33555,33517],{"align":33429},[485,33557,33558],{"align":33429},"26",[485,33560,2553],{"align":33429},[485,33562,2553],{"align":33429},[485,33564,33565],{"align":33429},"7.925",[485,33567,4084],{"align":33429},[485,33569,33492],{"align":33429},[485,33571,33535],{"align":33429},[485,33573,33508],{"align":33429},[485,33575,161],{"align":33429},[485,33577,33502],{"align":33429},[485,33579,33545],{"align":33429},[485,33581,310],{"align":33429},[467,33583,33584,33586,33588,33590,33593,33595,33597,33600,33602,33604,33606,33608,33610,33612,33614],{},[485,33585,802],{"align":33429},[485,33587,802],{"align":33429},[485,33589,33517],{"align":33429},[485,33591,33592],{"align":33429},"35",[485,33594,802],{"align":33429},[485,33596,2553],{"align":33429},[485,33598,33599],{"align":33429},"53.1",[485,33601,4084],{"align":33429},[485,33603,33532],{"align":33429},[485,33605,33535],{"align":33429},[485,33607,33508],{"align":33429},[485,33609,1514],{"align":33429},[485,33611,33502],{"align":33429},[485,33613,33545],{"align":33429},[485,33615,33508],{"align":33429},[467,33617,33618,33620,33622,33624,33626,33628,33630,33633,33635,33637,33639,33641,33643,33645,33647],{},[485,33619,2553],{"align":33429},[485,33621,4100],{"align":33429},[485,33623,33478],{"align":33429},[485,33625,33592],{"align":33429},[485,33627,2553],{"align":33429},[485,33629,2553],{"align":33429},[485,33631,33632],{"align":33429},"8.05",[485,33634,4084],{"align":33429},[485,33636,33492],{"align":33429},[485,33638,33495],{"align":33429},[485,33640,310],{"align":33429},[485,33642,161],{"align":33429},[485,33644,33502],{"align":33429},[485,33646,33505],{"align":33429},[485,33648,310],{"align":33429},[323,33650,33652],{"id":33651},"_2-valores-nulos-y-limpieza-de-datos","2. Valores Nulos y Limpieza de Datos",[12,33654,33655],{},"Ahora aplicamos una limpieza base, enfocada en:",[117,33657,33658,33661,33664],{},[33,33659,33660],{},"Eliminar columnas muy incompletas o redundantes.",[33,33662,33663],{},"Imputar nulos estratégicamente.",[33,33665,33666],{},"Codificar variables categóricas.",[16,33668,33669],{},[12,33670,33671],{},"Con imputar nos referimos a rellenar los valores faltantes con alguna estrategia (mediana, moda, etc.) para no perder filas completas, de manera que podamos seguir usando esa información, pero sin introducir sesgos o ruido innecesario.",[164,33673,33675],{"className":166,"code":33674,"language":168,"meta":169,"style":169},"print('Valores nulos por columna (dataset original):')\nprint(df.isnull().sum().sort_values(ascending=False))\n\n# Limpieza base\ncols_to_drop = ['deck', 'embark_town', 'alive', 'class', 'who', 'adult_male']\ndf = df.drop(columns=cols_to_drop)\n\n# Imputación\ndf['age'] = df['age'].fillna(df['age'].median())\ndf['embarked'] = df['embarked'].fillna(df['embarked'].mode()[0])\n\n# Codificación\ndf['sex'] = df['sex'].map({'male': 0, 'female': 1})\ndf = pd.get_dummies(df, columns=['embarked'], drop_first=True, dtype=int)\n\nprint('\\nValores nulos totales después de limpieza:')\nprint(df.isnull().sum().sum())\n",[145,33676,33677,33692,33726,33730,33735,33792,33817,33821,33826,33875,33927,33931,33936,33994,34044,34048,34065],{"__ignoreMap":169},[86,33678,33679,33681,33683,33685,33688,33690],{"class":174,"line":175},[86,33680,13294],{"class":812},[86,33682,243],{"class":219},[86,33684,10971],{"class":575},[86,33686,33687],{"class":579},"Valores nulos por columna (dataset original):",[86,33689,10971],{"class":575},[86,33691,273],{"class":219},[86,33693,33694,33696,33698,33700,33702,33705,33707,33710,33712,33715,33717,33720,33722,33724],{"class":174,"line":192},[86,33695,13294],{"class":812},[86,33697,243],{"class":219},[86,33699,569],{"class":182},[86,33701,61],{"class":219},[86,33703,33704],{"class":182},"isnull",[86,33706,11985],{"class":219},[86,33708,33709],{"class":182},"sum",[86,33711,11985],{"class":219},[86,33713,33714],{"class":182},"sort_values",[86,33716,243],{"class":219},[86,33718,33719],{"class":304},"ascending",[86,33721,258],{"class":219},[86,33723,33508],{"class":178},[86,33725,33401],{"class":219},[86,33727,33728],{"class":174,"line":205},[86,33729,209],{"emptyLinePlaceholder":208},[86,33731,33732],{"class":174,"line":212},[86,33733,33734],{"class":1360},"# Limpieza base\n",[86,33736,33737,33740,33742,33744,33746,33748,33750,33752,33754,33756,33758,33760,33762,33764,33766,33768,33770,33772,33774,33776,33778,33780,33782,33784,33786,33788,33790],{"class":174,"line":227},[86,33738,33739],{"class":182},"cols_to_drop ",[86,33741,258],{"class":219},[86,33743,726],{"class":219},[86,33745,10971],{"class":575},[86,33747,33407],{"class":579},[86,33749,10971],{"class":575},[86,33751,291],{"class":219},[86,33753,11970],{"class":575},[86,33755,33462],{"class":579},[86,33757,10971],{"class":575},[86,33759,291],{"class":219},[86,33761,11970],{"class":575},[86,33763,33411],{"class":579},[86,33765,10971],{"class":575},[86,33767,291],{"class":219},[86,33769,11970],{"class":575},[86,33771,33417],{"class":579},[86,33773,10971],{"class":575},[86,33775,291],{"class":219},[86,33777,11970],{"class":575},[86,33779,33454],{"class":579},[86,33781,10971],{"class":575},[86,33783,291],{"class":219},[86,33785,11970],{"class":575},[86,33787,33457],{"class":579},[86,33789,10971],{"class":575},[86,33791,752],{"class":219},[86,33793,33794,33796,33798,33800,33802,33805,33807,33810,33812,33815],{"class":174,"line":232},[86,33795,13168],{"class":182},[86,33797,258],{"class":219},[86,33799,590],{"class":182},[86,33801,61],{"class":219},[86,33803,33804],{"class":182},"drop",[86,33806,243],{"class":219},[86,33808,33809],{"class":304},"columns",[86,33811,258],{"class":219},[86,33813,33814],{"class":182},"cols_to_drop",[86,33816,273],{"class":219},[86,33818,33819],{"class":174,"line":252},[86,33820,209],{"emptyLinePlaceholder":208},[86,33822,33823],{"class":174,"line":276},[86,33824,33825],{"class":1360},"# Imputación\n",[86,33827,33828,33830,33832,33834,33836,33838,33840,33842,33844,33846,33848,33850,33852,33854,33857,33859,33861,33863,33865,33867,33869,33871,33873],{"class":174,"line":315},[86,33829,569],{"class":182},[86,33831,572],{"class":219},[86,33833,10971],{"class":575},[86,33835,33437],{"class":579},[86,33837,10971],{"class":575},[86,33839,585],{"class":219},[86,33841,220],{"class":219},[86,33843,590],{"class":182},[86,33845,572],{"class":219},[86,33847,10971],{"class":575},[86,33849,33437],{"class":579},[86,33851,10971],{"class":575},[86,33853,13224],{"class":219},[86,33855,33856],{"class":182},"fillna",[86,33858,243],{"class":219},[86,33860,569],{"class":182},[86,33862,572],{"class":219},[86,33864,10971],{"class":575},[86,33866,33437],{"class":579},[86,33868,10971],{"class":575},[86,33870,13224],{"class":219},[86,33872,13251],{"class":182},[86,33874,33288],{"class":219},[86,33876,33877,33879,33881,33883,33885,33887,33889,33891,33893,33895,33897,33899,33901,33903,33905,33907,33909,33911,33913,33915,33917,33919,33921,33923,33925],{"class":174,"line":3665},[86,33878,569],{"class":182},[86,33880,572],{"class":219},[86,33882,10971],{"class":575},[86,33884,33449],{"class":579},[86,33886,10971],{"class":575},[86,33888,585],{"class":219},[86,33890,220],{"class":219},[86,33892,590],{"class":182},[86,33894,572],{"class":219},[86,33896,10971],{"class":575},[86,33898,33449],{"class":579},[86,33900,10971],{"class":575},[86,33902,13224],{"class":219},[86,33904,33856],{"class":182},[86,33906,243],{"class":219},[86,33908,569],{"class":182},[86,33910,572],{"class":219},[86,33912,10971],{"class":575},[86,33914,33449],{"class":579},[86,33916,10971],{"class":575},[86,33918,13224],{"class":219},[86,33920,13276],{"class":182},[86,33922,13279],{"class":219},[86,33924,2553],{"class":223},[86,33926,1417],{"class":219},[86,33928,33929],{"class":174,"line":13256},[86,33930,209],{"emptyLinePlaceholder":208},[86,33932,33933],{"class":174,"line":13286},[86,33934,33935],{"class":1360},"# Codificación\n",[86,33937,33938,33940,33942,33944,33946,33948,33950,33952,33954,33956,33958,33960,33962,33964,33967,33969,33971,33973,33975,33977,33980,33982,33984,33986,33988,33990,33992],{"class":174,"line":13291},[86,33939,569],{"class":182},[86,33941,572],{"class":219},[86,33943,10971],{"class":575},[86,33945,33434],{"class":579},[86,33947,10971],{"class":575},[86,33949,585],{"class":219},[86,33951,220],{"class":219},[86,33953,590],{"class":182},[86,33955,572],{"class":219},[86,33957,10971],{"class":575},[86,33959,33434],{"class":579},[86,33961,10971],{"class":575},[86,33963,13224],{"class":219},[86,33965,33966],{"class":182},"map",[86,33968,13180],{"class":219},[86,33970,10971],{"class":575},[86,33972,33478],{"class":579},[86,33974,10971],{"class":575},[86,33976,162],{"class":219},[86,33978,33979],{"class":223}," 0",[86,33981,291],{"class":219},[86,33983,11970],{"class":575},[86,33985,33517],{"class":579},[86,33987,10971],{"class":575},[86,33989,162],{"class":219},[86,33991,786],{"class":223},[86,33993,13195],{"class":219},[86,33995,33996,33998,34000,34002,34004,34007,34009,34011,34013,34016,34018,34020,34022,34024,34026,34029,34031,34033,34035,34038,34040,34042],{"class":174,"line":13308},[86,33997,13168],{"class":182},[86,33999,258],{"class":219},[86,34001,261],{"class":182},[86,34003,61],{"class":219},[86,34005,34006],{"class":182},"get_dummies",[86,34008,243],{"class":219},[86,34010,569],{"class":182},[86,34012,291],{"class":219},[86,34014,34015],{"class":304}," columns",[86,34017,1119],{"class":219},[86,34019,10971],{"class":575},[86,34021,33449],{"class":579},[86,34023,10971],{"class":575},[86,34025,9750],{"class":219},[86,34027,34028],{"class":304}," drop_first",[86,34030,258],{"class":219},[86,34032,310],{"class":178},[86,34034,291],{"class":219},[86,34036,34037],{"class":304}," dtype",[86,34039,258],{"class":219},[86,34041,813],{"class":812},[86,34043,273],{"class":219},[86,34045,34046],{"class":174,"line":13334},[86,34047,209],{"emptyLinePlaceholder":208},[86,34049,34050,34052,34054,34056,34058,34061,34063],{"class":174,"line":13359},[86,34051,13294],{"class":812},[86,34053,243],{"class":219},[86,34055,10971],{"class":575},[86,34057,33305],{"class":215},[86,34059,34060],{"class":579},"Valores nulos totales después de limpieza:",[86,34062,10971],{"class":575},[86,34064,273],{"class":219},[86,34066,34067,34069,34071,34073,34075,34077,34079,34081,34083,34085],{"class":174,"line":13385},[86,34068,13294],{"class":812},[86,34070,243],{"class":219},[86,34072,569],{"class":182},[86,34074,61],{"class":219},[86,34076,33704],{"class":182},[86,34078,11985],{"class":219},[86,34080,33709],{"class":182},[86,34082,11985],{"class":219},[86,34084,33709],{"class":182},[86,34086,33288],{"class":219},[12,34088,34089,34090,34092,34093,34095],{},"Usamos mediana para ",[145,34091,33437],{}," porque es robusta ante outliers, y moda para ",[145,34094,33449],{}," porque es categórica.",[16,34097,34098],{},[12,34099,34100],{},"La mediana es el valor que se encuentra en el medio de un conjunto de datos ordenados, lo que la hace menos sensible a valores extremos (outliers) que podrían distorsionar la media. Por eso es común usarla para imputar edades, donde pueden haber pasajeros muy jóvenes o muy ancianos.",[16,34102,34103],{},[12,34104,34105,34106,34108],{},"La moda es el valor más frecuente en una columna, lo que la hace adecuada para variables categóricas como ",[145,34107,33449],{},", donde queremos rellenar los nulos con la categoría más común sin introducir nuevas categorías o sesgos.",[12,34110,34111,34112,34114,34115,34118],{},"También aplicamos One-Hot Encoding en ",[145,34113,33449],{}," con ",[145,34116,34117],{},"drop_first=True"," para evitar multicolinealidad.",[12,34120,34121,34124,34125,34127,34128,34130],{},[122,34122,34123],{},"Detengámonos un momento en esto",": al aplicar One-Hot Encoding a una variable con ",[145,34126,6896],{}," categorías, se crean ",[145,34129,6896],{}," columnas binarias (una para cada categoría).",[12,34132,34133],{},"Pasa de ser una sola columna como:",[461,34135,34136,34142],{},[464,34137,34138],{},[467,34139,34140],{},[470,34141,33449],{"align":33429},[480,34143,34144,34148,34152],{},[467,34145,34146],{},[485,34147,4084],{"align":33429},[467,34149,34150],{},[485,34151,1514],{"align":33429},[467,34153,34154],{},[485,34155,419],{"align":33429},[12,34157,34158],{},"A tres columnas binarias:",[461,34160,34161,34174],{},[464,34162,34163],{},[467,34164,34165,34168,34171],{},[470,34166,34167],{"align":33429},"embarked_C",[470,34169,34170],{"align":33429},"embarked_Q",[470,34172,34173],{"align":33429},"embarked_S",[480,34175,34176,34184,34192],{},[467,34177,34178,34180,34182],{},[485,34179,2553],{"align":33429},[485,34181,2553],{"align":33429},[485,34183,802],{"align":33429},[467,34185,34186,34188,34190],{},[485,34187,802],{"align":33429},[485,34189,2553],{"align":33429},[485,34191,2553],{"align":33429},[467,34193,34194,34196,34198],{},[485,34195,2553],{"align":33429},[485,34197,2553],{"align":33429},[485,34199,802],{"align":33429},[12,34201,34202,34203,34206,34207,34210],{},"El problema es que si se incluyen todas, siempre se puede deducir una a partir de las otras (porque si no es C ni Q, entonces necesariamente es S), lo que genera ",[122,34204,34205],{},"multicolinealidad",", es decir, información repetida que puede confundir a modelos como la regresión lineal o logística y hacer inestables sus resultados. Entonces, al usar drop_first=True, se elimina una de las categorías y esa pasa a ser la ",[122,34208,34209],{},"referencia implícita",", evitando esa redundancia y haciendo que el modelo funcione de forma más estable y clara.",[12,34212,34213,34214,34216,34217,34219],{},"Con referencia implícita nos referimos a que, si ",[145,34215,34173],{}," es 0 y ",[145,34218,34170],{}," es 0, entonces por descarte sabemos que el pasajero embarcó en C, sin necesidad de una columna explícita para eso.",[12,34221,34222],{},"Revisamos cómo quedó el dataset:",[164,34224,34226],{"className":166,"code":34225,"language":168,"meta":169,"style":169},"print('Primeras 5 filas después del preprocesamiento:')\ndisplay(df.head())\n\nprint('\\nResumen estadístico de variables numéricas:')\ndisplay(df.describe().T)\n",[145,34227,34228,34243,34257,34261,34278],{"__ignoreMap":169},[86,34229,34230,34232,34234,34236,34239,34241],{"class":174,"line":175},[86,34231,13294],{"class":812},[86,34233,243],{"class":219},[86,34235,10971],{"class":575},[86,34237,34238],{"class":579},"Primeras 5 filas después del preprocesamiento:",[86,34240,10971],{"class":575},[86,34242,273],{"class":219},[86,34244,34245,34247,34249,34251,34253,34255],{"class":174,"line":192},[86,34246,33276],{"class":182},[86,34248,243],{"class":219},[86,34250,569],{"class":182},[86,34252,61],{"class":219},[86,34254,33285],{"class":182},[86,34256,33288],{"class":219},[86,34258,34259],{"class":174,"line":205},[86,34260,209],{"emptyLinePlaceholder":208},[86,34262,34263,34265,34267,34269,34271,34274,34276],{"class":174,"line":212},[86,34264,13294],{"class":812},[86,34266,243],{"class":219},[86,34268,10971],{"class":575},[86,34270,33305],{"class":215},[86,34272,34273],{"class":579},"Resumen estadístico de variables numéricas:",[86,34275,10971],{"class":575},[86,34277,273],{"class":219},[86,34279,34280,34282,34284,34286,34288,34291,34293,34295],{"class":174,"line":227},[86,34281,33276],{"class":182},[86,34283,243],{"class":219},[86,34285,569],{"class":182},[86,34287,61],{"class":219},[86,34289,34290],{"class":182},"describe",[86,34292,11985],{"class":219},[86,34294,3489],{"class":182},[86,34296,273],{"class":219},[461,34298,34299,34323],{},[464,34300,34301],{},[467,34302,34303,34305,34307,34309,34311,34313,34315,34317,34319,34321],{},[470,34304,33042],{"align":33429},[470,34306,33420],{"align":33429},[470,34308,33434],{"align":33429},[470,34310,33437],{"align":33429},[470,34312,33440],{"align":33429},[470,34314,33443],{"align":33429},[470,34316,33446],{"align":33429},[470,34318,33467],{"align":33429},[470,34320,34170],{"align":33429},[470,34322,34173],{"align":33429},[480,34324,34325,34347,34369,34391,34413],{},[467,34326,34327,34329,34331,34333,34335,34337,34339,34341,34343,34345],{},[485,34328,2553],{"align":33429},[485,34330,4100],{"align":33429},[485,34332,2553],{"align":33429},[485,34334,22830],{"align":33429},[485,34336,802],{"align":33429},[485,34338,2553],{"align":33429},[485,34340,33487],{"align":33429},[485,34342,33508],{"align":33429},[485,34344,2553],{"align":33429},[485,34346,802],{"align":33429},[467,34348,34349,34351,34353,34355,34357,34359,34361,34363,34365,34367],{},[485,34350,802],{"align":33429},[485,34352,802],{"align":33429},[485,34354,802],{"align":33429},[485,34356,33520],{"align":33429},[485,34358,802],{"align":33429},[485,34360,2553],{"align":33429},[485,34362,33527],{"align":33429},[485,34364,33508],{"align":33429},[485,34366,2553],{"align":33429},[485,34368,2553],{"align":33429},[467,34370,34371,34373,34375,34377,34379,34381,34383,34385,34387,34389],{},[485,34372,802],{"align":33429},[485,34374,4100],{"align":33429},[485,34376,802],{"align":33429},[485,34378,33558],{"align":33429},[485,34380,2553],{"align":33429},[485,34382,2553],{"align":33429},[485,34384,33565],{"align":33429},[485,34386,310],{"align":33429},[485,34388,2553],{"align":33429},[485,34390,802],{"align":33429},[467,34392,34393,34395,34397,34399,34401,34403,34405,34407,34409,34411],{},[485,34394,802],{"align":33429},[485,34396,802],{"align":33429},[485,34398,802],{"align":33429},[485,34400,33592],{"align":33429},[485,34402,802],{"align":33429},[485,34404,2553],{"align":33429},[485,34406,33599],{"align":33429},[485,34408,33508],{"align":33429},[485,34410,2553],{"align":33429},[485,34412,802],{"align":33429},[467,34414,34415,34417,34419,34421,34423,34425,34427,34429,34431,34433],{},[485,34416,2553],{"align":33429},[485,34418,4100],{"align":33429},[485,34420,2553],{"align":33429},[485,34422,33592],{"align":33429},[485,34424,2553],{"align":33429},[485,34426,2553],{"align":33429},[485,34428,33632],{"align":33429},[485,34430,310],{"align":33429},[485,34432,2553],{"align":33429},[485,34434,802],{"align":33429},[461,34436,34437,34463],{},[464,34438,34439],{},[467,34440,34441,34443,34446,34448,34450,34452,34455,34458,34461],{},[470,34442],{"align":33429},[470,34444,34445],{"align":33429},"count",[470,34447,13227],{"align":33429},[470,34449,13487],{"align":33429},[470,34451,13436],{"align":33429},[470,34453,34454],{"align":33429},"25%",[470,34456,34457],{"align":33429},"50%",[470,34459,34460],{"align":33429},"75%",[470,34462,7260],{"align":33429},[480,34464,34465,34488,34510,34532,34556,34579,34601,34627,34649],{},[467,34466,34467,34469,34472,34475,34478,34480,34482,34484,34486],{},[485,34468,33042],{"align":33429},[485,34470,34471],{"align":33429},"891",[485,34473,34474],{"align":33429},"0.383838",[485,34476,34477],{"align":33429},"0.486592",[485,34479,2553],{"align":33429},[485,34481,2553],{"align":33429},[485,34483,2553],{"align":33429},[485,34485,802],{"align":33429},[485,34487,802],{"align":33429},[467,34489,34490,34492,34494,34497,34500,34502,34504,34506,34508],{},[485,34491,33420],{"align":33429},[485,34493,34471],{"align":33429},[485,34495,34496],{"align":33429},"2.308642",[485,34498,34499],{"align":33429},"0.836071",[485,34501,802],{"align":33429},[485,34503,980],{"align":33429},[485,34505,4100],{"align":33429},[485,34507,4100],{"align":33429},[485,34509,4100],{"align":33429},[467,34511,34512,34514,34516,34519,34522,34524,34526,34528,34530],{},[485,34513,33434],{"align":33429},[485,34515,34471],{"align":33429},[485,34517,34518],{"align":33429},"0.352413",[485,34520,34521],{"align":33429},"0.47799",[485,34523,2553],{"align":33429},[485,34525,2553],{"align":33429},[485,34527,2553],{"align":33429},[485,34529,802],{"align":33429},[485,34531,802],{"align":33429},[467,34533,34534,34536,34538,34541,34544,34547,34549,34552,34554],{},[485,34535,33437],{"align":33429},[485,34537,34471],{"align":33429},[485,34539,34540],{"align":33429},"29.361582",[485,34542,34543],{"align":33429},"13.019697",[485,34545,34546],{"align":33429},"0.42",[485,34548,22830],{"align":33429},[485,34550,34551],{"align":33429},"28",[485,34553,33592],{"align":33429},[485,34555,32056],{"align":33429},[467,34557,34558,34560,34562,34565,34568,34570,34572,34574,34576],{},[485,34559,33440],{"align":33429},[485,34561,34471],{"align":33429},[485,34563,34564],{"align":33429},"0.523008",[485,34566,34567],{"align":33429},"1.102743",[485,34569,2553],{"align":33429},[485,34571,2553],{"align":33429},[485,34573,2553],{"align":33429},[485,34575,802],{"align":33429},[485,34577,34578],{"align":33429},"8",[467,34580,34581,34583,34585,34588,34591,34593,34595,34597,34599],{},[485,34582,33443],{"align":33429},[485,34584,34471],{"align":33429},[485,34586,34587],{"align":33429},"0.381594",[485,34589,34590],{"align":33429},"0.806057",[485,34592,2553],{"align":33429},[485,34594,2553],{"align":33429},[485,34596,2553],{"align":33429},[485,34598,2553],{"align":33429},[485,34600,4114],{"align":33429},[467,34602,34603,34605,34607,34610,34613,34615,34618,34621,34624],{},[485,34604,33446],{"align":33429},[485,34606,34471],{"align":33429},[485,34608,34609],{"align":33429},"32.204208",[485,34611,34612],{"align":33429},"49.693429",[485,34614,2553],{"align":33429},[485,34616,34617],{"align":33429},"7.9104",[485,34619,34620],{"align":33429},"14.4542",[485,34622,34623],{"align":33429},"31",[485,34625,34626],{"align":33429},"512.3292",[467,34628,34629,34631,34633,34636,34639,34641,34643,34645,34647],{},[485,34630,34170],{"align":33429},[485,34632,34471],{"align":33429},[485,34634,34635],{"align":33429},"0.08642",[485,34637,34638],{"align":33429},"0.281141",[485,34640,2553],{"align":33429},[485,34642,2553],{"align":33429},[485,34644,2553],{"align":33429},[485,34646,2553],{"align":33429},[485,34648,802],{"align":33429},[467,34650,34651,34653,34655,34658,34661,34663,34665,34667,34669],{},[485,34652,34173],{"align":33429},[485,34654,34471],{"align":33429},[485,34656,34657],{"align":33429},"0.725028",[485,34659,34660],{"align":33429},"0.446751",[485,34662,2553],{"align":33429},[485,34664,2553],{"align":33429},[485,34666,802],{"align":33429},[485,34668,802],{"align":33429},[485,34670,802],{"align":33429},[12,34672,34673,34674,34676],{},"De esta estadística descriptiva vemos que la edad tiene un rango amplio (desde bebés hasta ancianos), y que la tarifa (",[145,34675,33446],{},") también varía mucho, con algunos pasajeros pagando tarifas muy altas (probablemente de primera clase).",[323,34678,34680],{"id":34679},"_3-eda-distribuciones-y-relaciones","3. EDA: Distribuciones y Relaciones",[12,34682,34683],{},"Con los datos limpios, comencemos a explorar visualmente:",[1612,34685,34687],{"id":34686},"distribución-de-la-variable-objetivo","Distribución de la variable objetivo",[164,34689,34691],{"className":166,"code":34690,"language":168,"meta":169,"style":169},"plt.figure(figsize=(7, 5))\nax = sns.countplot(data=df, x='survived', palette='viridis', hue='survived', legend=False)\nplt.title('Distribución de Supervivencia (0 = No, 1 = Sí)')\nplt.xlabel('Sobrevivió')\nplt.ylabel('Cantidad de pasajeros')\n\n# Etiquetas de porcentaje\ntotal = len(df)\nfor p in ax.patches:\n  height = p.get_height()\n  ax.annotate(f'{(height\u002Ftotal)*100:.1f}%',\n        (p.get_x() + p.get_width() \u002F 2, height),\n        ha='center', va='bottom', fontsize=10, xytext=(0, 4),\n        textcoords='offset points')\n\nplt.tight_layout()\nplt.show()\n",[145,34692,34693,34720,34793,34813,34833,34853,34857,34862,34878,34897,34914,34959,34996,35048,35064,35068,35079],{"__ignoreMap":169},[86,34694,34695,34697,34699,34702,34704,34707,34710,34713,34715,34718],{"class":174,"line":175},[86,34696,33172],{"class":182},[86,34698,61],{"class":219},[86,34700,34701],{"class":182},"figure",[86,34703,243],{"class":219},[86,34705,34706],{"class":304},"figsize",[86,34708,34709],{"class":219},"=(",[86,34711,34712],{"class":223},"7",[86,34714,291],{"class":219},[86,34716,34717],{"class":223}," 5",[86,34719,33401],{"class":219},[86,34721,34722,34725,34727,34729,34731,34734,34736,34738,34740,34742,34744,34747,34749,34751,34753,34755,34757,34760,34762,34764,34767,34769,34771,34774,34776,34778,34780,34782,34784,34787,34789,34791],{"class":174,"line":192},[86,34723,34724],{"class":182},"ax ",[86,34726,258],{"class":219},[86,34728,33220],{"class":182},[86,34730,61],{"class":219},[86,34732,34733],{"class":182},"countplot",[86,34735,243],{"class":219},[86,34737,11013],{"class":304},[86,34739,258],{"class":219},[86,34741,569],{"class":182},[86,34743,291],{"class":219},[86,34745,34746],{"class":304}," x",[86,34748,258],{"class":219},[86,34750,10971],{"class":575},[86,34752,33042],{"class":579},[86,34754,10971],{"class":575},[86,34756,291],{"class":219},[86,34758,34759],{"class":304}," palette",[86,34761,258],{"class":219},[86,34763,10971],{"class":575},[86,34765,34766],{"class":579},"viridis",[86,34768,10971],{"class":575},[86,34770,291],{"class":219},[86,34772,34773],{"class":304}," hue",[86,34775,258],{"class":219},[86,34777,10971],{"class":575},[86,34779,33042],{"class":579},[86,34781,10971],{"class":575},[86,34783,291],{"class":219},[86,34785,34786],{"class":304}," legend",[86,34788,258],{"class":219},[86,34790,33508],{"class":178},[86,34792,273],{"class":219},[86,34794,34795,34797,34799,34802,34804,34806,34809,34811],{"class":174,"line":205},[86,34796,33172],{"class":182},[86,34798,61],{"class":219},[86,34800,34801],{"class":182},"title",[86,34803,243],{"class":219},[86,34805,10971],{"class":575},[86,34807,34808],{"class":579},"Distribución de Supervivencia (0 = No, 1 = Sí)",[86,34810,10971],{"class":575},[86,34812,273],{"class":219},[86,34814,34815,34817,34819,34822,34824,34826,34829,34831],{"class":174,"line":212},[86,34816,33172],{"class":182},[86,34818,61],{"class":219},[86,34820,34821],{"class":182},"xlabel",[86,34823,243],{"class":219},[86,34825,10971],{"class":575},[86,34827,34828],{"class":579},"Sobrevivió",[86,34830,10971],{"class":575},[86,34832,273],{"class":219},[86,34834,34835,34837,34839,34842,34844,34846,34849,34851],{"class":174,"line":227},[86,34836,33172],{"class":182},[86,34838,61],{"class":219},[86,34840,34841],{"class":182},"ylabel",[86,34843,243],{"class":219},[86,34845,10971],{"class":575},[86,34847,34848],{"class":579},"Cantidad de pasajeros",[86,34850,10971],{"class":575},[86,34852,273],{"class":219},[86,34854,34855],{"class":174,"line":232},[86,34856,209],{"emptyLinePlaceholder":208},[86,34858,34859],{"class":174,"line":252},[86,34860,34861],{"class":1360},"# Etiquetas de porcentaje\n",[86,34863,34864,34867,34869,34872,34874,34876],{"class":174,"line":276},[86,34865,34866],{"class":182},"total ",[86,34868,258],{"class":219},[86,34870,34871],{"class":812}," len",[86,34873,243],{"class":219},[86,34875,569],{"class":182},[86,34877,273],{"class":219},[86,34879,34880,34882,34885,34887,34889,34891,34894],{"class":174,"line":315},[86,34881,9680],{"class":178},[86,34883,34884],{"class":182}," p ",[86,34886,12015],{"class":178},[86,34888,9753],{"class":182},[86,34890,61],{"class":219},[86,34892,34893],{"class":182},"patches",[86,34895,34896],{"class":219},":\n",[86,34898,34899,34902,34904,34907,34909,34912],{"class":174,"line":3665},[86,34900,34901],{"class":182},"  height ",[86,34903,258],{"class":219},[86,34905,34906],{"class":182}," p",[86,34908,61],{"class":219},[86,34910,34911],{"class":182},"get_height",[86,34913,11991],{"class":219},[86,34915,34916,34919,34921,34924,34926,34928,34930,34932,34934,34937,34939,34942,34944,34947,34949,34952,34954,34957],{"class":174,"line":13256},[86,34917,34918],{"class":182},"  ax",[86,34920,61],{"class":219},[86,34922,34923],{"class":182},"annotate",[86,34925,243],{"class":219},[86,34927,6178],{"class":235},[86,34929,10971],{"class":579},[86,34931,4089],{"class":215},[86,34933,243],{"class":219},[86,34935,34936],{"class":182},"height",[86,34938,16555],{"class":235},[86,34940,34941],{"class":182},"total",[86,34943,867],{"class":219},[86,34945,34946],{"class":235},"*",[86,34948,15026],{"class":223},[86,34950,34951],{"class":235},":.1f",[86,34953,4117],{"class":215},[86,34955,34956],{"class":579},"%'",[86,34958,1111],{"class":219},[86,34960,34961,34964,34966,34968,34971,34973,34976,34978,34980,34983,34985,34987,34989,34991,34994],{"class":174,"line":13286},[86,34962,34963],{"class":219},"        (",[86,34965,12],{"class":182},[86,34967,61],{"class":219},[86,34969,34970],{"class":182},"get_x",[86,34972,13418],{"class":219},[86,34974,34975],{"class":235}," +",[86,34977,34906],{"class":182},[86,34979,61],{"class":219},[86,34981,34982],{"class":182},"get_width",[86,34984,13418],{"class":219},[86,34986,603],{"class":235},[86,34988,624],{"class":223},[86,34990,291],{"class":219},[86,34992,34993],{"class":182}," height",[86,34995,1412],{"class":219},[86,34997,34998,35001,35003,35005,35007,35009,35011,35014,35016,35018,35021,35023,35025,35028,35030,35032,35034,35037,35039,35041,35043,35046],{"class":174,"line":13291},[86,34999,35000],{"class":304},"        ha",[86,35002,258],{"class":219},[86,35004,10971],{"class":575},[86,35006,29379],{"class":579},[86,35008,10971],{"class":575},[86,35010,291],{"class":219},[86,35012,35013],{"class":304}," va",[86,35015,258],{"class":219},[86,35017,10971],{"class":575},[86,35019,35020],{"class":579},"bottom",[86,35022,10971],{"class":575},[86,35024,291],{"class":219},[86,35026,35027],{"class":304}," fontsize",[86,35029,258],{"class":219},[86,35031,15021],{"class":223},[86,35033,291],{"class":219},[86,35035,35036],{"class":304}," xytext",[86,35038,34709],{"class":219},[86,35040,2553],{"class":223},[86,35042,291],{"class":219},[86,35044,35045],{"class":223}," 4",[86,35047,1412],{"class":219},[86,35049,35050,35053,35055,35057,35060,35062],{"class":174,"line":13308},[86,35051,35052],{"class":304},"        textcoords",[86,35054,258],{"class":219},[86,35056,10971],{"class":575},[86,35058,35059],{"class":579},"offset points",[86,35061,10971],{"class":575},[86,35063,273],{"class":219},[86,35065,35066],{"class":174,"line":13334},[86,35067,209],{"emptyLinePlaceholder":208},[86,35069,35070,35072,35074,35077],{"class":174,"line":13359},[86,35071,33172],{"class":182},[86,35073,61],{"class":219},[86,35075,35076],{"class":182},"tight_layout",[86,35078,11991],{"class":219},[86,35080,35081,35083,35085,35088],{"class":174,"line":13385},[86,35082,33172],{"class":182},[86,35084,61],{"class":219},[86,35086,35087],{"class":182},"show",[86,35089,11991],{"class":219},[12,35091,35092,35096],{},[1945,35093],{"alt":35094,"src":35095},"Distribución de Supervivencia","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Fsurvived_distribution.webp",[901,35097,35098],{},"De los 891 pasajeros, aproximadamente el 38% sobrevivió.",[12,35100,35101,35102,61],{},"Vemos una clase negativa más frecuente (más pasajeros NO sobrevivieron), así que conviene evaluar algo más que ",[122,35103,35104],{},"exactitud",[1612,35106,35108],{"id":35107},"supervivencia-por-sexo-y-clase","Supervivencia por sexo y clase",[164,35110,35112],{"className":166,"code":35111,"language":168,"meta":169,"style":169},"fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n\nsns.barplot(data=df, x='sex', y='survived', ax=axes[0], palette='Set2', hue='sex', legend=False)\naxes[0].set_title('Tasa de Supervivencia por Sexo (0 = Hombre, 1 = Mujer)')\naxes[0].set_xlabel('Sexo')\naxes[0].set_ylabel('Tasa media de supervivencia')\n\nsns.barplot(data=df, x='pclass', y='survived', ax=axes[1], palette='Set2', hue='pclass', legend=False)\naxes[1].set_title('Tasa de Supervivencia por Clase del Boleto')\naxes[1].set_xlabel('Clase del boleto')\naxes[1].set_ylabel('Tasa media de supervivencia')\n\nplt.tight_layout()\nplt.show()\n",[145,35113,35114,35158,35162,35251,35275,35299,35323,35327,35413,35436,35459,35481,35485,35495],{"__ignoreMap":169},[86,35115,35116,35119,35121,35124,35126,35129,35131,35134,35136,35138,35140,35142,35144,35147,35149,35152,35154,35156],{"class":174,"line":175},[86,35117,35118],{"class":182},"fig",[86,35120,291],{"class":219},[86,35122,35123],{"class":182}," axes ",[86,35125,258],{"class":219},[86,35127,35128],{"class":182}," plt",[86,35130,61],{"class":219},[86,35132,35133],{"class":182},"subplots",[86,35135,243],{"class":219},[86,35137,802],{"class":223},[86,35139,291],{"class":219},[86,35141,624],{"class":223},[86,35143,291],{"class":219},[86,35145,35146],{"class":304}," figsize",[86,35148,34709],{"class":219},[86,35150,35151],{"class":223},"14",[86,35153,291],{"class":219},[86,35155,34717],{"class":223},[86,35157,33401],{"class":219},[86,35159,35160],{"class":174,"line":192},[86,35161,209],{"emptyLinePlaceholder":208},[86,35163,35164,35166,35168,35171,35173,35175,35177,35179,35181,35183,35185,35187,35189,35191,35193,35195,35197,35199,35201,35203,35205,35207,35209,35212,35214,35216,35218,35220,35222,35224,35227,35229,35231,35233,35235,35237,35239,35241,35243,35245,35247,35249],{"class":174,"line":205},[86,35165,33151],{"class":182},[86,35167,61],{"class":219},[86,35169,35170],{"class":182},"barplot",[86,35172,243],{"class":219},[86,35174,11013],{"class":304},[86,35176,258],{"class":219},[86,35178,569],{"class":182},[86,35180,291],{"class":219},[86,35182,34746],{"class":304},[86,35184,258],{"class":219},[86,35186,10971],{"class":575},[86,35188,33434],{"class":579},[86,35190,10971],{"class":575},[86,35192,291],{"class":219},[86,35194,1098],{"class":304},[86,35196,258],{"class":219},[86,35198,10971],{"class":575},[86,35200,33042],{"class":579},[86,35202,10971],{"class":575},[86,35204,291],{"class":219},[86,35206,9753],{"class":304},[86,35208,258],{"class":219},[86,35210,35211],{"class":182},"axes",[86,35213,572],{"class":219},[86,35215,2553],{"class":223},[86,35217,9750],{"class":219},[86,35219,34759],{"class":304},[86,35221,258],{"class":219},[86,35223,10971],{"class":575},[86,35225,35226],{"class":579},"Set2",[86,35228,10971],{"class":575},[86,35230,291],{"class":219},[86,35232,34773],{"class":304},[86,35234,258],{"class":219},[86,35236,10971],{"class":575},[86,35238,33434],{"class":579},[86,35240,10971],{"class":575},[86,35242,291],{"class":219},[86,35244,34786],{"class":304},[86,35246,258],{"class":219},[86,35248,33508],{"class":178},[86,35250,273],{"class":219},[86,35252,35253,35255,35257,35259,35261,35264,35266,35268,35271,35273],{"class":174,"line":212},[86,35254,35211],{"class":182},[86,35256,572],{"class":219},[86,35258,2553],{"class":223},[86,35260,13224],{"class":219},[86,35262,35263],{"class":182},"set_title",[86,35265,243],{"class":219},[86,35267,10971],{"class":575},[86,35269,35270],{"class":579},"Tasa de Supervivencia por Sexo (0 = Hombre, 1 = Mujer)",[86,35272,10971],{"class":575},[86,35274,273],{"class":219},[86,35276,35277,35279,35281,35283,35285,35288,35290,35292,35295,35297],{"class":174,"line":227},[86,35278,35211],{"class":182},[86,35280,572],{"class":219},[86,35282,2553],{"class":223},[86,35284,13224],{"class":219},[86,35286,35287],{"class":182},"set_xlabel",[86,35289,243],{"class":219},[86,35291,10971],{"class":575},[86,35293,35294],{"class":579},"Sexo",[86,35296,10971],{"class":575},[86,35298,273],{"class":219},[86,35300,35301,35303,35305,35307,35309,35312,35314,35316,35319,35321],{"class":174,"line":232},[86,35302,35211],{"class":182},[86,35304,572],{"class":219},[86,35306,2553],{"class":223},[86,35308,13224],{"class":219},[86,35310,35311],{"class":182},"set_ylabel",[86,35313,243],{"class":219},[86,35315,10971],{"class":575},[86,35317,35318],{"class":579},"Tasa media de supervivencia",[86,35320,10971],{"class":575},[86,35322,273],{"class":219},[86,35324,35325],{"class":174,"line":252},[86,35326,209],{"emptyLinePlaceholder":208},[86,35328,35329,35331,35333,35335,35337,35339,35341,35343,35345,35347,35349,35351,35353,35355,35357,35359,35361,35363,35365,35367,35369,35371,35373,35375,35377,35379,35381,35383,35385,35387,35389,35391,35393,35395,35397,35399,35401,35403,35405,35407,35409,35411],{"class":174,"line":276},[86,35330,33151],{"class":182},[86,35332,61],{"class":219},[86,35334,35170],{"class":182},[86,35336,243],{"class":219},[86,35338,11013],{"class":304},[86,35340,258],{"class":219},[86,35342,569],{"class":182},[86,35344,291],{"class":219},[86,35346,34746],{"class":304},[86,35348,258],{"class":219},[86,35350,10971],{"class":575},[86,35352,33420],{"class":579},[86,35354,10971],{"class":575},[86,35356,291],{"class":219},[86,35358,1098],{"class":304},[86,35360,258],{"class":219},[86,35362,10971],{"class":575},[86,35364,33042],{"class":579},[86,35366,10971],{"class":575},[86,35368,291],{"class":219},[86,35370,9753],{"class":304},[86,35372,258],{"class":219},[86,35374,35211],{"class":182},[86,35376,572],{"class":219},[86,35378,802],{"class":223},[86,35380,9750],{"class":219},[86,35382,34759],{"class":304},[86,35384,258],{"class":219},[86,35386,10971],{"class":575},[86,35388,35226],{"class":579},[86,35390,10971],{"class":575},[86,35392,291],{"class":219},[86,35394,34773],{"class":304},[86,35396,258],{"class":219},[86,35398,10971],{"class":575},[86,35400,33420],{"class":579},[86,35402,10971],{"class":575},[86,35404,291],{"class":219},[86,35406,34786],{"class":304},[86,35408,258],{"class":219},[86,35410,33508],{"class":178},[86,35412,273],{"class":219},[86,35414,35415,35417,35419,35421,35423,35425,35427,35429,35432,35434],{"class":174,"line":315},[86,35416,35211],{"class":182},[86,35418,572],{"class":219},[86,35420,802],{"class":223},[86,35422,13224],{"class":219},[86,35424,35263],{"class":182},[86,35426,243],{"class":219},[86,35428,10971],{"class":575},[86,35430,35431],{"class":579},"Tasa de Supervivencia por Clase del Boleto",[86,35433,10971],{"class":575},[86,35435,273],{"class":219},[86,35437,35438,35440,35442,35444,35446,35448,35450,35452,35455,35457],{"class":174,"line":3665},[86,35439,35211],{"class":182},[86,35441,572],{"class":219},[86,35443,802],{"class":223},[86,35445,13224],{"class":219},[86,35447,35287],{"class":182},[86,35449,243],{"class":219},[86,35451,10971],{"class":575},[86,35453,35454],{"class":579},"Clase del boleto",[86,35456,10971],{"class":575},[86,35458,273],{"class":219},[86,35460,35461,35463,35465,35467,35469,35471,35473,35475,35477,35479],{"class":174,"line":13256},[86,35462,35211],{"class":182},[86,35464,572],{"class":219},[86,35466,802],{"class":223},[86,35468,13224],{"class":219},[86,35470,35311],{"class":182},[86,35472,243],{"class":219},[86,35474,10971],{"class":575},[86,35476,35318],{"class":579},[86,35478,10971],{"class":575},[86,35480,273],{"class":219},[86,35482,35483],{"class":174,"line":13286},[86,35484,209],{"emptyLinePlaceholder":208},[86,35486,35487,35489,35491,35493],{"class":174,"line":13291},[86,35488,33172],{"class":182},[86,35490,61],{"class":219},[86,35492,35076],{"class":182},[86,35494,11991],{"class":219},[86,35496,35497,35499,35501,35503],{"class":174,"line":13308},[86,35498,33172],{"class":182},[86,35500,61],{"class":219},[86,35502,35087],{"class":182},[86,35504,11991],{"class":219},[12,35506,35507,35511],{},[1945,35508],{"alt":35509,"src":35510},"Tasa de Supervivencia por Sexo y Clase","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Fsurvival_by_sex_and_class.webp",[901,35512,35513],{},"Mayor supervivencia en mujeres, además de una tendencia positiva cuanto mayor es la clase.",[12,35515,35516],{},"Se mantiene un patrón esperado: mayor supervivencia en mujeres y en clases más altas.",[1612,35518,35520],{"id":35519},"matriz-de-correlación","Matriz de correlación",[164,35522,35524],{"className":166,"code":35523,"language":168,"meta":169,"style":169},"corr = df.corr(numeric_only=True)\nplt.figure(figsize=(10, 8))\nsns.heatmap(corr, annot=True, fmt='.2f', cmap='coolwarm', square=True, linewidths=0.4)\nplt.title('Matriz de Correlación de Variables')\nplt.tight_layout()\nplt.show()\n",[145,35525,35526,35551,35573,35643,35662,35672],{"__ignoreMap":169},[86,35527,35528,35531,35533,35535,35537,35540,35542,35545,35547,35549],{"class":174,"line":175},[86,35529,35530],{"class":182},"corr ",[86,35532,258],{"class":219},[86,35534,590],{"class":182},[86,35536,61],{"class":219},[86,35538,35539],{"class":182},"corr",[86,35541,243],{"class":219},[86,35543,35544],{"class":304},"numeric_only",[86,35546,258],{"class":219},[86,35548,310],{"class":178},[86,35550,273],{"class":219},[86,35552,35553,35555,35557,35559,35561,35563,35565,35567,35569,35571],{"class":174,"line":192},[86,35554,33172],{"class":182},[86,35556,61],{"class":219},[86,35558,34701],{"class":182},[86,35560,243],{"class":219},[86,35562,34706],{"class":304},[86,35564,34709],{"class":219},[86,35566,15021],{"class":223},[86,35568,291],{"class":219},[86,35570,33199],{"class":223},[86,35572,33401],{"class":219},[86,35574,35575,35577,35579,35582,35584,35586,35588,35591,35593,35595,35597,35600,35602,35604,35607,35609,35611,35614,35616,35618,35621,35623,35625,35628,35630,35632,35634,35637,35639,35641],{"class":174,"line":205},[86,35576,33151],{"class":182},[86,35578,61],{"class":219},[86,35580,35581],{"class":182},"heatmap",[86,35583,243],{"class":219},[86,35585,35539],{"class":182},[86,35587,291],{"class":219},[86,35589,35590],{"class":304}," annot",[86,35592,258],{"class":219},[86,35594,310],{"class":178},[86,35596,291],{"class":219},[86,35598,35599],{"class":304}," fmt",[86,35601,258],{"class":219},[86,35603,10971],{"class":575},[86,35605,35606],{"class":579},".2f",[86,35608,10971],{"class":575},[86,35610,291],{"class":219},[86,35612,35613],{"class":304}," cmap",[86,35615,258],{"class":219},[86,35617,10971],{"class":575},[86,35619,35620],{"class":579},"coolwarm",[86,35622,10971],{"class":575},[86,35624,291],{"class":219},[86,35626,35627],{"class":304}," square",[86,35629,258],{"class":219},[86,35631,310],{"class":178},[86,35633,291],{"class":219},[86,35635,35636],{"class":304}," linewidths",[86,35638,258],{"class":219},[86,35640,5947],{"class":223},[86,35642,273],{"class":219},[86,35644,35645,35647,35649,35651,35653,35655,35658,35660],{"class":174,"line":212},[86,35646,33172],{"class":182},[86,35648,61],{"class":219},[86,35650,34801],{"class":182},[86,35652,243],{"class":219},[86,35654,10971],{"class":575},[86,35656,35657],{"class":579},"Matriz de Correlación de Variables",[86,35659,10971],{"class":575},[86,35661,273],{"class":219},[86,35663,35664,35666,35668,35670],{"class":174,"line":227},[86,35665,33172],{"class":182},[86,35667,61],{"class":219},[86,35669,35076],{"class":182},[86,35671,11991],{"class":219},[86,35673,35674,35676,35678,35680],{"class":174,"line":232},[86,35675,33172],{"class":182},[86,35677,61],{"class":219},[86,35679,35087],{"class":182},[86,35681,11991],{"class":219},[12,35683,35684,35688],{},[1945,35685],{"alt":35686,"src":35687},"Matriz de Correlación","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Fcorrelation_matrix.webp",[901,35689,35520],{},[12,35691,35692,35694],{},[145,35693,33042],{}," es nuestra variable objetivo, así que nos interesa ver qué variables influyen más:",[30,35696,35697,35705,35713,35721,35729],{},[33,35698,35699,35704],{},[122,35700,35701,35703],{},[145,35702,33434],{}," (0.54)"," - correlación positiva moderada-alta.\nEl sexo influye bastante en la supervivencia.",[33,35706,35707,35712],{},[122,35708,35709,35711],{},[145,35710,33420],{}," (-0.34)"," - correlación negativa moderada.\nA menor clase (3ra clase = número mayor), menor probabilidad de sobrevivir.",[33,35714,35715,35720],{},[122,35716,35717,35719],{},[145,35718,33446],{}," (0.26)"," - correlación positiva baja-moderada.\nA mayor tarifa pagada, mayor probabilidad de sobrevivir (relacionado con clase).",[33,35722,35723,35728],{},[122,35724,35725,35727],{},[145,35726,33467],{}," (-0.20)"," - correlación negativa leve.\nViajar solo disminuye ligeramente la probabilidad de sobrevivir.",[33,35730,35731,35736],{},[122,35732,35733,35735],{},[145,35734,33437],{}," (-0.06)"," - casi no hay relación lineal, es decir, la edad no influye de forma clara en la supervivencia para este caso.",[12,35738,35739],{},"Busquemos otras correlaciones altas entre variables independientes:",[30,35741,35742,35752,35762,35771],{},[33,35743,35744,35751],{},[122,35745,35746,392,35748,35750],{},[145,35747,33440],{},[145,35749,33443],{}," (0.41)","\nRelación moderada. Ambas miden familiares a bordo.",[33,35753,35754,35761],{},[122,35755,35756,392,35758,35760],{},[145,35757,33440],{},[145,35759,33467],{}," (-0.58)","\nFuerte relación negativa. Aunque bueno, es de esperar que si tienes hermanos\u002Fesposos a bordo, no viajas solo (?).",[33,35763,35764,35770],{},[122,35765,35766,392,35768,35760],{},[145,35767,33443],{},[145,35769,33467],{},"\nIgual lógica: si tienes padres\u002Fhijos a bordo, no viajas solo.",[33,35772,35773,35780],{},[122,35774,35775,392,35777,35779],{},[145,35776,33420],{},[145,35778,33446],{}," (-0.55)","\nFuerte correlación negativa. Mejor clase -> mayor precio.",[12,35782,35783],{},"Con lo anterior hemos detectado que algunas variables contienen información similar.",[30,35785,35786],{},[33,35787,35788,35795,35796,35798],{},[122,35789,35790,392,35792,35794],{},[145,35791,34170],{},[145,35793,34173],{}," (-0.50)","\nTiene sentido porque si una es 1, la otra probablemente es 0.\nEsto es típico cuando se crean variables dummy, y por eso normalmente se usa ",[145,35797,34117],{}," para evitar redundancia perfecta.",[12,35800,35801,35802,392,35804,34114,35806,35808],{},"Veámos ahora la relación entre ",[145,35803,33437],{},[145,35805,33446],{},[145,35807,33042],{}," usando boxplots:",[164,35810,35812],{"className":166,"code":35811,"language":168,"meta":169,"style":169},"fig, axes = plt.subplots(1, 2, figsize=(14, 5))\n\nsns.boxplot(data=df, x='survived', y='age', ax=axes[0])\naxes[0].set_title('Distribución de Edad por Supervivencia')\naxes[0].set_xlabel('Supervivencia')\naxes[0].set_ylabel('Edad')\n\nsns.boxplot(data=df, x='survived', y='fare', ax=axes[1])\naxes[1].set_title('Distribución de Tarifa por Supervivencia')\naxes[1].set_xlabel('Supervivencia')\naxes[1].set_ylabel('Tarifa')\n\nplt.tight_layout()\nplt.show()\n",[145,35813,35814,35852,35856,35911,35934,35957,35979,35983,36037,36060,36082,36105,36109,36119],{"__ignoreMap":169},[86,35815,35816,35818,35820,35822,35824,35826,35828,35830,35832,35834,35836,35838,35840,35842,35844,35846,35848,35850],{"class":174,"line":175},[86,35817,35118],{"class":182},[86,35819,291],{"class":219},[86,35821,35123],{"class":182},[86,35823,258],{"class":219},[86,35825,35128],{"class":182},[86,35827,61],{"class":219},[86,35829,35133],{"class":182},[86,35831,243],{"class":219},[86,35833,802],{"class":223},[86,35835,291],{"class":219},[86,35837,624],{"class":223},[86,35839,291],{"class":219},[86,35841,35146],{"class":304},[86,35843,34709],{"class":219},[86,35845,35151],{"class":223},[86,35847,291],{"class":219},[86,35849,34717],{"class":223},[86,35851,33401],{"class":219},[86,35853,35854],{"class":174,"line":192},[86,35855,209],{"emptyLinePlaceholder":208},[86,35857,35858,35860,35862,35865,35867,35869,35871,35873,35875,35877,35879,35881,35883,35885,35887,35889,35891,35893,35895,35897,35899,35901,35903,35905,35907,35909],{"class":174,"line":205},[86,35859,33151],{"class":182},[86,35861,61],{"class":219},[86,35863,35864],{"class":182},"boxplot",[86,35866,243],{"class":219},[86,35868,11013],{"class":304},[86,35870,258],{"class":219},[86,35872,569],{"class":182},[86,35874,291],{"class":219},[86,35876,34746],{"class":304},[86,35878,258],{"class":219},[86,35880,10971],{"class":575},[86,35882,33042],{"class":579},[86,35884,10971],{"class":575},[86,35886,291],{"class":219},[86,35888,1098],{"class":304},[86,35890,258],{"class":219},[86,35892,10971],{"class":575},[86,35894,33437],{"class":579},[86,35896,10971],{"class":575},[86,35898,291],{"class":219},[86,35900,9753],{"class":304},[86,35902,258],{"class":219},[86,35904,35211],{"class":182},[86,35906,572],{"class":219},[86,35908,2553],{"class":223},[86,35910,1417],{"class":219},[86,35912,35913,35915,35917,35919,35921,35923,35925,35927,35930,35932],{"class":174,"line":212},[86,35914,35211],{"class":182},[86,35916,572],{"class":219},[86,35918,2553],{"class":223},[86,35920,13224],{"class":219},[86,35922,35263],{"class":182},[86,35924,243],{"class":219},[86,35926,10971],{"class":575},[86,35928,35929],{"class":579},"Distribución de Edad por Supervivencia",[86,35931,10971],{"class":575},[86,35933,273],{"class":219},[86,35935,35936,35938,35940,35942,35944,35946,35948,35950,35953,35955],{"class":174,"line":227},[86,35937,35211],{"class":182},[86,35939,572],{"class":219},[86,35941,2553],{"class":223},[86,35943,13224],{"class":219},[86,35945,35287],{"class":182},[86,35947,243],{"class":219},[86,35949,10971],{"class":575},[86,35951,35952],{"class":579},"Supervivencia",[86,35954,10971],{"class":575},[86,35956,273],{"class":219},[86,35958,35959,35961,35963,35965,35967,35969,35971,35973,35975,35977],{"class":174,"line":232},[86,35960,35211],{"class":182},[86,35962,572],{"class":219},[86,35964,2553],{"class":223},[86,35966,13224],{"class":219},[86,35968,35311],{"class":182},[86,35970,243],{"class":219},[86,35972,10971],{"class":575},[86,35974,19849],{"class":579},[86,35976,10971],{"class":575},[86,35978,273],{"class":219},[86,35980,35981],{"class":174,"line":252},[86,35982,209],{"emptyLinePlaceholder":208},[86,35984,35985,35987,35989,35991,35993,35995,35997,35999,36001,36003,36005,36007,36009,36011,36013,36015,36017,36019,36021,36023,36025,36027,36029,36031,36033,36035],{"class":174,"line":276},[86,35986,33151],{"class":182},[86,35988,61],{"class":219},[86,35990,35864],{"class":182},[86,35992,243],{"class":219},[86,35994,11013],{"class":304},[86,35996,258],{"class":219},[86,35998,569],{"class":182},[86,36000,291],{"class":219},[86,36002,34746],{"class":304},[86,36004,258],{"class":219},[86,36006,10971],{"class":575},[86,36008,33042],{"class":579},[86,36010,10971],{"class":575},[86,36012,291],{"class":219},[86,36014,1098],{"class":304},[86,36016,258],{"class":219},[86,36018,10971],{"class":575},[86,36020,33446],{"class":579},[86,36022,10971],{"class":575},[86,36024,291],{"class":219},[86,36026,9753],{"class":304},[86,36028,258],{"class":219},[86,36030,35211],{"class":182},[86,36032,572],{"class":219},[86,36034,802],{"class":223},[86,36036,1417],{"class":219},[86,36038,36039,36041,36043,36045,36047,36049,36051,36053,36056,36058],{"class":174,"line":315},[86,36040,35211],{"class":182},[86,36042,572],{"class":219},[86,36044,802],{"class":223},[86,36046,13224],{"class":219},[86,36048,35263],{"class":182},[86,36050,243],{"class":219},[86,36052,10971],{"class":575},[86,36054,36055],{"class":579},"Distribución de Tarifa por Supervivencia",[86,36057,10971],{"class":575},[86,36059,273],{"class":219},[86,36061,36062,36064,36066,36068,36070,36072,36074,36076,36078,36080],{"class":174,"line":3665},[86,36063,35211],{"class":182},[86,36065,572],{"class":219},[86,36067,802],{"class":223},[86,36069,13224],{"class":219},[86,36071,35287],{"class":182},[86,36073,243],{"class":219},[86,36075,10971],{"class":575},[86,36077,35952],{"class":579},[86,36079,10971],{"class":575},[86,36081,273],{"class":219},[86,36083,36084,36086,36088,36090,36092,36094,36096,36098,36101,36103],{"class":174,"line":13256},[86,36085,35211],{"class":182},[86,36087,572],{"class":219},[86,36089,802],{"class":223},[86,36091,13224],{"class":219},[86,36093,35311],{"class":182},[86,36095,243],{"class":219},[86,36097,10971],{"class":575},[86,36099,36100],{"class":579},"Tarifa",[86,36102,10971],{"class":575},[86,36104,273],{"class":219},[86,36106,36107],{"class":174,"line":13286},[86,36108,209],{"emptyLinePlaceholder":208},[86,36110,36111,36113,36115,36117],{"class":174,"line":13291},[86,36112,33172],{"class":182},[86,36114,61],{"class":219},[86,36116,35076],{"class":182},[86,36118,11991],{"class":219},[86,36120,36121,36123,36125,36127],{"class":174,"line":13308},[86,36122,33172],{"class":182},[86,36124,61],{"class":219},[86,36126,35087],{"class":182},[86,36128,11991],{"class":219},[12,36130,36131,36135],{},[1945,36132],{"alt":36133,"src":36134},"Boxplots de Edad y Tarifa por Supervivencia","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Fboxplots_age_fare.webp",[901,36136,36133],{},[12,36138,36139],{},"Los boxplots muestran cómo se distribuyen la edad y la tarifa según si la persona sobrevivió o no. En el caso de la edad, las cajas y las líneas centrales (medianas) son muy parecidas entre ambos grupos, lo que indica que la edad, en general, no marca una diferencia clara en la supervivencia. Sin embargo, se observan algunos valores extremos como niños muy pequeños y personas mayores, lo que sugiere que podrían existir diferencias si se analizan por grupos de edad. En cambio, en el gráfico de la tarifa sí se nota una diferencia más clara: las personas que sobrevivieron pagaron, en promedio, tarifas más altas.",[12,36141,36142],{},"Esto indica que el precio del boleto (relacionado con la clase social) tuvo mayor influencia en la probabilidad de sobrevivir que la edad.",[1612,36144,36146],{"id":36145},"ingeniería-de-variables-y-análisis-por-tasa-de-supervivencia","Ingeniería de variables y análisis por tasa de supervivencia",[12,36148,36149,36150,36153,36154,36156],{},"Para profundizar el EDA, ahora crearemos nuevas variables y analizamos combinaciones entre categóricas y numéricas usando ",[122,36151,36152],{},"tasas de supervivencia"," (media de ",[145,36155,33042],{},") en lugar de solo conteos.",[36158,36159,36161,36162],"h5",{"id":36160},"_1-crear-family_size","1) Crear ",[145,36163,36164],{},"family_size",[12,36166,36167],{},"Esto nos da una idea del tamaño del grupo familiar a bordo, lo que podría influir en la supervivencia (por ejemplo, familias grandes podrían tener más dificultades para evacuar).",[164,36169,36171],{"className":166,"code":36170,"language":168,"meta":169,"style":169},"# family_size = pasajero + familiares cercanos a bordo\ndf['family_size'] = df['sibsp'] + df['parch'] + 1\n\nprint('Resumen de family_size:')\ndisplay(df['family_size'].describe())\n\nplt.figure(figsize=(8, 5))\nsns.countplot(data=df, x='family_size', palette='crest', hue='family_size', legend=False)\nplt.title('Distribución de Family Size')\nplt.xlabel('Tamaño de familia')\nplt.ylabel('Cantidad de pasajeros')\nplt.tight_layout()\nplt.show()\n",[145,36172,36173,36178,36225,36229,36244,36266,36270,36292,36355,36374,36393,36411,36421],{"__ignoreMap":169},[86,36174,36175],{"class":174,"line":175},[86,36176,36177],{"class":1360},"# family_size = pasajero + familiares cercanos a bordo\n",[86,36179,36180,36182,36184,36186,36188,36190,36192,36194,36196,36198,36200,36202,36204,36206,36208,36210,36212,36214,36216,36218,36220,36222],{"class":174,"line":192},[86,36181,569],{"class":182},[86,36183,572],{"class":219},[86,36185,10971],{"class":575},[86,36187,36164],{"class":579},[86,36189,10971],{"class":575},[86,36191,585],{"class":219},[86,36193,220],{"class":219},[86,36195,590],{"class":182},[86,36197,572],{"class":219},[86,36199,10971],{"class":575},[86,36201,33440],{"class":579},[86,36203,10971],{"class":575},[86,36205,585],{"class":219},[86,36207,34975],{"class":235},[86,36209,590],{"class":182},[86,36211,572],{"class":219},[86,36213,10971],{"class":575},[86,36215,33443],{"class":579},[86,36217,10971],{"class":575},[86,36219,585],{"class":219},[86,36221,34975],{"class":235},[86,36223,36224],{"class":223}," 1\n",[86,36226,36227],{"class":174,"line":205},[86,36228,209],{"emptyLinePlaceholder":208},[86,36230,36231,36233,36235,36237,36240,36242],{"class":174,"line":212},[86,36232,13294],{"class":812},[86,36234,243],{"class":219},[86,36236,10971],{"class":575},[86,36238,36239],{"class":579},"Resumen de family_size:",[86,36241,10971],{"class":575},[86,36243,273],{"class":219},[86,36245,36246,36248,36250,36252,36254,36256,36258,36260,36262,36264],{"class":174,"line":227},[86,36247,33276],{"class":182},[86,36249,243],{"class":219},[86,36251,569],{"class":182},[86,36253,572],{"class":219},[86,36255,10971],{"class":575},[86,36257,36164],{"class":579},[86,36259,10971],{"class":575},[86,36261,13224],{"class":219},[86,36263,34290],{"class":182},[86,36265,33288],{"class":219},[86,36267,36268],{"class":174,"line":232},[86,36269,209],{"emptyLinePlaceholder":208},[86,36271,36272,36274,36276,36278,36280,36282,36284,36286,36288,36290],{"class":174,"line":252},[86,36273,33172],{"class":182},[86,36275,61],{"class":219},[86,36277,34701],{"class":182},[86,36279,243],{"class":219},[86,36281,34706],{"class":304},[86,36283,34709],{"class":219},[86,36285,34578],{"class":223},[86,36287,291],{"class":219},[86,36289,34717],{"class":223},[86,36291,33401],{"class":219},[86,36293,36294,36296,36298,36300,36302,36304,36306,36308,36310,36312,36314,36316,36318,36320,36322,36324,36326,36328,36331,36333,36335,36337,36339,36341,36343,36345,36347,36349,36351,36353],{"class":174,"line":276},[86,36295,33151],{"class":182},[86,36297,61],{"class":219},[86,36299,34733],{"class":182},[86,36301,243],{"class":219},[86,36303,11013],{"class":304},[86,36305,258],{"class":219},[86,36307,569],{"class":182},[86,36309,291],{"class":219},[86,36311,34746],{"class":304},[86,36313,258],{"class":219},[86,36315,10971],{"class":575},[86,36317,36164],{"class":579},[86,36319,10971],{"class":575},[86,36321,291],{"class":219},[86,36323,34759],{"class":304},[86,36325,258],{"class":219},[86,36327,10971],{"class":575},[86,36329,36330],{"class":579},"crest",[86,36332,10971],{"class":575},[86,36334,291],{"class":219},[86,36336,34773],{"class":304},[86,36338,258],{"class":219},[86,36340,10971],{"class":575},[86,36342,36164],{"class":579},[86,36344,10971],{"class":575},[86,36346,291],{"class":219},[86,36348,34786],{"class":304},[86,36350,258],{"class":219},[86,36352,33508],{"class":178},[86,36354,273],{"class":219},[86,36356,36357,36359,36361,36363,36365,36367,36370,36372],{"class":174,"line":315},[86,36358,33172],{"class":182},[86,36360,61],{"class":219},[86,36362,34801],{"class":182},[86,36364,243],{"class":219},[86,36366,10971],{"class":575},[86,36368,36369],{"class":579},"Distribución de Family Size",[86,36371,10971],{"class":575},[86,36373,273],{"class":219},[86,36375,36376,36378,36380,36382,36384,36386,36389,36391],{"class":174,"line":3665},[86,36377,33172],{"class":182},[86,36379,61],{"class":219},[86,36381,34821],{"class":182},[86,36383,243],{"class":219},[86,36385,10971],{"class":575},[86,36387,36388],{"class":579},"Tamaño de familia",[86,36390,10971],{"class":575},[86,36392,273],{"class":219},[86,36394,36395,36397,36399,36401,36403,36405,36407,36409],{"class":174,"line":13256},[86,36396,33172],{"class":182},[86,36398,61],{"class":219},[86,36400,34841],{"class":182},[86,36402,243],{"class":219},[86,36404,10971],{"class":575},[86,36406,34848],{"class":579},[86,36408,10971],{"class":575},[86,36410,273],{"class":219},[86,36412,36413,36415,36417,36419],{"class":174,"line":13286},[86,36414,33172],{"class":182},[86,36416,61],{"class":219},[86,36418,35076],{"class":182},[86,36420,11991],{"class":219},[86,36422,36423,36425,36427,36429],{"class":174,"line":13291},[86,36424,33172],{"class":182},[86,36426,61],{"class":219},[86,36428,35087],{"class":182},[86,36430,11991],{"class":219},[36158,36432,36434,36435,867],{"id":36433},"_2-agrupar-edad-en-bins-age_group","2) Agrupar edad en bins (",[145,36436,36437],{},"age_group",[12,36439,36440],{},"Aqui podemos crear grupos de edad para ver si hay diferencias más claras en supervivencia entre niños, jóvenes, adultos y ancianos.",[164,36442,36444],{"className":166,"code":36443,"language":168,"meta":169,"style":169},"age_bins = [0, 12, 18, 35, 60, np.inf]\nage_labels = ['child', 'teen', 'young_adult', 'adult', 'senior']\n\ndf['age_group'] = pd.cut(df['age'], bins=age_bins, labels=age_labels, right=False)\n\nprint('Distribución por grupos de edad:')\ndisplay(df['age_group'].value_counts(dropna=False).sort_index())\n",[145,36445,36446,36488,36542,36546,36612,36616,36631],{"__ignoreMap":169},[86,36447,36448,36451,36453,36455,36457,36459,36462,36464,36467,36469,36472,36474,36477,36479,36481,36483,36486],{"class":174,"line":175},[86,36449,36450],{"class":182},"age_bins ",[86,36452,258],{"class":219},[86,36454,726],{"class":219},[86,36456,2553],{"class":223},[86,36458,291],{"class":219},[86,36460,36461],{"class":223}," 12",[86,36463,291],{"class":219},[86,36465,36466],{"class":223}," 18",[86,36468,291],{"class":219},[86,36470,36471],{"class":223}," 35",[86,36473,291],{"class":219},[86,36475,36476],{"class":223}," 60",[86,36478,291],{"class":219},[86,36480,294],{"class":182},[86,36482,61],{"class":219},[86,36484,36485],{"class":182},"inf",[86,36487,752],{"class":219},[86,36489,36490,36493,36495,36497,36499,36502,36504,36506,36508,36511,36513,36515,36517,36520,36522,36524,36526,36529,36531,36533,36535,36538,36540],{"class":174,"line":192},[86,36491,36492],{"class":182},"age_labels ",[86,36494,258],{"class":219},[86,36496,726],{"class":219},[86,36498,10971],{"class":575},[86,36500,36501],{"class":579},"child",[86,36503,10971],{"class":575},[86,36505,291],{"class":219},[86,36507,11970],{"class":575},[86,36509,36510],{"class":579},"teen",[86,36512,10971],{"class":575},[86,36514,291],{"class":219},[86,36516,11970],{"class":575},[86,36518,36519],{"class":579},"young_adult",[86,36521,10971],{"class":575},[86,36523,291],{"class":219},[86,36525,11970],{"class":575},[86,36527,36528],{"class":579},"adult",[86,36530,10971],{"class":575},[86,36532,291],{"class":219},[86,36534,11970],{"class":575},[86,36536,36537],{"class":579},"senior",[86,36539,10971],{"class":575},[86,36541,752],{"class":219},[86,36543,36544],{"class":174,"line":205},[86,36545,209],{"emptyLinePlaceholder":208},[86,36547,36548,36550,36552,36554,36556,36558,36560,36562,36564,36566,36569,36571,36573,36575,36577,36579,36581,36583,36586,36588,36591,36593,36596,36598,36601,36603,36606,36608,36610],{"class":174,"line":212},[86,36549,569],{"class":182},[86,36551,572],{"class":219},[86,36553,10971],{"class":575},[86,36555,36437],{"class":579},[86,36557,10971],{"class":575},[86,36559,585],{"class":219},[86,36561,220],{"class":219},[86,36563,261],{"class":182},[86,36565,61],{"class":219},[86,36567,36568],{"class":182},"cut",[86,36570,243],{"class":219},[86,36572,569],{"class":182},[86,36574,572],{"class":219},[86,36576,10971],{"class":575},[86,36578,33437],{"class":579},[86,36580,10971],{"class":575},[86,36582,9750],{"class":219},[86,36584,36585],{"class":304}," bins",[86,36587,258],{"class":219},[86,36589,36590],{"class":182},"age_bins",[86,36592,291],{"class":219},[86,36594,36595],{"class":304}," labels",[86,36597,258],{"class":219},[86,36599,36600],{"class":182},"age_labels",[86,36602,291],{"class":219},[86,36604,36605],{"class":304}," right",[86,36607,258],{"class":219},[86,36609,33508],{"class":178},[86,36611,273],{"class":219},[86,36613,36614],{"class":174,"line":227},[86,36615,209],{"emptyLinePlaceholder":208},[86,36617,36618,36620,36622,36624,36627,36629],{"class":174,"line":232},[86,36619,13294],{"class":812},[86,36621,243],{"class":219},[86,36623,10971],{"class":575},[86,36625,36626],{"class":579},"Distribución por grupos de edad:",[86,36628,10971],{"class":575},[86,36630,273],{"class":219},[86,36632,36633,36635,36637,36639,36641,36643,36645,36647,36649,36652,36654,36657,36659,36661,36663,36666],{"class":174,"line":252},[86,36634,33276],{"class":182},[86,36636,243],{"class":219},[86,36638,569],{"class":182},[86,36640,572],{"class":219},[86,36642,10971],{"class":575},[86,36644,36437],{"class":579},[86,36646,10971],{"class":575},[86,36648,13224],{"class":219},[86,36650,36651],{"class":182},"value_counts",[86,36653,243],{"class":219},[86,36655,36656],{"class":304},"dropna",[86,36658,258],{"class":219},[86,36660,33508],{"class":178},[86,36662,789],{"class":219},[86,36664,36665],{"class":182},"sort_index",[86,36667,33288],{"class":219},[36158,36669,36671,36672],{"id":36670},"_3-aplicar-transformación-logarítmica-a-fare","3) Aplicar transformación logarítmica a ",[145,36673,33446],{},[12,36675,36676],{},"Al aplicar logaritmo, reducimos el impacto de valores extremos y podemos visualizar mejor la distribución de tarifas.",[164,36678,36680],{"className":166,"code":36679,"language":168,"meta":169,"style":169},"# log1p maneja correctamente tarifas en 0\ndf['fare_log'] = np.log1p(df['fare'])\n\nfig, axes = plt.subplots(1, 2, figsize=(14, 5))\n\nsns.histplot(df['fare'], kde=True, ax=axes[0], color='#2a9d8f')\naxes[0].set_title('Distribución original de Fare')\naxes[0].set_xlabel('Fare')\n\nsns.histplot(df['fare_log'], kde=True, ax=axes[1], color='#e76f51')\naxes[1].set_title('Distribución transformada: log(1 + Fare)')\naxes[1].set_xlabel('Fare (log1p)')\n\nplt.tight_layout()\nplt.show()\n",[145,36681,36682,36687,36725,36729,36767,36771,36829,36852,36875,36879,36934,36957,36980,36984,36994],{"__ignoreMap":169},[86,36683,36684],{"class":174,"line":175},[86,36685,36686],{"class":1360},"# log1p maneja correctamente tarifas en 0\n",[86,36688,36689,36691,36693,36695,36698,36700,36702,36704,36706,36708,36711,36713,36715,36717,36719,36721,36723],{"class":174,"line":192},[86,36690,569],{"class":182},[86,36692,572],{"class":219},[86,36694,10971],{"class":575},[86,36696,36697],{"class":579},"fare_log",[86,36699,10971],{"class":575},[86,36701,585],{"class":219},[86,36703,220],{"class":219},[86,36705,294],{"class":182},[86,36707,61],{"class":219},[86,36709,36710],{"class":182},"log1p",[86,36712,243],{"class":219},[86,36714,569],{"class":182},[86,36716,572],{"class":219},[86,36718,10971],{"class":575},[86,36720,33446],{"class":579},[86,36722,10971],{"class":575},[86,36724,1417],{"class":219},[86,36726,36727],{"class":174,"line":205},[86,36728,209],{"emptyLinePlaceholder":208},[86,36730,36731,36733,36735,36737,36739,36741,36743,36745,36747,36749,36751,36753,36755,36757,36759,36761,36763,36765],{"class":174,"line":212},[86,36732,35118],{"class":182},[86,36734,291],{"class":219},[86,36736,35123],{"class":182},[86,36738,258],{"class":219},[86,36740,35128],{"class":182},[86,36742,61],{"class":219},[86,36744,35133],{"class":182},[86,36746,243],{"class":219},[86,36748,802],{"class":223},[86,36750,291],{"class":219},[86,36752,624],{"class":223},[86,36754,291],{"class":219},[86,36756,35146],{"class":304},[86,36758,34709],{"class":219},[86,36760,35151],{"class":223},[86,36762,291],{"class":219},[86,36764,34717],{"class":223},[86,36766,33401],{"class":219},[86,36768,36769],{"class":174,"line":227},[86,36770,209],{"emptyLinePlaceholder":208},[86,36772,36773,36775,36777,36780,36782,36784,36786,36788,36790,36792,36794,36797,36799,36801,36803,36805,36807,36809,36811,36813,36815,36818,36820,36822,36825,36827],{"class":174,"line":232},[86,36774,33151],{"class":182},[86,36776,61],{"class":219},[86,36778,36779],{"class":182},"histplot",[86,36781,243],{"class":219},[86,36783,569],{"class":182},[86,36785,572],{"class":219},[86,36787,10971],{"class":575},[86,36789,33446],{"class":579},[86,36791,10971],{"class":575},[86,36793,9750],{"class":219},[86,36795,36796],{"class":304}," kde",[86,36798,258],{"class":219},[86,36800,310],{"class":178},[86,36802,291],{"class":219},[86,36804,9753],{"class":304},[86,36806,258],{"class":219},[86,36808,35211],{"class":182},[86,36810,572],{"class":219},[86,36812,2553],{"class":223},[86,36814,9750],{"class":219},[86,36816,36817],{"class":304}," color",[86,36819,258],{"class":219},[86,36821,10971],{"class":575},[86,36823,36824],{"class":579},"#2a9d8f",[86,36826,10971],{"class":575},[86,36828,273],{"class":219},[86,36830,36831,36833,36835,36837,36839,36841,36843,36845,36848,36850],{"class":174,"line":252},[86,36832,35211],{"class":182},[86,36834,572],{"class":219},[86,36836,2553],{"class":223},[86,36838,13224],{"class":219},[86,36840,35263],{"class":182},[86,36842,243],{"class":219},[86,36844,10971],{"class":575},[86,36846,36847],{"class":579},"Distribución original de Fare",[86,36849,10971],{"class":575},[86,36851,273],{"class":219},[86,36853,36854,36856,36858,36860,36862,36864,36866,36868,36871,36873],{"class":174,"line":276},[86,36855,35211],{"class":182},[86,36857,572],{"class":219},[86,36859,2553],{"class":223},[86,36861,13224],{"class":219},[86,36863,35287],{"class":182},[86,36865,243],{"class":219},[86,36867,10971],{"class":575},[86,36869,36870],{"class":579},"Fare",[86,36872,10971],{"class":575},[86,36874,273],{"class":219},[86,36876,36877],{"class":174,"line":315},[86,36878,209],{"emptyLinePlaceholder":208},[86,36880,36881,36883,36885,36887,36889,36891,36893,36895,36897,36899,36901,36903,36905,36907,36909,36911,36913,36915,36917,36919,36921,36923,36925,36927,36930,36932],{"class":174,"line":3665},[86,36882,33151],{"class":182},[86,36884,61],{"class":219},[86,36886,36779],{"class":182},[86,36888,243],{"class":219},[86,36890,569],{"class":182},[86,36892,572],{"class":219},[86,36894,10971],{"class":575},[86,36896,36697],{"class":579},[86,36898,10971],{"class":575},[86,36900,9750],{"class":219},[86,36902,36796],{"class":304},[86,36904,258],{"class":219},[86,36906,310],{"class":178},[86,36908,291],{"class":219},[86,36910,9753],{"class":304},[86,36912,258],{"class":219},[86,36914,35211],{"class":182},[86,36916,572],{"class":219},[86,36918,802],{"class":223},[86,36920,9750],{"class":219},[86,36922,36817],{"class":304},[86,36924,258],{"class":219},[86,36926,10971],{"class":575},[86,36928,36929],{"class":579},"#e76f51",[86,36931,10971],{"class":575},[86,36933,273],{"class":219},[86,36935,36936,36938,36940,36942,36944,36946,36948,36950,36953,36955],{"class":174,"line":13256},[86,36937,35211],{"class":182},[86,36939,572],{"class":219},[86,36941,802],{"class":223},[86,36943,13224],{"class":219},[86,36945,35263],{"class":182},[86,36947,243],{"class":219},[86,36949,10971],{"class":575},[86,36951,36952],{"class":579},"Distribución transformada: log(1 + Fare)",[86,36954,10971],{"class":575},[86,36956,273],{"class":219},[86,36958,36959,36961,36963,36965,36967,36969,36971,36973,36976,36978],{"class":174,"line":13286},[86,36960,35211],{"class":182},[86,36962,572],{"class":219},[86,36964,802],{"class":223},[86,36966,13224],{"class":219},[86,36968,35287],{"class":182},[86,36970,243],{"class":219},[86,36972,10971],{"class":575},[86,36974,36975],{"class":579},"Fare (log1p)",[86,36977,10971],{"class":575},[86,36979,273],{"class":219},[86,36981,36982],{"class":174,"line":13291},[86,36983,209],{"emptyLinePlaceholder":208},[86,36985,36986,36988,36990,36992],{"class":174,"line":13308},[86,36987,33172],{"class":182},[86,36989,61],{"class":219},[86,36991,35076],{"class":182},[86,36993,11991],{"class":219},[86,36995,36996,36998,37000,37002],{"class":174,"line":13334},[86,36997,33172],{"class":182},[86,36999,61],{"class":219},[86,37001,35087],{"class":182},[86,37003,11991],{"class":219},[36158,37005,37007],{"id":37006},"_4-tablas-cruzadas","4) Tablas cruzadas",[12,37009,37010],{},"Gráficamos combinaciones de variables categóricas para ver cómo se distribuyen los pasajeros según sexo, clase, grupos de edad y tarifas agrupadas.",[164,37012,37014],{"className":166,"code":37013,"language":168,"meta":169,"style":169},"# sex + pclass (recordatorio: sex esta codificado 0=male, 1=female)\nct_sex_pclass = pd.crosstab(df['sex'], df['pclass'], margins=True)\nprint('Tabla cruzada: sex + pclass')\ndisplay(ct_sex_pclass)\n\n# pclass + fare (fare agrupado por cuantiles)\ndf['fare_group'] = pd.qcut(df['fare'], q=4, labels=['Q1', 'Q2', 'Q3', 'Q4'])\nct_pclass_fare = pd.crosstab(df['pclass'], df['fare_group'], margins=True)\nprint('Tabla cruzada: pclass + fare_group')\ndisplay(ct_pclass_fare)\n\n# age_group + survived\nct_age_survived = pd.crosstab(df['age_group'], df['survived'], margins=True)\nprint('Tabla cruzada: age_group + survived')\ndisplay(ct_age_survived)\n",[145,37015,37016,37021,37070,37085,37096,37100,37105,37188,37235,37250,37261,37265,37270,37317,37332],{"__ignoreMap":169},[86,37017,37018],{"class":174,"line":175},[86,37019,37020],{"class":1360},"# sex + pclass (recordatorio: sex esta codificado 0=male, 1=female)\n",[86,37022,37023,37026,37028,37030,37032,37035,37037,37039,37041,37043,37045,37047,37049,37051,37053,37055,37057,37059,37061,37064,37066,37068],{"class":174,"line":192},[86,37024,37025],{"class":182},"ct_sex_pclass ",[86,37027,258],{"class":219},[86,37029,261],{"class":182},[86,37031,61],{"class":219},[86,37033,37034],{"class":182},"crosstab",[86,37036,243],{"class":219},[86,37038,569],{"class":182},[86,37040,572],{"class":219},[86,37042,10971],{"class":575},[86,37044,33434],{"class":579},[86,37046,10971],{"class":575},[86,37048,9750],{"class":219},[86,37050,590],{"class":182},[86,37052,572],{"class":219},[86,37054,10971],{"class":575},[86,37056,33420],{"class":579},[86,37058,10971],{"class":575},[86,37060,9750],{"class":219},[86,37062,37063],{"class":304}," margins",[86,37065,258],{"class":219},[86,37067,310],{"class":178},[86,37069,273],{"class":219},[86,37071,37072,37074,37076,37078,37081,37083],{"class":174,"line":205},[86,37073,13294],{"class":812},[86,37075,243],{"class":219},[86,37077,10971],{"class":575},[86,37079,37080],{"class":579},"Tabla cruzada: sex + pclass",[86,37082,10971],{"class":575},[86,37084,273],{"class":219},[86,37086,37087,37089,37091,37094],{"class":174,"line":212},[86,37088,33276],{"class":182},[86,37090,243],{"class":219},[86,37092,37093],{"class":182},"ct_sex_pclass",[86,37095,273],{"class":219},[86,37097,37098],{"class":174,"line":227},[86,37099,209],{"emptyLinePlaceholder":208},[86,37101,37102],{"class":174,"line":232},[86,37103,37104],{"class":1360},"# pclass + fare (fare agrupado por cuantiles)\n",[86,37106,37107,37109,37111,37113,37116,37118,37120,37122,37124,37126,37129,37131,37133,37135,37137,37139,37141,37143,37146,37148,37150,37152,37154,37156,37158,37160,37162,37164,37166,37168,37170,37172,37174,37176,37178,37180,37182,37184,37186],{"class":174,"line":252},[86,37108,569],{"class":182},[86,37110,572],{"class":219},[86,37112,10971],{"class":575},[86,37114,37115],{"class":579},"fare_group",[86,37117,10971],{"class":575},[86,37119,585],{"class":219},[86,37121,220],{"class":219},[86,37123,261],{"class":182},[86,37125,61],{"class":219},[86,37127,37128],{"class":182},"qcut",[86,37130,243],{"class":219},[86,37132,569],{"class":182},[86,37134,572],{"class":219},[86,37136,10971],{"class":575},[86,37138,33446],{"class":579},[86,37140,10971],{"class":575},[86,37142,9750],{"class":219},[86,37144,37145],{"class":304}," q",[86,37147,258],{"class":219},[86,37149,4105],{"class":223},[86,37151,291],{"class":219},[86,37153,36595],{"class":304},[86,37155,1119],{"class":219},[86,37157,10971],{"class":575},[86,37159,525],{"class":579},[86,37161,10971],{"class":575},[86,37163,291],{"class":219},[86,37165,11970],{"class":575},[86,37167,529],{"class":579},[86,37169,10971],{"class":575},[86,37171,291],{"class":219},[86,37173,11970],{"class":575},[86,37175,533],{"class":579},[86,37177,10971],{"class":575},[86,37179,291],{"class":219},[86,37181,11970],{"class":575},[86,37183,558],{"class":579},[86,37185,10971],{"class":575},[86,37187,1417],{"class":219},[86,37189,37190,37193,37195,37197,37199,37201,37203,37205,37207,37209,37211,37213,37215,37217,37219,37221,37223,37225,37227,37229,37231,37233],{"class":174,"line":276},[86,37191,37192],{"class":182},"ct_pclass_fare ",[86,37194,258],{"class":219},[86,37196,261],{"class":182},[86,37198,61],{"class":219},[86,37200,37034],{"class":182},[86,37202,243],{"class":219},[86,37204,569],{"class":182},[86,37206,572],{"class":219},[86,37208,10971],{"class":575},[86,37210,33420],{"class":579},[86,37212,10971],{"class":575},[86,37214,9750],{"class":219},[86,37216,590],{"class":182},[86,37218,572],{"class":219},[86,37220,10971],{"class":575},[86,37222,37115],{"class":579},[86,37224,10971],{"class":575},[86,37226,9750],{"class":219},[86,37228,37063],{"class":304},[86,37230,258],{"class":219},[86,37232,310],{"class":178},[86,37234,273],{"class":219},[86,37236,37237,37239,37241,37243,37246,37248],{"class":174,"line":315},[86,37238,13294],{"class":812},[86,37240,243],{"class":219},[86,37242,10971],{"class":575},[86,37244,37245],{"class":579},"Tabla cruzada: pclass + fare_group",[86,37247,10971],{"class":575},[86,37249,273],{"class":219},[86,37251,37252,37254,37256,37259],{"class":174,"line":3665},[86,37253,33276],{"class":182},[86,37255,243],{"class":219},[86,37257,37258],{"class":182},"ct_pclass_fare",[86,37260,273],{"class":219},[86,37262,37263],{"class":174,"line":13256},[86,37264,209],{"emptyLinePlaceholder":208},[86,37266,37267],{"class":174,"line":13286},[86,37268,37269],{"class":1360},"# age_group + survived\n",[86,37271,37272,37275,37277,37279,37281,37283,37285,37287,37289,37291,37293,37295,37297,37299,37301,37303,37305,37307,37309,37311,37313,37315],{"class":174,"line":13291},[86,37273,37274],{"class":182},"ct_age_survived ",[86,37276,258],{"class":219},[86,37278,261],{"class":182},[86,37280,61],{"class":219},[86,37282,37034],{"class":182},[86,37284,243],{"class":219},[86,37286,569],{"class":182},[86,37288,572],{"class":219},[86,37290,10971],{"class":575},[86,37292,36437],{"class":579},[86,37294,10971],{"class":575},[86,37296,9750],{"class":219},[86,37298,590],{"class":182},[86,37300,572],{"class":219},[86,37302,10971],{"class":575},[86,37304,33042],{"class":579},[86,37306,10971],{"class":575},[86,37308,9750],{"class":219},[86,37310,37063],{"class":304},[86,37312,258],{"class":219},[86,37314,310],{"class":178},[86,37316,273],{"class":219},[86,37318,37319,37321,37323,37325,37328,37330],{"class":174,"line":13308},[86,37320,13294],{"class":812},[86,37322,243],{"class":219},[86,37324,10971],{"class":575},[86,37326,37327],{"class":579},"Tabla cruzada: age_group + survived",[86,37329,10971],{"class":575},[86,37331,273],{"class":219},[86,37333,37334,37336,37338,37341],{"class":174,"line":13334},[86,37335,33276],{"class":182},[86,37337,243],{"class":219},[86,37339,37340],{"class":182},"ct_age_survived",[86,37342,273],{"class":219},[36158,37344,37346,37347,37350],{"id":37345},"_5-visualizar-survival-rate-en-lugar-de-solo-distribución","5) Visualizar ",[122,37348,37349],{},"survival rate"," en lugar de solo distribución",[12,37352,37353,37354,37356],{},"Ahora vamos a graficar la tasa de supervivencia (media de ",[145,37355,33042],{},") para combinaciones clave, lo que nos da una visión más clara de cómo cambian las probabilidades de sobrevivir según diferentes características.",[164,37358,37360],{"className":166,"code":37359,"language":168,"meta":169,"style":169},"fig, axes = plt.subplots(1, 3, figsize=(18, 5))\n\n# Survival rate por combinacion sex + pclass\nsurvival_sex_pclass = (\n  df.groupby(['sex', 'pclass'])['survived']\n  .mean()\n  .reset_index()\n)\nsns.barplot(\n  data=survival_sex_pclass,\n  x='pclass',\n  y='survived',\n  hue='sex',\n  palette='Set2',\n  ax=axes[0]\n)\naxes[0].set_title('Survival Rate por Sexo y Clase')\naxes[0].set_xlabel('Clase')\naxes[0].set_ylabel('Tasa de supervivencia')\naxes[0].set_ylim(0, 1)\naxes[0].legend(title='Sexo (0=male, 1=female)')\n\n# Survival rate por pclass + fare_group\nsurvival_pclass_fare = (\n  df.groupby(['pclass', 'fare_group'], observed=False)['survived']\n  .mean()\n  .reset_index()\n)\nsns.barplot(\n  data=survival_pclass_fare,\n  x='pclass',\n  y='survived',\n  hue='fare_group',\n  palette='viridis',\n  ax=axes[1]\n)\naxes[1].set_title('Survival Rate por Clase y Cuartil de Fare')\naxes[1].set_xlabel('Clase')\naxes[1].set_ylabel('Tasa de supervivencia')\naxes[1].set_ylim(0, 1)\naxes[1].legend(title='Fare group')\n\n# Survival rate por age_group\nsurvival_age = df.groupby('age_group', observed=False)['survived'].mean().reset_index()\nsns.barplot(data=survival_age, x='age_group', y='survived', palette='mako', hue='age_group', legend=False, ax=axes[2])\naxes[2].set_title('Survival Rate por Grupo de Edad')\naxes[2].set_xlabel('Grupo de edad')\naxes[2].set_ylabel('Tasa de supervivencia')\naxes[2].set_ylim(0, 1)\n\nplt.tight_layout()\nplt.show()\n",[145,37361,37362,37402,37406,37411,37421,37458,37467,37476,37480,37490,37502,37517,37532,37547,37562,37576,37580,37603,37626,37649,37672,37700,37704,37709,37718,37762,37770,37778,37782,37793,37805,37820,37835,37850,37865,37880,37885,37909,37932,37955,37978,38006,38011,38017,38065,38154,38178,38202,38225,38248,38253,38264],{"__ignoreMap":169},[86,37363,37364,37366,37368,37370,37372,37374,37376,37378,37380,37382,37384,37387,37389,37391,37393,37396,37398,37400],{"class":174,"line":175},[86,37365,35118],{"class":182},[86,37367,291],{"class":219},[86,37369,35123],{"class":182},[86,37371,258],{"class":219},[86,37373,35128],{"class":182},[86,37375,61],{"class":219},[86,37377,35133],{"class":182},[86,37379,243],{"class":219},[86,37381,802],{"class":223},[86,37383,291],{"class":219},[86,37385,37386],{"class":223}," 3",[86,37388,291],{"class":219},[86,37390,35146],{"class":304},[86,37392,34709],{"class":219},[86,37394,37395],{"class":223},"18",[86,37397,291],{"class":219},[86,37399,34717],{"class":223},[86,37401,33401],{"class":219},[86,37403,37404],{"class":174,"line":192},[86,37405,209],{"emptyLinePlaceholder":208},[86,37407,37408],{"class":174,"line":205},[86,37409,37410],{"class":1360},"# Survival rate por combinacion sex + pclass\n",[86,37412,37413,37416,37418],{"class":174,"line":212},[86,37414,37415],{"class":182},"survival_sex_pclass ",[86,37417,258],{"class":219},[86,37419,37420],{"class":219}," (\n",[86,37422,37423,37426,37428,37431,37433,37435,37437,37439,37441,37443,37445,37447,37450,37452,37454,37456],{"class":174,"line":227},[86,37424,37425],{"class":182},"  df",[86,37427,61],{"class":219},[86,37429,37430],{"class":182},"groupby",[86,37432,32924],{"class":219},[86,37434,10971],{"class":575},[86,37436,33434],{"class":579},[86,37438,10971],{"class":575},[86,37440,291],{"class":219},[86,37442,11970],{"class":575},[86,37444,33420],{"class":579},[86,37446,10971],{"class":575},[86,37448,37449],{"class":219},"])[",[86,37451,10971],{"class":575},[86,37453,33042],{"class":579},[86,37455,10971],{"class":575},[86,37457,752],{"class":219},[86,37459,37460,37463,37465],{"class":174,"line":232},[86,37461,37462],{"class":219},"  .",[86,37464,13227],{"class":182},[86,37466,11991],{"class":219},[86,37468,37469,37471,37474],{"class":174,"line":252},[86,37470,37462],{"class":219},[86,37472,37473],{"class":182},"reset_index",[86,37475,11991],{"class":219},[86,37477,37478],{"class":174,"line":276},[86,37479,273],{"class":219},[86,37481,37482,37484,37486,37488],{"class":174,"line":315},[86,37483,33151],{"class":182},[86,37485,61],{"class":219},[86,37487,35170],{"class":182},[86,37489,1083],{"class":219},[86,37491,37492,37495,37497,37500],{"class":174,"line":3665},[86,37493,37494],{"class":304},"  data",[86,37496,258],{"class":219},[86,37498,37499],{"class":182},"survival_sex_pclass",[86,37501,1111],{"class":219},[86,37503,37504,37507,37509,37511,37513,37515],{"class":174,"line":13256},[86,37505,37506],{"class":304},"  x",[86,37508,258],{"class":219},[86,37510,10971],{"class":575},[86,37512,33420],{"class":579},[86,37514,10971],{"class":575},[86,37516,1111],{"class":219},[86,37518,37519,37522,37524,37526,37528,37530],{"class":174,"line":13286},[86,37520,37521],{"class":304},"  y",[86,37523,258],{"class":219},[86,37525,10971],{"class":575},[86,37527,33042],{"class":579},[86,37529,10971],{"class":575},[86,37531,1111],{"class":219},[86,37533,37534,37537,37539,37541,37543,37545],{"class":174,"line":13291},[86,37535,37536],{"class":304},"  hue",[86,37538,258],{"class":219},[86,37540,10971],{"class":575},[86,37542,33434],{"class":579},[86,37544,10971],{"class":575},[86,37546,1111],{"class":219},[86,37548,37549,37552,37554,37556,37558,37560],{"class":174,"line":13308},[86,37550,37551],{"class":304},"  palette",[86,37553,258],{"class":219},[86,37555,10971],{"class":575},[86,37557,35226],{"class":579},[86,37559,10971],{"class":575},[86,37561,1111],{"class":219},[86,37563,37564,37566,37568,37570,37572,37574],{"class":174,"line":13334},[86,37565,34918],{"class":304},[86,37567,258],{"class":219},[86,37569,35211],{"class":182},[86,37571,572],{"class":219},[86,37573,2553],{"class":223},[86,37575,752],{"class":219},[86,37577,37578],{"class":174,"line":13359},[86,37579,273],{"class":219},[86,37581,37582,37584,37586,37588,37590,37592,37594,37596,37599,37601],{"class":174,"line":13385},[86,37583,35211],{"class":182},[86,37585,572],{"class":219},[86,37587,2553],{"class":223},[86,37589,13224],{"class":219},[86,37591,35263],{"class":182},[86,37593,243],{"class":219},[86,37595,10971],{"class":575},[86,37597,37598],{"class":579},"Survival Rate por Sexo y Clase",[86,37600,10971],{"class":575},[86,37602,273],{"class":219},[86,37604,37605,37607,37609,37611,37613,37615,37617,37619,37622,37624],{"class":174,"line":13390},[86,37606,35211],{"class":182},[86,37608,572],{"class":219},[86,37610,2553],{"class":223},[86,37612,13224],{"class":219},[86,37614,35287],{"class":182},[86,37616,243],{"class":219},[86,37618,10971],{"class":575},[86,37620,37621],{"class":579},"Clase",[86,37623,10971],{"class":575},[86,37625,273],{"class":219},[86,37627,37628,37630,37632,37634,37636,37638,37640,37642,37645,37647],{"class":174,"line":13396},[86,37629,35211],{"class":182},[86,37631,572],{"class":219},[86,37633,2553],{"class":223},[86,37635,13224],{"class":219},[86,37637,35311],{"class":182},[86,37639,243],{"class":219},[86,37641,10971],{"class":575},[86,37643,37644],{"class":579},"Tasa de supervivencia",[86,37646,10971],{"class":575},[86,37648,273],{"class":219},[86,37650,37651,37653,37655,37657,37659,37662,37664,37666,37668,37670],{"class":174,"line":3615},[86,37652,35211],{"class":182},[86,37654,572],{"class":219},[86,37656,2553],{"class":223},[86,37658,13224],{"class":219},[86,37660,37661],{"class":182},"set_ylim",[86,37663,243],{"class":219},[86,37665,2553],{"class":223},[86,37667,291],{"class":219},[86,37669,786],{"class":223},[86,37671,273],{"class":219},[86,37673,37674,37676,37678,37680,37682,37685,37687,37689,37691,37693,37696,37698],{"class":174,"line":2254},[86,37675,35211],{"class":182},[86,37677,572],{"class":219},[86,37679,2553],{"class":223},[86,37681,13224],{"class":219},[86,37683,37684],{"class":182},"legend",[86,37686,243],{"class":219},[86,37688,34801],{"class":304},[86,37690,258],{"class":219},[86,37692,10971],{"class":575},[86,37694,37695],{"class":579},"Sexo (0=male, 1=female)",[86,37697,10971],{"class":575},[86,37699,273],{"class":219},[86,37701,37702],{"class":174,"line":13492},[86,37703,209],{"emptyLinePlaceholder":208},[86,37705,37706],{"class":174,"line":13545},[86,37707,37708],{"class":1360},"# Survival rate por pclass + fare_group\n",[86,37710,37711,37714,37716],{"class":174,"line":13550},[86,37712,37713],{"class":182},"survival_pclass_fare ",[86,37715,258],{"class":219},[86,37717,37420],{"class":219},[86,37719,37720,37722,37724,37726,37728,37730,37732,37734,37736,37738,37740,37742,37744,37747,37749,37751,37754,37756,37758,37760],{"class":174,"line":13566},[86,37721,37425],{"class":182},[86,37723,61],{"class":219},[86,37725,37430],{"class":182},[86,37727,32924],{"class":219},[86,37729,10971],{"class":575},[86,37731,33420],{"class":579},[86,37733,10971],{"class":575},[86,37735,291],{"class":219},[86,37737,11970],{"class":575},[86,37739,37115],{"class":579},[86,37741,10971],{"class":575},[86,37743,9750],{"class":219},[86,37745,37746],{"class":304}," observed",[86,37748,258],{"class":219},[86,37750,33508],{"class":178},[86,37752,37753],{"class":219},")[",[86,37755,10971],{"class":575},[86,37757,33042],{"class":579},[86,37759,10971],{"class":575},[86,37761,752],{"class":219},[86,37763,37764,37766,37768],{"class":174,"line":13591},[86,37765,37462],{"class":219},[86,37767,13227],{"class":182},[86,37769,11991],{"class":219},[86,37771,37772,37774,37776],{"class":174,"line":13616},[86,37773,37462],{"class":219},[86,37775,37473],{"class":182},[86,37777,11991],{"class":219},[86,37779,37780],{"class":174,"line":13641},[86,37781,273],{"class":219},[86,37783,37785,37787,37789,37791],{"class":174,"line":37784},29,[86,37786,33151],{"class":182},[86,37788,61],{"class":219},[86,37790,35170],{"class":182},[86,37792,1083],{"class":219},[86,37794,37796,37798,37800,37803],{"class":174,"line":37795},30,[86,37797,37494],{"class":304},[86,37799,258],{"class":219},[86,37801,37802],{"class":182},"survival_pclass_fare",[86,37804,1111],{"class":219},[86,37806,37808,37810,37812,37814,37816,37818],{"class":174,"line":37807},31,[86,37809,37506],{"class":304},[86,37811,258],{"class":219},[86,37813,10971],{"class":575},[86,37815,33420],{"class":579},[86,37817,10971],{"class":575},[86,37819,1111],{"class":219},[86,37821,37823,37825,37827,37829,37831,37833],{"class":174,"line":37822},32,[86,37824,37521],{"class":304},[86,37826,258],{"class":219},[86,37828,10971],{"class":575},[86,37830,33042],{"class":579},[86,37832,10971],{"class":575},[86,37834,1111],{"class":219},[86,37836,37838,37840,37842,37844,37846,37848],{"class":174,"line":37837},33,[86,37839,37536],{"class":304},[86,37841,258],{"class":219},[86,37843,10971],{"class":575},[86,37845,37115],{"class":579},[86,37847,10971],{"class":575},[86,37849,1111],{"class":219},[86,37851,37853,37855,37857,37859,37861,37863],{"class":174,"line":37852},34,[86,37854,37551],{"class":304},[86,37856,258],{"class":219},[86,37858,10971],{"class":575},[86,37860,34766],{"class":579},[86,37862,10971],{"class":575},[86,37864,1111],{"class":219},[86,37866,37868,37870,37872,37874,37876,37878],{"class":174,"line":37867},35,[86,37869,34918],{"class":304},[86,37871,258],{"class":219},[86,37873,35211],{"class":182},[86,37875,572],{"class":219},[86,37877,802],{"class":223},[86,37879,752],{"class":219},[86,37881,37883],{"class":174,"line":37882},36,[86,37884,273],{"class":219},[86,37886,37888,37890,37892,37894,37896,37898,37900,37902,37905,37907],{"class":174,"line":37887},37,[86,37889,35211],{"class":182},[86,37891,572],{"class":219},[86,37893,802],{"class":223},[86,37895,13224],{"class":219},[86,37897,35263],{"class":182},[86,37899,243],{"class":219},[86,37901,10971],{"class":575},[86,37903,37904],{"class":579},"Survival Rate por Clase y Cuartil de Fare",[86,37906,10971],{"class":575},[86,37908,273],{"class":219},[86,37910,37912,37914,37916,37918,37920,37922,37924,37926,37928,37930],{"class":174,"line":37911},38,[86,37913,35211],{"class":182},[86,37915,572],{"class":219},[86,37917,802],{"class":223},[86,37919,13224],{"class":219},[86,37921,35287],{"class":182},[86,37923,243],{"class":219},[86,37925,10971],{"class":575},[86,37927,37621],{"class":579},[86,37929,10971],{"class":575},[86,37931,273],{"class":219},[86,37933,37935,37937,37939,37941,37943,37945,37947,37949,37951,37953],{"class":174,"line":37934},39,[86,37936,35211],{"class":182},[86,37938,572],{"class":219},[86,37940,802],{"class":223},[86,37942,13224],{"class":219},[86,37944,35311],{"class":182},[86,37946,243],{"class":219},[86,37948,10971],{"class":575},[86,37950,37644],{"class":579},[86,37952,10971],{"class":575},[86,37954,273],{"class":219},[86,37956,37958,37960,37962,37964,37966,37968,37970,37972,37974,37976],{"class":174,"line":37957},40,[86,37959,35211],{"class":182},[86,37961,572],{"class":219},[86,37963,802],{"class":223},[86,37965,13224],{"class":219},[86,37967,37661],{"class":182},[86,37969,243],{"class":219},[86,37971,2553],{"class":223},[86,37973,291],{"class":219},[86,37975,786],{"class":223},[86,37977,273],{"class":219},[86,37979,37981,37983,37985,37987,37989,37991,37993,37995,37997,37999,38002,38004],{"class":174,"line":37980},41,[86,37982,35211],{"class":182},[86,37984,572],{"class":219},[86,37986,802],{"class":223},[86,37988,13224],{"class":219},[86,37990,37684],{"class":182},[86,37992,243],{"class":219},[86,37994,34801],{"class":304},[86,37996,258],{"class":219},[86,37998,10971],{"class":575},[86,38000,38001],{"class":579},"Fare group",[86,38003,10971],{"class":575},[86,38005,273],{"class":219},[86,38007,38009],{"class":174,"line":38008},42,[86,38010,209],{"emptyLinePlaceholder":208},[86,38012,38014],{"class":174,"line":38013},43,[86,38015,38016],{"class":1360},"# Survival rate por age_group\n",[86,38018,38020,38023,38025,38027,38029,38031,38033,38035,38037,38039,38041,38043,38045,38047,38049,38051,38053,38055,38057,38059,38061,38063],{"class":174,"line":38019},44,[86,38021,38022],{"class":182},"survival_age ",[86,38024,258],{"class":219},[86,38026,590],{"class":182},[86,38028,61],{"class":219},[86,38030,37430],{"class":182},[86,38032,243],{"class":219},[86,38034,10971],{"class":575},[86,38036,36437],{"class":579},[86,38038,10971],{"class":575},[86,38040,291],{"class":219},[86,38042,37746],{"class":304},[86,38044,258],{"class":219},[86,38046,33508],{"class":178},[86,38048,37753],{"class":219},[86,38050,10971],{"class":575},[86,38052,33042],{"class":579},[86,38054,10971],{"class":575},[86,38056,13224],{"class":219},[86,38058,13227],{"class":182},[86,38060,11985],{"class":219},[86,38062,37473],{"class":182},[86,38064,11991],{"class":219},[86,38066,38068,38070,38072,38074,38076,38078,38080,38083,38085,38087,38089,38091,38093,38095,38097,38099,38101,38103,38105,38107,38109,38111,38113,38115,38118,38120,38122,38124,38126,38128,38130,38132,38134,38136,38138,38140,38142,38144,38146,38148,38150,38152],{"class":174,"line":38067},45,[86,38069,33151],{"class":182},[86,38071,61],{"class":219},[86,38073,35170],{"class":182},[86,38075,243],{"class":219},[86,38077,11013],{"class":304},[86,38079,258],{"class":219},[86,38081,38082],{"class":182},"survival_age",[86,38084,291],{"class":219},[86,38086,34746],{"class":304},[86,38088,258],{"class":219},[86,38090,10971],{"class":575},[86,38092,36437],{"class":579},[86,38094,10971],{"class":575},[86,38096,291],{"class":219},[86,38098,1098],{"class":304},[86,38100,258],{"class":219},[86,38102,10971],{"class":575},[86,38104,33042],{"class":579},[86,38106,10971],{"class":575},[86,38108,291],{"class":219},[86,38110,34759],{"class":304},[86,38112,258],{"class":219},[86,38114,10971],{"class":575},[86,38116,38117],{"class":579},"mako",[86,38119,10971],{"class":575},[86,38121,291],{"class":219},[86,38123,34773],{"class":304},[86,38125,258],{"class":219},[86,38127,10971],{"class":575},[86,38129,36437],{"class":579},[86,38131,10971],{"class":575},[86,38133,291],{"class":219},[86,38135,34786],{"class":304},[86,38137,258],{"class":219},[86,38139,33508],{"class":178},[86,38141,291],{"class":219},[86,38143,9753],{"class":304},[86,38145,258],{"class":219},[86,38147,35211],{"class":182},[86,38149,572],{"class":219},[86,38151,980],{"class":223},[86,38153,1417],{"class":219},[86,38155,38157,38159,38161,38163,38165,38167,38169,38171,38174,38176],{"class":174,"line":38156},46,[86,38158,35211],{"class":182},[86,38160,572],{"class":219},[86,38162,980],{"class":223},[86,38164,13224],{"class":219},[86,38166,35263],{"class":182},[86,38168,243],{"class":219},[86,38170,10971],{"class":575},[86,38172,38173],{"class":579},"Survival Rate por Grupo de Edad",[86,38175,10971],{"class":575},[86,38177,273],{"class":219},[86,38179,38181,38183,38185,38187,38189,38191,38193,38195,38198,38200],{"class":174,"line":38180},47,[86,38182,35211],{"class":182},[86,38184,572],{"class":219},[86,38186,980],{"class":223},[86,38188,13224],{"class":219},[86,38190,35287],{"class":182},[86,38192,243],{"class":219},[86,38194,10971],{"class":575},[86,38196,38197],{"class":579},"Grupo de edad",[86,38199,10971],{"class":575},[86,38201,273],{"class":219},[86,38203,38205,38207,38209,38211,38213,38215,38217,38219,38221,38223],{"class":174,"line":38204},48,[86,38206,35211],{"class":182},[86,38208,572],{"class":219},[86,38210,980],{"class":223},[86,38212,13224],{"class":219},[86,38214,35311],{"class":182},[86,38216,243],{"class":219},[86,38218,10971],{"class":575},[86,38220,37644],{"class":579},[86,38222,10971],{"class":575},[86,38224,273],{"class":219},[86,38226,38228,38230,38232,38234,38236,38238,38240,38242,38244,38246],{"class":174,"line":38227},49,[86,38229,35211],{"class":182},[86,38231,572],{"class":219},[86,38233,980],{"class":223},[86,38235,13224],{"class":219},[86,38237,37661],{"class":182},[86,38239,243],{"class":219},[86,38241,2553],{"class":223},[86,38243,291],{"class":219},[86,38245,786],{"class":223},[86,38247,273],{"class":219},[86,38249,38251],{"class":174,"line":38250},50,[86,38252,209],{"emptyLinePlaceholder":208},[86,38254,38256,38258,38260,38262],{"class":174,"line":38255},51,[86,38257,33172],{"class":182},[86,38259,61],{"class":219},[86,38261,35076],{"class":182},[86,38263,11991],{"class":219},[86,38265,38267,38269,38271,38273],{"class":174,"line":38266},52,[86,38268,33172],{"class":182},[86,38270,61],{"class":219},[86,38272,35087],{"class":182},[86,38274,11991],{"class":219},[12,38276,38277],{},"Aquí ya se observan patrones mucho más claros y estructurales en los datos.",[12,38279,38280,38281,38284],{},"Primero, el ",[122,38282,38283],{},"tamaño de familia"," muestra que la mayoría de pasajeros viajaban solos (family size = 1) y que los grupos grandes eran poco comunes. Esto sugiere que las variables relacionadas con familia están muy concentradas en valores bajos y que viajar solo es el caso dominante, lo cual puede influir en el modelo.",[12,38286,38287,38288,38291],{},"En la ",[122,38289,38290],{},"tarifa",", la distribución original está fuertemente sesgada a la derecha: la mayoría pagó poco y unos pocos pagaron cantidades muy altas. Al aplicar la transformación logarítmica (log(1 + fare)), la distribución se vuelve mucho más equilibrada y manejable para modelos estadísticos, reduciendo el impacto de valores extremos.",[12,38293,38287,38294,38297],{},[122,38295,38296],{},"supervivencia por sexo y clase",", el patrón es contundente: las mujeres sobreviven mucho más que los hombres en todas las clases, y la primera clase tiene mayores tasas de supervivencia. Esto reafirma que el sexo y la clase social fueron factores determinantes en la supervivencia.",[12,38299,38300,38301,38304],{},"Cuando se analiza ",[122,38302,38303],{},"clase junto con cuartiles de tarifa",", se confirma que pagar más dentro de cada clase generalmente aumenta la probabilidad de sobrevivir, especialmente en primera y segunda clase. Esto refuerza la importancia del estatus socioeconómico.",[12,38306,38307,38308,38311],{},"Finalmente, la ",[122,38309,38310],{},"supervivencia por grupo de edad"," indica que los niños tienen mayor tasa de supervivencia, mientras que los adultos mayores tienen la menor. Esto demuestra que la edad sí influye, pero de forma segmentada (no lineal), algo que la correlación simple no lograba mostrar.",[12,38313,38314],{},"En conjunto, estos gráficos revelan que la supervivencia no dependió de un solo factor aislado, sino de la combinación de sexo, clase social, tarifa pagada y grupo de edad.",[323,38316,38318],{"id":38317},"_4-preparación-para-modelado","4. Preparación para Modelado",[12,38320,38321,38322,93,38324,789],{},"Antes de entrenar, separamos features\u002Ftarget, hacemos split estratificado y escalamos variables continuas (",[145,38323,33437],{},[145,38325,33446],{},[164,38327,38329],{"className":166,"code":38328,"language":168,"meta":169,"style":169},"from sklearn.model_selection import train_test_split, StratifiedKFold, cross_val_score\nfrom sklearn.preprocessing import StandardScaler\n\n# Features y target\nX = df.drop(columns=['survived'])\ny = df['survived']\n\n# Split estratificado 80\u002F20\nX_train, X_test, y_train, y_test = train_test_split(\n  X, y, test_size=0.2, random_state=42, stratify=y\n)\n\nprint('Distribución de clases en entrenamiento:')\nprint(y_train.value_counts(normalize=True).rename('proporcion').round(3))\n\n# Escalado de variables continuas\nscaler = StandardScaler()\ncols_to_scale = ['age', 'fare']\n\nX_train_scaled = X_train.copy()\nX_test_scaled = X_test.copy()\n\nX_train_scaled[cols_to_scale] = scaler.fit_transform(X_train[cols_to_scale])\nX_test_scaled[cols_to_scale] = scaler.transform(X_test[cols_to_scale])\n\nprint('\\nForma de train:', X_train_scaled.shape)\nprint('Forma de test:', X_test_scaled.shape)\n",[145,38330,38331,38356,38372,38376,38381,38407,38426,38430,38435,38460,38498,38502,38506,38521,38568,38572,38577,38589,38614,38618,38634,38649,38653,38684,38715,38719,38745],{"__ignoreMap":169},[86,38332,38333,38335,38337,38339,38341,38343,38346,38348,38351,38353],{"class":174,"line":175},[86,38334,1053],{"class":178},[86,38336,1056],{"class":182},[86,38338,61],{"class":219},[86,38340,1061],{"class":182},[86,38342,179],{"class":178},[86,38344,38345],{"class":182}," train_test_split",[86,38347,291],{"class":219},[86,38349,38350],{"class":182}," StratifiedKFold",[86,38352,291],{"class":219},[86,38354,38355],{"class":182}," cross_val_score\n",[86,38357,38358,38360,38362,38364,38367,38369],{"class":174,"line":192},[86,38359,1053],{"class":178},[86,38361,1056],{"class":182},[86,38363,61],{"class":219},[86,38365,38366],{"class":182},"preprocessing ",[86,38368,179],{"class":178},[86,38370,38371],{"class":182}," StandardScaler\n",[86,38373,38374],{"class":174,"line":205},[86,38375,209],{"emptyLinePlaceholder":208},[86,38377,38378],{"class":174,"line":212},[86,38379,38380],{"class":1360},"# Features y target\n",[86,38382,38383,38385,38387,38389,38391,38393,38395,38397,38399,38401,38403,38405],{"class":174,"line":227},[86,38384,12095],{"class":182},[86,38386,258],{"class":219},[86,38388,590],{"class":182},[86,38390,61],{"class":219},[86,38392,33804],{"class":182},[86,38394,243],{"class":219},[86,38396,33809],{"class":304},[86,38398,1119],{"class":219},[86,38400,10971],{"class":575},[86,38402,33042],{"class":579},[86,38404,10971],{"class":575},[86,38406,1417],{"class":219},[86,38408,38409,38412,38414,38416,38418,38420,38422,38424],{"class":174,"line":232},[86,38410,38411],{"class":182},"y ",[86,38413,258],{"class":219},[86,38415,590],{"class":182},[86,38417,572],{"class":219},[86,38419,10971],{"class":575},[86,38421,33042],{"class":579},[86,38423,10971],{"class":575},[86,38425,752],{"class":219},[86,38427,38428],{"class":174,"line":252},[86,38429,209],{"emptyLinePlaceholder":208},[86,38431,38432],{"class":174,"line":276},[86,38433,38434],{"class":1360},"# Split estratificado 80\u002F20\n",[86,38436,38437,38439,38441,38444,38446,38449,38451,38454,38456,38458],{"class":174,"line":315},[86,38438,9710],{"class":182},[86,38440,291],{"class":219},[86,38442,38443],{"class":182}," X_test",[86,38445,291],{"class":219},[86,38447,38448],{"class":182}," y_train",[86,38450,291],{"class":219},[86,38452,38453],{"class":182}," y_test ",[86,38455,258],{"class":219},[86,38457,38345],{"class":182},[86,38459,1083],{"class":219},[86,38461,38462,38465,38467,38469,38471,38474,38476,38479,38481,38484,38486,38488,38490,38493,38495],{"class":174,"line":3665},[86,38463,38464],{"class":182},"  X",[86,38466,291],{"class":219},[86,38468,1098],{"class":182},[86,38470,291],{"class":219},[86,38472,38473],{"class":304}," test_size",[86,38475,258],{"class":219},[86,38477,38478],{"class":223},"0.2",[86,38480,291],{"class":219},[86,38482,38483],{"class":304}," random_state",[86,38485,258],{"class":219},[86,38487,1387],{"class":223},[86,38489,291],{"class":219},[86,38491,38492],{"class":304}," stratify",[86,38494,258],{"class":219},[86,38496,38497],{"class":182},"y\n",[86,38499,38500],{"class":174,"line":13256},[86,38501,273],{"class":219},[86,38503,38504],{"class":174,"line":13286},[86,38505,209],{"emptyLinePlaceholder":208},[86,38507,38508,38510,38512,38514,38517,38519],{"class":174,"line":13291},[86,38509,13294],{"class":812},[86,38511,243],{"class":219},[86,38513,10971],{"class":575},[86,38515,38516],{"class":579},"Distribución de clases en entrenamiento:",[86,38518,10971],{"class":575},[86,38520,273],{"class":219},[86,38522,38523,38525,38527,38530,38532,38534,38536,38539,38541,38543,38545,38548,38550,38552,38555,38557,38559,38562,38564,38566],{"class":174,"line":13308},[86,38524,13294],{"class":812},[86,38526,243],{"class":219},[86,38528,38529],{"class":182},"y_train",[86,38531,61],{"class":219},[86,38533,36651],{"class":182},[86,38535,243],{"class":219},[86,38537,38538],{"class":304},"normalize",[86,38540,258],{"class":219},[86,38542,310],{"class":178},[86,38544,789],{"class":219},[86,38546,38547],{"class":182},"rename",[86,38549,243],{"class":219},[86,38551,10971],{"class":575},[86,38553,38554],{"class":579},"proporcion",[86,38556,10971],{"class":575},[86,38558,789],{"class":219},[86,38560,38561],{"class":182},"round",[86,38563,243],{"class":219},[86,38565,4100],{"class":223},[86,38567,33401],{"class":219},[86,38569,38570],{"class":174,"line":13334},[86,38571,209],{"emptyLinePlaceholder":208},[86,38573,38574],{"class":174,"line":13359},[86,38575,38576],{"class":1360},"# Escalado de variables continuas\n",[86,38578,38579,38582,38584,38587],{"class":174,"line":13385},[86,38580,38581],{"class":182},"scaler ",[86,38583,258],{"class":219},[86,38585,38586],{"class":182}," StandardScaler",[86,38588,11991],{"class":219},[86,38590,38591,38594,38596,38598,38600,38602,38604,38606,38608,38610,38612],{"class":174,"line":13390},[86,38592,38593],{"class":182},"cols_to_scale ",[86,38595,258],{"class":219},[86,38597,726],{"class":219},[86,38599,10971],{"class":575},[86,38601,33437],{"class":579},[86,38603,10971],{"class":575},[86,38605,291],{"class":219},[86,38607,11970],{"class":575},[86,38609,33446],{"class":579},[86,38611,10971],{"class":575},[86,38613,752],{"class":219},[86,38615,38616],{"class":174,"line":13396},[86,38617,209],{"emptyLinePlaceholder":208},[86,38619,38620,38623,38625,38628,38630,38632],{"class":174,"line":3615},[86,38621,38622],{"class":182},"X_train_scaled ",[86,38624,258],{"class":219},[86,38626,38627],{"class":182}," X_train",[86,38629,61],{"class":219},[86,38631,33250],{"class":182},[86,38633,11991],{"class":219},[86,38635,38636,38639,38641,38643,38645,38647],{"class":174,"line":2254},[86,38637,38638],{"class":182},"X_test_scaled ",[86,38640,258],{"class":219},[86,38642,38443],{"class":182},[86,38644,61],{"class":219},[86,38646,33250],{"class":182},[86,38648,11991],{"class":219},[86,38650,38651],{"class":174,"line":13492},[86,38652,209],{"emptyLinePlaceholder":208},[86,38654,38655,38658,38660,38663,38665,38667,38670,38672,38674,38676,38678,38680,38682],{"class":174,"line":13545},[86,38656,38657],{"class":182},"X_train_scaled",[86,38659,572],{"class":219},[86,38661,38662],{"class":182},"cols_to_scale",[86,38664,585],{"class":219},[86,38666,220],{"class":219},[86,38668,38669],{"class":182}," scaler",[86,38671,61],{"class":219},[86,38673,11003],{"class":182},[86,38675,243],{"class":219},[86,38677,9710],{"class":182},[86,38679,572],{"class":219},[86,38681,38662],{"class":182},[86,38683,1417],{"class":219},[86,38685,38686,38689,38691,38693,38695,38697,38699,38701,38704,38706,38709,38711,38713],{"class":174,"line":13550},[86,38687,38688],{"class":182},"X_test_scaled",[86,38690,572],{"class":219},[86,38692,38662],{"class":182},[86,38694,585],{"class":219},[86,38696,220],{"class":219},[86,38698,38669],{"class":182},[86,38700,61],{"class":219},[86,38702,38703],{"class":182},"transform",[86,38705,243],{"class":219},[86,38707,38708],{"class":182},"X_test",[86,38710,572],{"class":219},[86,38712,38662],{"class":182},[86,38714,1417],{"class":219},[86,38716,38717],{"class":174,"line":13566},[86,38718,209],{"emptyLinePlaceholder":208},[86,38720,38721,38723,38725,38727,38729,38732,38734,38736,38739,38741,38743],{"class":174,"line":13591},[86,38722,13294],{"class":812},[86,38724,243],{"class":219},[86,38726,10971],{"class":575},[86,38728,33305],{"class":215},[86,38730,38731],{"class":579},"Forma de train:",[86,38733,10971],{"class":575},[86,38735,291],{"class":219},[86,38737,38738],{"class":182}," X_train_scaled",[86,38740,61],{"class":219},[86,38742,33317],{"class":182},[86,38744,273],{"class":219},[86,38746,38747,38749,38751,38753,38756,38758,38760,38763,38765,38767],{"class":174,"line":13616},[86,38748,13294],{"class":812},[86,38750,243],{"class":219},[86,38752,10971],{"class":575},[86,38754,38755],{"class":579},"Forma de test:",[86,38757,10971],{"class":575},[86,38759,291],{"class":219},[86,38761,38762],{"class":182}," X_test_scaled",[86,38764,61],{"class":219},[86,38766,33317],{"class":182},[86,38768,273],{"class":219},[323,38770,38772],{"id":38771},"_5-baseline-con-regresión-logística","5. Baseline con Regresión Logística",[12,38774,38775,38776,38778],{},"Entrenamos una regresión logística con ",[145,38777,1263],{}," para manejar mejor el desbalance relativo de clases.",[164,38780,38782],{"className":166,"code":38781,"language":168,"meta":169,"style":169},"from sklearn.linear_model import LogisticRegression\n\nmodel = LogisticRegression(random_state=42, max_iter=1000, class_weight='balanced')\nmodel.fit(X_train_scaled, y_train)\n\ny_pred = model.predict(X_test_scaled)\ny_pred_proba = model.predict_proba(X_test_scaled)[:, 1]\n\n# Validación cruzada en entrenamiento\ncv = StratifiedKFold(n_splits=5, shuffle=True, random_state=42)\ncv_auc = cross_val_score(model, X_train_scaled, y_train, cv=cv, scoring='roc_auc')\n\nprint(f'ROC-AUC en validación cruzada (train): {cv_auc.mean():.3f} +\u002F- {cv_auc.std():.3f}')\n",[145,38783,38784,38800,38804,38848,38866,38870,38890,38915,38919,38924,38961,39008,39012],{"__ignoreMap":169},[86,38785,38786,38788,38790,38792,38795,38797],{"class":174,"line":175},[86,38787,1053],{"class":178},[86,38789,1056],{"class":182},[86,38791,61],{"class":219},[86,38793,38794],{"class":182},"linear_model ",[86,38796,179],{"class":178},[86,38798,38799],{"class":182}," LogisticRegression\n",[86,38801,38802],{"class":174,"line":192},[86,38803,209],{"emptyLinePlaceholder":208},[86,38805,38806,38809,38811,38814,38816,38818,38820,38822,38824,38827,38829,38832,38834,38837,38839,38841,38844,38846],{"class":174,"line":205},[86,38807,38808],{"class":182},"model ",[86,38810,258],{"class":219},[86,38812,38813],{"class":182}," LogisticRegression",[86,38815,243],{"class":219},[86,38817,1382],{"class":304},[86,38819,258],{"class":219},[86,38821,1387],{"class":223},[86,38823,291],{"class":219},[86,38825,38826],{"class":304}," max_iter",[86,38828,258],{"class":219},[86,38830,38831],{"class":223},"1000",[86,38833,291],{"class":219},[86,38835,38836],{"class":304}," class_weight",[86,38838,258],{"class":219},[86,38840,10971],{"class":575},[86,38842,38843],{"class":579},"balanced",[86,38845,10971],{"class":575},[86,38847,273],{"class":219},[86,38849,38850,38852,38854,38856,38858,38860,38862,38864],{"class":174,"line":212},[86,38851,1402],{"class":182},[86,38853,61],{"class":219},[86,38855,11051],{"class":182},[86,38857,243],{"class":219},[86,38859,38657],{"class":182},[86,38861,291],{"class":219},[86,38863,38448],{"class":182},[86,38865,273],{"class":219},[86,38867,38868],{"class":174,"line":227},[86,38869,209],{"emptyLinePlaceholder":208},[86,38871,38872,38875,38877,38879,38881,38884,38886,38888],{"class":174,"line":232},[86,38873,38874],{"class":182},"y_pred ",[86,38876,258],{"class":219},[86,38878,1409],{"class":182},[86,38880,61],{"class":219},[86,38882,38883],{"class":182},"predict",[86,38885,243],{"class":219},[86,38887,38688],{"class":182},[86,38889,273],{"class":219},[86,38891,38892,38895,38897,38899,38901,38904,38906,38908,38911,38913],{"class":174,"line":252},[86,38893,38894],{"class":182},"y_pred_proba ",[86,38896,258],{"class":219},[86,38898,1409],{"class":182},[86,38900,61],{"class":219},[86,38902,38903],{"class":182},"predict_proba",[86,38905,243],{"class":219},[86,38907,38688],{"class":182},[86,38909,38910],{"class":219},")[:,",[86,38912,786],{"class":223},[86,38914,752],{"class":219},[86,38916,38917],{"class":174,"line":276},[86,38918,209],{"emptyLinePlaceholder":208},[86,38920,38921],{"class":174,"line":315},[86,38922,38923],{"class":1360},"# Validación cruzada en entrenamiento\n",[86,38925,38926,38929,38931,38933,38935,38938,38940,38942,38944,38947,38949,38951,38953,38955,38957,38959],{"class":174,"line":3665},[86,38927,38928],{"class":182},"cv ",[86,38930,258],{"class":219},[86,38932,38350],{"class":182},[86,38934,243],{"class":219},[86,38936,38937],{"class":304},"n_splits",[86,38939,258],{"class":219},[86,38941,1108],{"class":223},[86,38943,291],{"class":219},[86,38945,38946],{"class":304}," shuffle",[86,38948,258],{"class":219},[86,38950,310],{"class":178},[86,38952,291],{"class":219},[86,38954,38483],{"class":304},[86,38956,258],{"class":219},[86,38958,1387],{"class":223},[86,38960,273],{"class":219},[86,38962,38963,38966,38968,38971,38973,38975,38977,38979,38981,38983,38985,38987,38989,38992,38994,38997,38999,39001,39004,39006],{"class":174,"line":13256},[86,38964,38965],{"class":182},"cv_auc ",[86,38967,258],{"class":219},[86,38969,38970],{"class":182}," cross_val_score",[86,38972,243],{"class":219},[86,38974,1402],{"class":182},[86,38976,291],{"class":219},[86,38978,38738],{"class":182},[86,38980,291],{"class":219},[86,38982,38448],{"class":182},[86,38984,291],{"class":219},[86,38986,1103],{"class":304},[86,38988,258],{"class":219},[86,38990,38991],{"class":182},"cv",[86,38993,291],{"class":219},[86,38995,38996],{"class":304}," scoring",[86,38998,258],{"class":219},[86,39000,10971],{"class":575},[86,39002,39003],{"class":579},"roc_auc",[86,39005,10971],{"class":575},[86,39007,273],{"class":219},[86,39009,39010],{"class":174,"line":13286},[86,39011,209],{"emptyLinePlaceholder":208},[86,39013,39014,39016,39018,39020,39023,39025,39028,39030,39032,39034,39037,39039,39042,39044,39046,39048,39050,39052,39054,39056,39058],{"class":174,"line":13291},[86,39015,13294],{"class":812},[86,39017,243],{"class":219},[86,39019,6178],{"class":235},[86,39021,39022],{"class":579},"'ROC-AUC en validación cruzada (train): ",[86,39024,4089],{"class":215},[86,39026,39027],{"class":182},"cv_auc",[86,39029,61],{"class":219},[86,39031,13227],{"class":182},[86,39033,13418],{"class":219},[86,39035,39036],{"class":235},":.3f",[86,39038,4117],{"class":215},[86,39040,39041],{"class":579}," +\u002F- ",[86,39043,4089],{"class":215},[86,39045,39027],{"class":182},[86,39047,61],{"class":219},[86,39049,13487],{"class":182},[86,39051,13418],{"class":219},[86,39053,39036],{"class":235},[86,39055,4117],{"class":215},[86,39057,10971],{"class":579},[86,39059,273],{"class":219},[12,39061,39062],{},"Dando como resultado:",[164,39064,39067],{"className":39065,"code":39066,"language":3141},[3139],"Cross-validated ROC-AUC (train, mean +\u002F- std): 0.856 +\u002F- 0.021\n",[145,39068,39066],{"__ignoreMap":169},[12,39070,39071],{},"En términos simples:\nSi se toma al azar una persona que sobrevivió y otra que no, el modelo tiene aproximadamente 85.6% de probabilidad de asignar mayor probabilidad al que realmente sobrevivió... Tal vez esto no suene muy claro, asi que veámoslo de otra forma:",[117,39073,39074,39077,39080,39083],{},[33,39075,39076],{},"Tomas a un pasajero que sobrevivió.",[33,39078,39079],{},"Tomas a otro pasajero que no sobrevivió.",[33,39081,39082],{},"Le preguntamos al modelo ¿Qué probabilidad le das a cada uno de haber sobrevivido?",[33,39084,39085],{},"El modelo le asigna una probabilidad de supervivencia a cada uno, por ejemplo, 0.8 para el sobreviviente y 0.3 para el no sobreviviente.",[12,39087,39088],{},"Si el pasajero que realmente sobrevivió tiene una probabilidad asignada más alta que el que no sobrevivió, entonces el modelo acertó en esa comparación. El ROC-AUC mide la proporción de veces que esto ocurre a lo largo de todas las posibles combinaciones de pasajeros sobrevivientes y no sobrevivientes.",[16,39090,39091],{},[12,39092,39093,39096],{},[122,39094,39095],{},"ROC-AUC"," (Receiver Operating Characteristic - Area Under the Curve) es una métrica que evalúa la capacidad de un modelo para distinguir entre clases. En este caso, mide qué tan bien el modelo puede diferenciar entre pasajeros que sobrevivieron y los que no.\nVa de 0.5 (azar total) a 1.0 (clasificación perfecta).\n0.856 indica que el modelo tiene una muy buena capacidad de discriminación.",[323,39098,39100],{"id":39099},"_6-evaluación-completa-del-modelo","6. Evaluación Completa del Modelo",[12,39102,39103,39104,39107],{},"Además del ",[145,39105,39106],{},"classification_report",", agregamos métricas globales y curvas complementarias para tener una visión más realista del rendimiento.",[164,39109,39111],{"className":166,"code":39110,"language":168,"meta":169,"style":169},"from sklearn.metrics import (\n  classification_report,\n  confusion_matrix,\n  roc_auc_score,\n  roc_curve,\n  precision_recall_curve,\n  average_precision_score,\n  accuracy_score,\n  f1_score,\n  precision_score,\n  recall_score,\n  ConfusionMatrixDisplay,\n)\n\n# Métricas principales\nacc = accuracy_score(y_test, y_pred)\nprec = precision_score(y_test, y_pred)\nrec = recall_score(y_test, y_pred)\nf1 = f1_score(y_test, y_pred)\nroc_auc = roc_auc_score(y_test, y_pred_proba)\nap = average_precision_score(y_test, y_pred_proba)\n\nprint('Métricas en test:')\nprint(f'Accuracy:  {acc:.3f}')\nprint(f'Precision: {prec:.3f}')\nprint(f'Recall:    {rec:.3f}')\nprint(f'F1-score:  {f1:.3f}')\nprint(f'ROC-AUC:   {roc_auc:.3f}')\nprint(f'PR-AUC:    {ap:.3f}\\n')\n\nprint('Reporte de clasificación:')\nprint(classification_report(y_test, y_pred, target_names=['No Sobrevivio', 'Sobrevivio']))\n\n# Matriz de confusión\ncm = confusion_matrix(y_test, y_pred)\nfig, ax = plt.subplots(figsize=(6, 5))\ndisp = ConfusionMatrixDisplay(confusion_matrix=cm, display_labels=['No Sobrevivio', 'Sobrevivio'])\ndisp.plot(ax=ax, cmap='Blues', colorbar=False)\nax.set_title('Matriz de Confusion - Regresion Logistica (Titanic)')\nplt.tight_layout()\nplt.show()\n\n# Curva ROC\nfpr, tpr, _ = roc_curve(y_test, y_pred_proba)\nplt.figure(figsize=(8, 6))\nplt.plot(fpr, tpr, color='darkorange', lw=2, label=f'Curva ROC (AUC = {roc_auc:.2f})')\nplt.plot([0, 1], [0, 1], color='navy', lw=2, linestyle='--', label='Referencia aleatoria')\nplt.title('Curva ROC - Regresion Logistica (Titanic)')\nplt.xlabel('False Positive Rate')\nplt.ylabel('True Positive Rate')\nplt.legend(loc='lower right')\nplt.tight_layout()\nplt.show()\n\n# Curva Precision-Recall\nprecision_vals, recall_vals, _ = precision_recall_curve(y_test, y_pred_proba)\nplt.figure(figsize=(8, 6))\nplt.plot(recall_vals, precision_vals, color='teal', lw=2, label=f'Curva PR (AP = {ap:.2f})')\nplt.title('Curva Precision-Recall - Regresion Logistica (Titanic)')\nplt.xlabel('Recall')\nplt.ylabel('Precision')\nplt.legend(loc='lower left')\nplt.tight_layout()\nplt.show()\n",[145,39112,39113,39128,39135,39142,39149,39156,39163,39170,39177,39184,39191,39198,39205,39209,39213,39218,39240,39260,39280,39300,39321,39341,39345,39360,39384,39408,39432,39456,39479,39503,39507,39522,39564,39568,39573,39593,39624,39667,39709,39728,39738,39748,39752,39757,39787,39810,39873,39949,39968,39987,40006,40030,40040,40051,40056,40062,40092,40115,40178,40198,40217,40236,40260,40271],{"__ignoreMap":169},[86,39114,39115,39117,39119,39121,39124,39126],{"class":174,"line":175},[86,39116,1053],{"class":178},[86,39118,1056],{"class":182},[86,39120,61],{"class":219},[86,39122,39123],{"class":182},"metrics ",[86,39125,179],{"class":178},[86,39127,37420],{"class":219},[86,39129,39130,39133],{"class":174,"line":192},[86,39131,39132],{"class":182},"  classification_report",[86,39134,1111],{"class":219},[86,39136,39137,39140],{"class":174,"line":205},[86,39138,39139],{"class":182},"  confusion_matrix",[86,39141,1111],{"class":219},[86,39143,39144,39147],{"class":174,"line":212},[86,39145,39146],{"class":182},"  roc_auc_score",[86,39148,1111],{"class":219},[86,39150,39151,39154],{"class":174,"line":227},[86,39152,39153],{"class":182},"  roc_curve",[86,39155,1111],{"class":219},[86,39157,39158,39161],{"class":174,"line":232},[86,39159,39160],{"class":182},"  precision_recall_curve",[86,39162,1111],{"class":219},[86,39164,39165,39168],{"class":174,"line":252},[86,39166,39167],{"class":182},"  average_precision_score",[86,39169,1111],{"class":219},[86,39171,39172,39175],{"class":174,"line":276},[86,39173,39174],{"class":182},"  accuracy_score",[86,39176,1111],{"class":219},[86,39178,39179,39182],{"class":174,"line":315},[86,39180,39181],{"class":182},"  f1_score",[86,39183,1111],{"class":219},[86,39185,39186,39189],{"class":174,"line":3665},[86,39187,39188],{"class":182},"  precision_score",[86,39190,1111],{"class":219},[86,39192,39193,39196],{"class":174,"line":13256},[86,39194,39195],{"class":182},"  recall_score",[86,39197,1111],{"class":219},[86,39199,39200,39203],{"class":174,"line":13286},[86,39201,39202],{"class":182},"  ConfusionMatrixDisplay",[86,39204,1111],{"class":219},[86,39206,39207],{"class":174,"line":13291},[86,39208,273],{"class":219},[86,39210,39211],{"class":174,"line":13308},[86,39212,209],{"emptyLinePlaceholder":208},[86,39214,39215],{"class":174,"line":13334},[86,39216,39217],{"class":1360},"# Métricas principales\n",[86,39219,39220,39223,39225,39228,39230,39233,39235,39238],{"class":174,"line":13359},[86,39221,39222],{"class":182},"acc ",[86,39224,258],{"class":219},[86,39226,39227],{"class":182}," accuracy_score",[86,39229,243],{"class":219},[86,39231,39232],{"class":182},"y_test",[86,39234,291],{"class":219},[86,39236,39237],{"class":182}," y_pred",[86,39239,273],{"class":219},[86,39241,39242,39245,39247,39250,39252,39254,39256,39258],{"class":174,"line":13385},[86,39243,39244],{"class":182},"prec ",[86,39246,258],{"class":219},[86,39248,39249],{"class":182}," precision_score",[86,39251,243],{"class":219},[86,39253,39232],{"class":182},[86,39255,291],{"class":219},[86,39257,39237],{"class":182},[86,39259,273],{"class":219},[86,39261,39262,39265,39267,39270,39272,39274,39276,39278],{"class":174,"line":13390},[86,39263,39264],{"class":182},"rec ",[86,39266,258],{"class":219},[86,39268,39269],{"class":182}," recall_score",[86,39271,243],{"class":219},[86,39273,39232],{"class":182},[86,39275,291],{"class":219},[86,39277,39237],{"class":182},[86,39279,273],{"class":219},[86,39281,39282,39285,39287,39290,39292,39294,39296,39298],{"class":174,"line":13396},[86,39283,39284],{"class":182},"f1 ",[86,39286,258],{"class":219},[86,39288,39289],{"class":182}," f1_score",[86,39291,243],{"class":219},[86,39293,39232],{"class":182},[86,39295,291],{"class":219},[86,39297,39237],{"class":182},[86,39299,273],{"class":219},[86,39301,39302,39305,39307,39310,39312,39314,39316,39319],{"class":174,"line":3615},[86,39303,39304],{"class":182},"roc_auc ",[86,39306,258],{"class":219},[86,39308,39309],{"class":182}," roc_auc_score",[86,39311,243],{"class":219},[86,39313,39232],{"class":182},[86,39315,291],{"class":219},[86,39317,39318],{"class":182}," y_pred_proba",[86,39320,273],{"class":219},[86,39322,39323,39326,39328,39331,39333,39335,39337,39339],{"class":174,"line":2254},[86,39324,39325],{"class":182},"ap ",[86,39327,258],{"class":219},[86,39329,39330],{"class":182}," average_precision_score",[86,39332,243],{"class":219},[86,39334,39232],{"class":182},[86,39336,291],{"class":219},[86,39338,39318],{"class":182},[86,39340,273],{"class":219},[86,39342,39343],{"class":174,"line":13492},[86,39344,209],{"emptyLinePlaceholder":208},[86,39346,39347,39349,39351,39353,39356,39358],{"class":174,"line":13545},[86,39348,13294],{"class":812},[86,39350,243],{"class":219},[86,39352,10971],{"class":575},[86,39354,39355],{"class":579},"Métricas en test:",[86,39357,10971],{"class":575},[86,39359,273],{"class":219},[86,39361,39362,39364,39366,39368,39371,39373,39376,39378,39380,39382],{"class":174,"line":13550},[86,39363,13294],{"class":812},[86,39365,243],{"class":219},[86,39367,6178],{"class":235},[86,39369,39370],{"class":579},"'Accuracy:  ",[86,39372,4089],{"class":215},[86,39374,39375],{"class":182},"acc",[86,39377,39036],{"class":235},[86,39379,4117],{"class":215},[86,39381,10971],{"class":579},[86,39383,273],{"class":219},[86,39385,39386,39388,39390,39392,39395,39397,39400,39402,39404,39406],{"class":174,"line":13566},[86,39387,13294],{"class":812},[86,39389,243],{"class":219},[86,39391,6178],{"class":235},[86,39393,39394],{"class":579},"'Precision: ",[86,39396,4089],{"class":215},[86,39398,39399],{"class":182},"prec",[86,39401,39036],{"class":235},[86,39403,4117],{"class":215},[86,39405,10971],{"class":579},[86,39407,273],{"class":219},[86,39409,39410,39412,39414,39416,39419,39421,39424,39426,39428,39430],{"class":174,"line":13591},[86,39411,13294],{"class":812},[86,39413,243],{"class":219},[86,39415,6178],{"class":235},[86,39417,39418],{"class":579},"'Recall:    ",[86,39420,4089],{"class":215},[86,39422,39423],{"class":182},"rec",[86,39425,39036],{"class":235},[86,39427,4117],{"class":215},[86,39429,10971],{"class":579},[86,39431,273],{"class":219},[86,39433,39434,39436,39438,39440,39443,39445,39448,39450,39452,39454],{"class":174,"line":13616},[86,39435,13294],{"class":812},[86,39437,243],{"class":219},[86,39439,6178],{"class":235},[86,39441,39442],{"class":579},"'F1-score:  ",[86,39444,4089],{"class":215},[86,39446,39447],{"class":182},"f1",[86,39449,39036],{"class":235},[86,39451,4117],{"class":215},[86,39453,10971],{"class":579},[86,39455,273],{"class":219},[86,39457,39458,39460,39462,39464,39467,39469,39471,39473,39475,39477],{"class":174,"line":13641},[86,39459,13294],{"class":812},[86,39461,243],{"class":219},[86,39463,6178],{"class":235},[86,39465,39466],{"class":579},"'ROC-AUC:   ",[86,39468,4089],{"class":215},[86,39470,39003],{"class":182},[86,39472,39036],{"class":235},[86,39474,4117],{"class":215},[86,39476,10971],{"class":579},[86,39478,273],{"class":219},[86,39480,39481,39483,39485,39487,39490,39492,39495,39497,39499,39501],{"class":174,"line":37784},[86,39482,13294],{"class":812},[86,39484,243],{"class":219},[86,39486,6178],{"class":235},[86,39488,39489],{"class":579},"'PR-AUC:    ",[86,39491,4089],{"class":215},[86,39493,39494],{"class":182},"ap",[86,39496,39036],{"class":235},[86,39498,13378],{"class":215},[86,39500,10971],{"class":579},[86,39502,273],{"class":219},[86,39504,39505],{"class":174,"line":37795},[86,39506,209],{"emptyLinePlaceholder":208},[86,39508,39509,39511,39513,39515,39518,39520],{"class":174,"line":37807},[86,39510,13294],{"class":812},[86,39512,243],{"class":219},[86,39514,10971],{"class":575},[86,39516,39517],{"class":579},"Reporte de clasificación:",[86,39519,10971],{"class":575},[86,39521,273],{"class":219},[86,39523,39524,39526,39528,39530,39532,39534,39536,39538,39540,39543,39545,39547,39550,39552,39554,39556,39559,39561],{"class":174,"line":37822},[86,39525,13294],{"class":812},[86,39527,243],{"class":219},[86,39529,39106],{"class":182},[86,39531,243],{"class":219},[86,39533,39232],{"class":182},[86,39535,291],{"class":219},[86,39537,39237],{"class":182},[86,39539,291],{"class":219},[86,39541,39542],{"class":304}," target_names",[86,39544,1119],{"class":219},[86,39546,10971],{"class":575},[86,39548,39549],{"class":579},"No Sobrevivio",[86,39551,10971],{"class":575},[86,39553,291],{"class":219},[86,39555,11970],{"class":575},[86,39557,39558],{"class":579},"Sobrevivio",[86,39560,10971],{"class":575},[86,39562,39563],{"class":219},"]))\n",[86,39565,39566],{"class":174,"line":37837},[86,39567,209],{"emptyLinePlaceholder":208},[86,39569,39570],{"class":174,"line":37852},[86,39571,39572],{"class":1360},"# Matriz de confusión\n",[86,39574,39575,39578,39580,39583,39585,39587,39589,39591],{"class":174,"line":37867},[86,39576,39577],{"class":182},"cm ",[86,39579,258],{"class":219},[86,39581,39582],{"class":182}," confusion_matrix",[86,39584,243],{"class":219},[86,39586,39232],{"class":182},[86,39588,291],{"class":219},[86,39590,39237],{"class":182},[86,39592,273],{"class":219},[86,39594,39595,39597,39599,39602,39604,39606,39608,39610,39612,39614,39616,39618,39620,39622],{"class":174,"line":37882},[86,39596,35118],{"class":182},[86,39598,291],{"class":219},[86,39600,39601],{"class":182}," ax ",[86,39603,258],{"class":219},[86,39605,35128],{"class":182},[86,39607,61],{"class":219},[86,39609,35133],{"class":182},[86,39611,243],{"class":219},[86,39613,34706],{"class":304},[86,39615,34709],{"class":219},[86,39617,4114],{"class":223},[86,39619,291],{"class":219},[86,39621,34717],{"class":223},[86,39623,33401],{"class":219},[86,39625,39626,39629,39631,39634,39636,39639,39641,39644,39646,39649,39651,39653,39655,39657,39659,39661,39663,39665],{"class":174,"line":37887},[86,39627,39628],{"class":182},"disp ",[86,39630,258],{"class":219},[86,39632,39633],{"class":182}," ConfusionMatrixDisplay",[86,39635,243],{"class":219},[86,39637,39638],{"class":304},"confusion_matrix",[86,39640,258],{"class":219},[86,39642,39643],{"class":182},"cm",[86,39645,291],{"class":219},[86,39647,39648],{"class":304}," display_labels",[86,39650,1119],{"class":219},[86,39652,10971],{"class":575},[86,39654,39549],{"class":579},[86,39656,10971],{"class":575},[86,39658,291],{"class":219},[86,39660,11970],{"class":575},[86,39662,39558],{"class":579},[86,39664,10971],{"class":575},[86,39666,1417],{"class":219},[86,39668,39669,39672,39674,39677,39679,39681,39683,39685,39687,39689,39691,39693,39696,39698,39700,39703,39705,39707],{"class":174,"line":37911},[86,39670,39671],{"class":182},"disp",[86,39673,61],{"class":219},[86,39675,39676],{"class":182},"plot",[86,39678,243],{"class":219},[86,39680,9758],{"class":304},[86,39682,258],{"class":219},[86,39684,9758],{"class":182},[86,39686,291],{"class":219},[86,39688,35613],{"class":304},[86,39690,258],{"class":219},[86,39692,10971],{"class":575},[86,39694,39695],{"class":579},"Blues",[86,39697,10971],{"class":575},[86,39699,291],{"class":219},[86,39701,39702],{"class":304}," colorbar",[86,39704,258],{"class":219},[86,39706,33508],{"class":178},[86,39708,273],{"class":219},[86,39710,39711,39713,39715,39717,39719,39721,39724,39726],{"class":174,"line":37934},[86,39712,9758],{"class":182},[86,39714,61],{"class":219},[86,39716,35263],{"class":182},[86,39718,243],{"class":219},[86,39720,10971],{"class":575},[86,39722,39723],{"class":579},"Matriz de Confusion - Regresion Logistica (Titanic)",[86,39725,10971],{"class":575},[86,39727,273],{"class":219},[86,39729,39730,39732,39734,39736],{"class":174,"line":37957},[86,39731,33172],{"class":182},[86,39733,61],{"class":219},[86,39735,35076],{"class":182},[86,39737,11991],{"class":219},[86,39739,39740,39742,39744,39746],{"class":174,"line":37980},[86,39741,33172],{"class":182},[86,39743,61],{"class":219},[86,39745,35087],{"class":182},[86,39747,11991],{"class":219},[86,39749,39750],{"class":174,"line":38008},[86,39751,209],{"emptyLinePlaceholder":208},[86,39753,39754],{"class":174,"line":38013},[86,39755,39756],{"class":1360},"# Curva ROC\n",[86,39758,39759,39762,39764,39767,39769,39772,39774,39777,39779,39781,39783,39785],{"class":174,"line":38019},[86,39760,39761],{"class":182},"fpr",[86,39763,291],{"class":219},[86,39765,39766],{"class":182}," tpr",[86,39768,291],{"class":219},[86,39770,39771],{"class":182}," _ ",[86,39773,258],{"class":219},[86,39775,39776],{"class":182}," roc_curve",[86,39778,243],{"class":219},[86,39780,39232],{"class":182},[86,39782,291],{"class":219},[86,39784,39318],{"class":182},[86,39786,273],{"class":219},[86,39788,39789,39791,39793,39795,39797,39799,39801,39803,39805,39808],{"class":174,"line":38067},[86,39790,33172],{"class":182},[86,39792,61],{"class":219},[86,39794,34701],{"class":182},[86,39796,243],{"class":219},[86,39798,34706],{"class":304},[86,39800,34709],{"class":219},[86,39802,34578],{"class":223},[86,39804,291],{"class":219},[86,39806,39807],{"class":223}," 6",[86,39809,33401],{"class":219},[86,39811,39812,39814,39816,39818,39820,39822,39824,39826,39828,39830,39832,39834,39837,39839,39841,39844,39846,39848,39850,39853,39855,39857,39860,39862,39864,39866,39868,39871],{"class":174,"line":38156},[86,39813,33172],{"class":182},[86,39815,61],{"class":219},[86,39817,39676],{"class":182},[86,39819,243],{"class":219},[86,39821,39761],{"class":182},[86,39823,291],{"class":219},[86,39825,39766],{"class":182},[86,39827,291],{"class":219},[86,39829,36817],{"class":304},[86,39831,258],{"class":219},[86,39833,10971],{"class":575},[86,39835,39836],{"class":579},"darkorange",[86,39838,10971],{"class":575},[86,39840,291],{"class":219},[86,39842,39843],{"class":304}," lw",[86,39845,258],{"class":219},[86,39847,980],{"class":223},[86,39849,291],{"class":219},[86,39851,39852],{"class":304}," label",[86,39854,258],{"class":219},[86,39856,6178],{"class":235},[86,39858,39859],{"class":579},"'Curva ROC (AUC = ",[86,39861,4089],{"class":215},[86,39863,39003],{"class":182},[86,39865,13325],{"class":235},[86,39867,4117],{"class":215},[86,39869,39870],{"class":579},")'",[86,39872,273],{"class":219},[86,39874,39875,39877,39879,39881,39883,39885,39887,39889,39891,39893,39895,39897,39899,39901,39903,39905,39907,39910,39912,39914,39916,39918,39920,39922,39925,39927,39929,39932,39934,39936,39938,39940,39942,39945,39947],{"class":174,"line":38180},[86,39876,33172],{"class":182},[86,39878,61],{"class":219},[86,39880,39676],{"class":182},[86,39882,32924],{"class":219},[86,39884,2553],{"class":223},[86,39886,291],{"class":219},[86,39888,786],{"class":223},[86,39890,9750],{"class":219},[86,39892,726],{"class":219},[86,39894,2553],{"class":223},[86,39896,291],{"class":219},[86,39898,786],{"class":223},[86,39900,9750],{"class":219},[86,39902,36817],{"class":304},[86,39904,258],{"class":219},[86,39906,10971],{"class":575},[86,39908,39909],{"class":579},"navy",[86,39911,10971],{"class":575},[86,39913,291],{"class":219},[86,39915,39843],{"class":304},[86,39917,258],{"class":219},[86,39919,980],{"class":223},[86,39921,291],{"class":219},[86,39923,39924],{"class":304}," linestyle",[86,39926,258],{"class":219},[86,39928,10971],{"class":575},[86,39930,39931],{"class":579},"--",[86,39933,10971],{"class":575},[86,39935,291],{"class":219},[86,39937,39852],{"class":304},[86,39939,258],{"class":219},[86,39941,10971],{"class":575},[86,39943,39944],{"class":579},"Referencia aleatoria",[86,39946,10971],{"class":575},[86,39948,273],{"class":219},[86,39950,39951,39953,39955,39957,39959,39961,39964,39966],{"class":174,"line":38204},[86,39952,33172],{"class":182},[86,39954,61],{"class":219},[86,39956,34801],{"class":182},[86,39958,243],{"class":219},[86,39960,10971],{"class":575},[86,39962,39963],{"class":579},"Curva ROC - Regresion Logistica (Titanic)",[86,39965,10971],{"class":575},[86,39967,273],{"class":219},[86,39969,39970,39972,39974,39976,39978,39980,39983,39985],{"class":174,"line":38227},[86,39971,33172],{"class":182},[86,39973,61],{"class":219},[86,39975,34821],{"class":182},[86,39977,243],{"class":219},[86,39979,10971],{"class":575},[86,39981,39982],{"class":579},"False Positive Rate",[86,39984,10971],{"class":575},[86,39986,273],{"class":219},[86,39988,39989,39991,39993,39995,39997,39999,40002,40004],{"class":174,"line":38250},[86,39990,33172],{"class":182},[86,39992,61],{"class":219},[86,39994,34841],{"class":182},[86,39996,243],{"class":219},[86,39998,10971],{"class":575},[86,40000,40001],{"class":579},"True Positive Rate",[86,40003,10971],{"class":575},[86,40005,273],{"class":219},[86,40007,40008,40010,40012,40014,40016,40019,40021,40023,40026,40028],{"class":174,"line":38255},[86,40009,33172],{"class":182},[86,40011,61],{"class":219},[86,40013,37684],{"class":182},[86,40015,243],{"class":219},[86,40017,40018],{"class":304},"loc",[86,40020,258],{"class":219},[86,40022,10971],{"class":575},[86,40024,40025],{"class":579},"lower right",[86,40027,10971],{"class":575},[86,40029,273],{"class":219},[86,40031,40032,40034,40036,40038],{"class":174,"line":38266},[86,40033,33172],{"class":182},[86,40035,61],{"class":219},[86,40037,35076],{"class":182},[86,40039,11991],{"class":219},[86,40041,40043,40045,40047,40049],{"class":174,"line":40042},53,[86,40044,33172],{"class":182},[86,40046,61],{"class":219},[86,40048,35087],{"class":182},[86,40050,11991],{"class":219},[86,40052,40054],{"class":174,"line":40053},54,[86,40055,209],{"emptyLinePlaceholder":208},[86,40057,40059],{"class":174,"line":40058},55,[86,40060,40061],{"class":1360},"# Curva Precision-Recall\n",[86,40063,40065,40068,40070,40073,40075,40077,40079,40082,40084,40086,40088,40090],{"class":174,"line":40064},56,[86,40066,40067],{"class":182},"precision_vals",[86,40069,291],{"class":219},[86,40071,40072],{"class":182}," recall_vals",[86,40074,291],{"class":219},[86,40076,39771],{"class":182},[86,40078,258],{"class":219},[86,40080,40081],{"class":182}," precision_recall_curve",[86,40083,243],{"class":219},[86,40085,39232],{"class":182},[86,40087,291],{"class":219},[86,40089,39318],{"class":182},[86,40091,273],{"class":219},[86,40093,40095,40097,40099,40101,40103,40105,40107,40109,40111,40113],{"class":174,"line":40094},57,[86,40096,33172],{"class":182},[86,40098,61],{"class":219},[86,40100,34701],{"class":182},[86,40102,243],{"class":219},[86,40104,34706],{"class":304},[86,40106,34709],{"class":219},[86,40108,34578],{"class":223},[86,40110,291],{"class":219},[86,40112,39807],{"class":223},[86,40114,33401],{"class":219},[86,40116,40118,40120,40122,40124,40126,40129,40131,40134,40136,40138,40140,40142,40145,40147,40149,40151,40153,40155,40157,40159,40161,40163,40166,40168,40170,40172,40174,40176],{"class":174,"line":40117},58,[86,40119,33172],{"class":182},[86,40121,61],{"class":219},[86,40123,39676],{"class":182},[86,40125,243],{"class":219},[86,40127,40128],{"class":182},"recall_vals",[86,40130,291],{"class":219},[86,40132,40133],{"class":182}," precision_vals",[86,40135,291],{"class":219},[86,40137,36817],{"class":304},[86,40139,258],{"class":219},[86,40141,10971],{"class":575},[86,40143,40144],{"class":579},"teal",[86,40146,10971],{"class":575},[86,40148,291],{"class":219},[86,40150,39843],{"class":304},[86,40152,258],{"class":219},[86,40154,980],{"class":223},[86,40156,291],{"class":219},[86,40158,39852],{"class":304},[86,40160,258],{"class":219},[86,40162,6178],{"class":235},[86,40164,40165],{"class":579},"'Curva PR (AP = ",[86,40167,4089],{"class":215},[86,40169,39494],{"class":182},[86,40171,13325],{"class":235},[86,40173,4117],{"class":215},[86,40175,39870],{"class":579},[86,40177,273],{"class":219},[86,40179,40181,40183,40185,40187,40189,40191,40194,40196],{"class":174,"line":40180},59,[86,40182,33172],{"class":182},[86,40184,61],{"class":219},[86,40186,34801],{"class":182},[86,40188,243],{"class":219},[86,40190,10971],{"class":575},[86,40192,40193],{"class":579},"Curva Precision-Recall - Regresion Logistica (Titanic)",[86,40195,10971],{"class":575},[86,40197,273],{"class":219},[86,40199,40201,40203,40205,40207,40209,40211,40213,40215],{"class":174,"line":40200},60,[86,40202,33172],{"class":182},[86,40204,61],{"class":219},[86,40206,34821],{"class":182},[86,40208,243],{"class":219},[86,40210,10971],{"class":575},[86,40212,12146],{"class":579},[86,40214,10971],{"class":575},[86,40216,273],{"class":219},[86,40218,40220,40222,40224,40226,40228,40230,40232,40234],{"class":174,"line":40219},61,[86,40221,33172],{"class":182},[86,40223,61],{"class":219},[86,40225,34841],{"class":182},[86,40227,243],{"class":219},[86,40229,10971],{"class":575},[86,40231,12143],{"class":579},[86,40233,10971],{"class":575},[86,40235,273],{"class":219},[86,40237,40239,40241,40243,40245,40247,40249,40251,40253,40256,40258],{"class":174,"line":40238},62,[86,40240,33172],{"class":182},[86,40242,61],{"class":219},[86,40244,37684],{"class":182},[86,40246,243],{"class":219},[86,40248,40018],{"class":304},[86,40250,258],{"class":219},[86,40252,10971],{"class":575},[86,40254,40255],{"class":579},"lower left",[86,40257,10971],{"class":575},[86,40259,273],{"class":219},[86,40261,40263,40265,40267,40269],{"class":174,"line":40262},63,[86,40264,33172],{"class":182},[86,40266,61],{"class":219},[86,40268,35076],{"class":182},[86,40270,11991],{"class":219},[86,40272,40274,40276,40278,40280],{"class":174,"line":40273},64,[86,40275,33172],{"class":182},[86,40277,61],{"class":219},[86,40279,35087],{"class":182},[86,40281,11991],{"class":219},[12,40283,40284],{},"Con este pipeline, en test obtuvimos aproximadamente:",[117,40286,40287,40293,40299,40305,40311,40317],{},[33,40288,40289,40290],{},"Accuracy: ",[145,40291,40292],{},"0.793",[33,40294,40295,40296],{},"Precision: ",[145,40297,40298],{},"0.722",[33,40300,40301,40302],{},"Recall: ",[145,40303,40304],{},"0.754",[33,40306,40307,40308],{},"F1-score: ",[145,40309,40310],{},"0.738",[33,40312,40313,40314],{},"ROC-AUC: ",[145,40315,40316],{},"0.851",[33,40318,40319,40320],{},"PR-AUC: ",[145,40321,40322],{},"0.796",[12,40324,40325,40326,40329],{},"Estos resultados indican que tu modelo tiene un desempeño ",[122,40327,40328],{},"sólido y bastante equilibrado"," en el conjunto de prueba. Vamos a interpretarlo paso a paso.",[12,40331,40332,40333,40336],{},"Primero, la ",[122,40334,40335],{},"accuracy (0.793)"," significa que el modelo clasifica correctamente aproximadamente el 79.3% de los pasajeros. Es un buen valor, pero por sí sola no es suficiente, especialmente porque el dataset está algo desbalanceado (110 no sobrevivieron vs 69 sobrevivieron).",[12,40338,40339,40340,162],{},"En la clase ",[122,40341,40342],{},"\"Survived\"",[30,40344,40345,40351,40357],{},[33,40346,40347,40350],{},[122,40348,40349],{},"Precision = 0.722","\nDe todas las personas que el modelo predijo como sobrevivientes, el 72.2% realmente sobrevivió.\nEsto mide qué tan \"confiables\" son las predicciones positivas.",[33,40352,40353,40356],{},[122,40354,40355],{},"Recall = 0.754","\nDe todos los que realmente sobrevivieron, el modelo logró identificar el 75.4%.\nEsto mide qué tanto se le escapan casos reales.",[33,40358,40359,40362],{},[122,40360,40361],{},"F1-score = 0.738","\nEs el equilibrio entre precision y recall.\nIndica que el modelo mantiene un buen balance entre detectar sobrevivientes y no generar demasiados falsos positivos.",[12,40364,40339,40365,40368],{},[122,40366,40367],{},"\"Did Not Survive\""," el rendimiento es incluso un poco mejor (F1 ~ 0.83), lo cual es normal porque hay más ejemplos de esa clase.",[12,40370,40371],{},"Ahora las métricas de discriminación:",[30,40373,40374,40380],{},[33,40375,40376,40379],{},[122,40377,40378],{},"ROC-AUC = 0.851","\nEl modelo separa bastante bien a sobrevivientes de no sobrevivientes (muy buena capacidad de discriminación).",[33,40381,40382,40385],{},[122,40383,40384],{},"PR-AUC = 0.796","\nEsta métrica es especialmente útil cuando hay desbalance. Un 0.796 indica que el modelo mantiene buena relación entre precision y recall al variar el umbral.",[12,40387,40388,40391],{},[1945,40389],{"alt":1951,"src":40390},"\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Fconfusion_matrix.webp",[901,40392,1951],{},[12,40394,40395,40399],{},[1945,40396],{"alt":40397,"src":40398},"Curva ROC","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Froc_curve.webp",[901,40400,40397],{},[12,40402,40403,40407],{},[1945,40404],{"alt":40405,"src":40406},"Curva Precision-Recall","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Fpr_curve.webp",[901,40408,40405],{},[43,40410],{},[46,40412,40414],{"id":40413},"conclusiones","Conclusiones",[12,40416,40417],{},"Siempre ten en cuenta que:",[117,40419,40420,40423,40426],{},[33,40421,40422],{},"Un buen EDA reduce sorpresas durante el modelado.",[33,40424,40425],{},"Limpiar e imputar correctamente puede impactar tanto como elegir el modelo.",[33,40427,40428],{},"Evaluar con varias métricas (no solo accuracy) da una lectura mucho más real del comportamiento del clasificador.",[12,40430,40431],{},"Puedes buscar otros datasets y experimentar por tu cuenta, aplicando este mismo flujo de trabajo. ¡Es la mejor forma de aprender!",[12,40433,40434],{},"Algunas fuentes de datasets interesantes para practicar EDA y modelado:",[30,40436,40437,40444,40451,40458],{},[33,40438,40439],{},[22,40440,40443],{"href":40441,"rel":40442},"https:\u002F\u002Fwww.kaggle.com\u002Fdatasets",[26],"Kaggle Datasets",[33,40445,40446],{},[22,40447,40450],{"href":40448,"rel":40449},"https:\u002F\u002Farchive.ics.uci.edu\u002F",[26],"UCI Machine Learning Repository",[33,40452,40453],{},[22,40454,40457],{"href":40455,"rel":40456},"https:\u002F\u002Fdatasetsearch.research.google.com\u002F",[26],"Google Dataset Search",[33,40459,40460],{},[22,40461,40464],{"href":40462,"rel":40463},"https:\u002F\u002Fgithub.com\u002Fawesomedata\u002Fawesome-public-datasets",[26],"Awesome Public Datasets",[2218,40466,40467],{},"html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}html pre.shiki code .scnC2, html code.shiki .scnC2{--shiki-default:#B5695977;--shiki-dark:#C98A7D77}html pre.shiki code .spP0B, html code.shiki .spP0B{--shiki-default:#B56959;--shiki-dark:#C98A7D}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html pre.shiki code .s5TCs, html code.shiki .s5TCs{--shiki-default:#AB5959;--shiki-dark:#CB7676}html pre.shiki code .sfsYZ, html code.shiki .sfsYZ{--shiki-default:#A65E2B;--shiki-dark:#C99076}html pre.shiki code .s9nN2, html code.shiki .s9nN2{--shiki-default:#B07D48;--shiki-dark:#BD976A}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":169,"searchDepth":205,"depth":205,"links":40469},[40470,40483],{"id":33035,"depth":192,"text":33036,"children":40471},[40472,40473,40474,40480,40481,40482],{"id":33079,"depth":205,"text":33080},{"id":33651,"depth":205,"text":33652},{"id":34679,"depth":205,"text":34680,"children":40475},[40476,40477,40478,40479],{"id":34686,"depth":212,"text":34687},{"id":35107,"depth":212,"text":35108},{"id":35519,"depth":212,"text":35520},{"id":36145,"depth":212,"text":36146},{"id":38317,"depth":205,"text":38318},{"id":38771,"depth":205,"text":38772},{"id":39099,"depth":205,"text":39100},{"id":40413,"depth":192,"text":40414},"2026-04-23","\u002Fblog\u002Fexperimenting-with-titanic-dataset\u002Fshared\u002Ftitanic.webp",{},"\u002Fblog\u002Fblog\u002Fexperimenting-with-titanic-dataset",{"title":19791,"description":33020},{"loc":40490,"priority":2259,"lastmod":40484},"\u002Fes\u002Fblog\u002Fexperimenting-with-titanic-dataset","experimenting-with-titanic-dataset","blog\u002Fblog\u002Fexperimenting-with-titanic-dataset","Exploremos el dataset de supervivencia del Titanic utilizando técnicas de análisis exploratorio de datos (EDA) para descubrir patrones y relaciones entre las características de los pasajeros y su supervivencia.",[3625,3675,40495,40496,40497],"eda","proyectos de machine learning","análisis exploratorio","sKydf7tOqNy6HNlVk-yBWIPs5FZ3hYcZJbHeCbh-QX4",{"id":40500,"title":33028,"author":7,"body":40501,"date":44583,"description":40505,"extension":2250,"image":44584,"lastmod":44583,"meta":44585,"navigation":208,"order":227,"path":44586,"seo":44587,"sitemap":44588,"slug":44590,"stem":44591,"summary":44592,"tags":44593,"__hash__":44594},"content_es\u002Fblog\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis.md",{"type":9,"value":40502,"toc":44574},[40503,40506,40513,40515,40517,40521,40528,40536,40540,40553,41240,41244,41255,41303,41306,41699,41702,41737,41740,41744,41747,41767,42191,42200,42215,42220,42227,42230,42241,42247,42252,42266,42269,42281,42284,42295,42298,42309,42318,42321,42328,42335,42342,42349,42356,42359,42361,42375,42378,42383,42386,42393,42396,42399,42410,42416,42422,42436,42439,42446,42449,42684,42687,42690,43010,43013,43024,43033,43036,43056,43063,43069,43072,43078,43081,43108,43115,43166,43173,43217,43224,43262,43269,43308,43315,43318,43356,43359,43373,43378,43381,43387,43390,43393,43396,43404,43407,43410,43413,43433,43452,43456,43462,43731,43735,43738,43886,43888,43894,43900,43961,43964,44107,44112,44291,44300,44303,44306,44405,44408,44474,44477,44522,44525,44571],[12,40504,40505],{},"El análisis exploratorio de datos (EDA) es una etapa crucial en cualquier proyecto de aprendizaje automático. En este articulo realizaremos algunos experimentos con EDA para entender mejor cómo podemos utilizarlo para obtener insights valiosos de nuestros datos y mejorar el rendimiento de nuestros modelos.",[12,40507,19786,40508],{},[22,40509,40512],{"href":40510,"rel":40511},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fworkflow-machine-learning-projects",[26],"El flujo en proyectos de aprendizaje automático",[40,40514],{},[43,40516],{},[46,40518,40520],{"id":40519},"un-ejercicio-práctico-estimando-las-ventas-de-una-cafetería","Un Ejercicio Práctico: Estimando las Ventas de una Cafetería",[12,40522,40523,40524,40527],{},"Para entender el verdadero impacto de un Análisis Exploratorio de Datos (EDA), salgamos de la teoría y vayamos a la práctica con un escenario comercial: ",[122,40525,40526],{},"Estimar cuántos ingresos generará una cafetería al mes",". Este tipo de ejercicios permite que gerentes y dueños de negocio tomen decisiones basadas en datos (Data-Driven) y no en corazonadas.",[12,40529,40530,40531],{},"Puedes seguir este ejercicio interactivo en Google Colab: ",[22,40532,40535],{"href":40533,"target":27,"rel":40534},"https:\u002F\u002Fcolab.research.google.com\u002Fdrive\u002F12NPwGTp9JE0Vl926_ODlqpDRLkbnJimz?usp=sharing",[7760,7761],"EDA para Estimar Ventas de una Cafetería",[323,40537,40539],{"id":40538},"paso-1-generación-y-carga-de-datos","Paso 1: Generación y Carga de Datos",[12,40541,40542,40543,40545,40546,16555,40549,40552],{},"Como primer paso, necesitamos un historial. Simularemos los datos de 365 días operativos de la cafetería, con variables que van desde la temperatura ambiente hasta inversión en publicidad (Ads en redes sociales). Importamos herramientas esenciales del stack clásico de Python: ",[145,40544,13085],{}," para manejar las tablas, y ",[145,40547,40548],{},"matplotlib",[145,40550,40551],{},"seaborn"," para gráficos.",[164,40554,40556],{"className":166,"code":40555,"language":168,"meta":169,"style":169},"import pandas as pd\nimport numpy as np\nimport random\nimport matplotlib.pyplot as plt\nimport seaborn as sns\n\n# Semilla para que los datos sean reproducibles\nnp.random.seed(42)\nrandom.seed(42)\n\n# Generación del dataset (365 días operativos)\nn = 365\nclimas = [\"Soleado\", \"Lluvioso\", \"Nublado\"]\ndata = []\n\nfor _ in range(n):\n    temperatura = round(random.uniform(15.0, 35.0), 1)\n    inversion_publicidad = round(random.uniform(10.0, 150.0), 2)\n    eventos_cercanos = random.choice([0, 1])\n    descuento_aplicado = random.choice([0, 10, 15, 20])\n    clima = random.choice(climas)\n    \n    # Lógica de negocio (Correlaciones simuladas):\n    # La temperatura baja y los eventos suben ventas. El clima lluvioso invita a tomar café.\n    ventas = (\n        500 + \n        (inversion_publicidad * 2.5) - \n        (temperatura * 8) + \n        (eventos_cercanos * 250) + \n        (descuento_aplicado * 5)\n    )\n    \n    if clima == \"Lluvioso\": ventas += 150\n    elif clima == \"Soleado\": ventas -= 50\n    \n    # Añadimos ruido estadístico para hacerlo realista\n    ventas += np.random.normal(0, 80)\n    \n    data.append([temperatura, inversion_publicidad, eventos_cercanos, descuento_aplicado, clima, round(ventas, 2)])\n\ncolumns = [\"temperatura_c\", \"inversion_publicidad\", \"evento_local\", \"descuento\", \"clima\", \"ventas_diarias\"]\ndf = pd.DataFrame(data, columns=columns)\ndf.head()\n",[145,40557,40558,40568,40578,40585,40599,40609,40613,40618,40639,40653,40657,40662,40672,40708,40718,40722,40738,40773,40806,40831,40865,40885,40890,40895,40900,40909,40919,40937,40954,40972,40985,40990,40994,41021,41046,41050,41055,41082,41086,41137,41141,41204,41230],{"__ignoreMap":169},[86,40559,40560,40562,40564,40566],{"class":174,"line":175},[86,40561,179],{"class":178},[86,40563,197],{"class":182},[86,40565,186],{"class":178},[86,40567,202],{"class":182},[86,40569,40570,40572,40574,40576],{"class":174,"line":192},[86,40571,179],{"class":178},[86,40573,183],{"class":182},[86,40575,186],{"class":178},[86,40577,189],{"class":182},[86,40579,40580,40582],{"class":174,"line":205},[86,40581,179],{"class":178},[86,40583,40584],{"class":182}," random\n",[86,40586,40587,40589,40591,40593,40595,40597],{"class":174,"line":212},[86,40588,179],{"class":178},[86,40590,33115],{"class":182},[86,40592,61],{"class":219},[86,40594,33120],{"class":182},[86,40596,186],{"class":178},[86,40598,33125],{"class":182},[86,40600,40601,40603,40605,40607],{"class":174,"line":227},[86,40602,179],{"class":178},[86,40604,33132],{"class":182},[86,40606,186],{"class":178},[86,40608,33137],{"class":182},[86,40610,40611],{"class":174,"line":232},[86,40612,209],{"emptyLinePlaceholder":208},[86,40614,40615],{"class":174,"line":252},[86,40616,40617],{"class":1360},"# Semilla para que los datos sean reproducibles\n",[86,40619,40620,40623,40625,40628,40630,40633,40635,40637],{"class":174,"line":276},[86,40621,40622],{"class":182},"np",[86,40624,61],{"class":219},[86,40626,40627],{"class":182},"random",[86,40629,61],{"class":219},[86,40631,40632],{"class":182},"seed",[86,40634,243],{"class":219},[86,40636,1387],{"class":223},[86,40638,273],{"class":219},[86,40640,40641,40643,40645,40647,40649,40651],{"class":174,"line":315},[86,40642,40627],{"class":182},[86,40644,61],{"class":219},[86,40646,40632],{"class":182},[86,40648,243],{"class":219},[86,40650,1387],{"class":223},[86,40652,273],{"class":219},[86,40654,40655],{"class":174,"line":3665},[86,40656,209],{"emptyLinePlaceholder":208},[86,40658,40659],{"class":174,"line":13256},[86,40660,40661],{"class":1360},"# Generación del dataset (365 días operativos)\n",[86,40663,40664,40667,40669],{"class":174,"line":13286},[86,40665,40666],{"class":182},"n ",[86,40668,258],{"class":219},[86,40670,40671],{"class":223}," 365\n",[86,40673,40674,40677,40679,40681,40683,40686,40688,40690,40692,40695,40697,40699,40701,40704,40706],{"class":174,"line":13291},[86,40675,40676],{"class":182},"climas ",[86,40678,258],{"class":219},[86,40680,726],{"class":219},[86,40682,576],{"class":575},[86,40684,40685],{"class":579},"Soleado",[86,40687,576],{"class":575},[86,40689,291],{"class":219},[86,40691,737],{"class":575},[86,40693,40694],{"class":579},"Lluvioso",[86,40696,576],{"class":575},[86,40698,291],{"class":219},[86,40700,737],{"class":575},[86,40702,40703],{"class":579},"Nublado",[86,40705,576],{"class":575},[86,40707,752],{"class":219},[86,40709,40710,40713,40715],{"class":174,"line":13308},[86,40711,40712],{"class":182},"data ",[86,40714,258],{"class":219},[86,40716,40717],{"class":219}," []\n",[86,40719,40720],{"class":174,"line":13334},[86,40721,209],{"emptyLinePlaceholder":208},[86,40723,40724,40726,40728,40730,40732,40734,40736],{"class":174,"line":13359},[86,40725,9680],{"class":178},[86,40727,39771],{"class":182},[86,40729,12015],{"class":178},[86,40731,9689],{"class":812},[86,40733,243],{"class":219},[86,40735,6896],{"class":182},[86,40737,249],{"class":219},[86,40739,40740,40743,40745,40748,40750,40752,40754,40757,40759,40762,40764,40767,40769,40771],{"class":174,"line":13385},[86,40741,40742],{"class":182},"    temperatura ",[86,40744,258],{"class":219},[86,40746,40747],{"class":812}," round",[86,40749,243],{"class":219},[86,40751,40627],{"class":182},[86,40753,61],{"class":219},[86,40755,40756],{"class":182},"uniform",[86,40758,243],{"class":219},[86,40760,40761],{"class":223},"15.0",[86,40763,291],{"class":219},[86,40765,40766],{"class":223}," 35.0",[86,40768,1357],{"class":219},[86,40770,786],{"class":223},[86,40772,273],{"class":219},[86,40774,40775,40778,40780,40782,40784,40786,40788,40790,40792,40795,40797,40800,40802,40804],{"class":174,"line":13390},[86,40776,40777],{"class":182},"    inversion_publicidad ",[86,40779,258],{"class":219},[86,40781,40747],{"class":812},[86,40783,243],{"class":219},[86,40785,40627],{"class":182},[86,40787,61],{"class":219},[86,40789,40756],{"class":182},[86,40791,243],{"class":219},[86,40793,40794],{"class":223},"10.0",[86,40796,291],{"class":219},[86,40798,40799],{"class":223}," 150.0",[86,40801,1357],{"class":219},[86,40803,624],{"class":223},[86,40805,273],{"class":219},[86,40807,40808,40811,40813,40816,40818,40821,40823,40825,40827,40829],{"class":174,"line":13396},[86,40809,40810],{"class":182},"    eventos_cercanos ",[86,40812,258],{"class":219},[86,40814,40815],{"class":182}," random",[86,40817,61],{"class":219},[86,40819,40820],{"class":182},"choice",[86,40822,32924],{"class":219},[86,40824,2553],{"class":223},[86,40826,291],{"class":219},[86,40828,786],{"class":223},[86,40830,1417],{"class":219},[86,40832,40833,40836,40838,40840,40842,40844,40846,40848,40850,40853,40855,40858,40860,40863],{"class":174,"line":3615},[86,40834,40835],{"class":182},"    descuento_aplicado ",[86,40837,258],{"class":219},[86,40839,40815],{"class":182},[86,40841,61],{"class":219},[86,40843,40820],{"class":182},[86,40845,32924],{"class":219},[86,40847,2553],{"class":223},[86,40849,291],{"class":219},[86,40851,40852],{"class":223}," 10",[86,40854,291],{"class":219},[86,40856,40857],{"class":223}," 15",[86,40859,291],{"class":219},[86,40861,40862],{"class":223}," 20",[86,40864,1417],{"class":219},[86,40866,40867,40870,40872,40874,40876,40878,40880,40883],{"class":174,"line":2254},[86,40868,40869],{"class":182},"    clima ",[86,40871,258],{"class":219},[86,40873,40815],{"class":182},[86,40875,61],{"class":219},[86,40877,40820],{"class":182},[86,40879,243],{"class":219},[86,40881,40882],{"class":182},"climas",[86,40884,273],{"class":219},[86,40886,40887],{"class":174,"line":13492},[86,40888,40889],{"class":182},"    \n",[86,40891,40892],{"class":174,"line":13545},[86,40893,40894],{"class":1360},"    # Lógica de negocio (Correlaciones simuladas):\n",[86,40896,40897],{"class":174,"line":13550},[86,40898,40899],{"class":1360},"    # La temperatura baja y los eventos suben ventas. El clima lluvioso invita a tomar café.\n",[86,40901,40902,40905,40907],{"class":174,"line":13566},[86,40903,40904],{"class":182},"    ventas ",[86,40906,258],{"class":219},[86,40908,37420],{"class":219},[86,40910,40911,40914,40916],{"class":174,"line":13591},[86,40912,40913],{"class":223},"        500",[86,40915,34975],{"class":235},[86,40917,40918],{"class":182}," \n",[86,40920,40921,40923,40926,40928,40931,40933,40935],{"class":174,"line":13616},[86,40922,34963],{"class":219},[86,40924,40925],{"class":182},"inversion_publicidad ",[86,40927,34946],{"class":235},[86,40929,40930],{"class":223}," 2.5",[86,40932,867],{"class":219},[86,40934,13421],{"class":235},[86,40936,40918],{"class":182},[86,40938,40939,40941,40944,40946,40948,40950,40952],{"class":174,"line":13641},[86,40940,34963],{"class":219},[86,40942,40943],{"class":182},"temperatura ",[86,40945,34946],{"class":235},[86,40947,33199],{"class":223},[86,40949,867],{"class":219},[86,40951,34975],{"class":235},[86,40953,40918],{"class":182},[86,40955,40956,40958,40961,40963,40966,40968,40970],{"class":174,"line":37784},[86,40957,34963],{"class":219},[86,40959,40960],{"class":182},"eventos_cercanos ",[86,40962,34946],{"class":235},[86,40964,40965],{"class":223}," 250",[86,40967,867],{"class":219},[86,40969,34975],{"class":235},[86,40971,40918],{"class":182},[86,40973,40974,40976,40979,40981,40983],{"class":174,"line":37795},[86,40975,34963],{"class":219},[86,40977,40978],{"class":182},"descuento_aplicado ",[86,40980,34946],{"class":235},[86,40982,34717],{"class":223},[86,40984,273],{"class":219},[86,40986,40987],{"class":174,"line":37807},[86,40988,40989],{"class":219},"    )\n",[86,40991,40992],{"class":174,"line":37822},[86,40993,40889],{"class":182},[86,40995,40996,40999,41002,41004,41006,41008,41010,41012,41015,41018],{"class":174,"line":37837},[86,40997,40998],{"class":178},"    if",[86,41000,41001],{"class":182}," clima ",[86,41003,9718],{"class":235},[86,41005,737],{"class":575},[86,41007,40694],{"class":579},[86,41009,576],{"class":575},[86,41011,162],{"class":219},[86,41013,41014],{"class":182}," ventas ",[86,41016,41017],{"class":219},"+=",[86,41019,41020],{"class":223}," 150\n",[86,41022,41023,41026,41028,41030,41032,41034,41036,41038,41040,41043],{"class":174,"line":37852},[86,41024,41025],{"class":178},"    elif",[86,41027,41001],{"class":182},[86,41029,9718],{"class":235},[86,41031,737],{"class":575},[86,41033,40685],{"class":579},[86,41035,576],{"class":575},[86,41037,162],{"class":219},[86,41039,41014],{"class":182},[86,41041,41042],{"class":219},"-=",[86,41044,41045],{"class":223}," 50\n",[86,41047,41048],{"class":174,"line":37867},[86,41049,40889],{"class":182},[86,41051,41052],{"class":174,"line":37882},[86,41053,41054],{"class":1360},"    # Añadimos ruido estadístico para hacerlo realista\n",[86,41056,41057,41059,41061,41063,41065,41067,41069,41071,41073,41075,41077,41080],{"class":174,"line":37887},[86,41058,40904],{"class":182},[86,41060,41017],{"class":219},[86,41062,294],{"class":182},[86,41064,61],{"class":219},[86,41066,40627],{"class":182},[86,41068,61],{"class":219},[86,41070,4327],{"class":182},[86,41072,243],{"class":219},[86,41074,2553],{"class":223},[86,41076,291],{"class":219},[86,41078,41079],{"class":223}," 80",[86,41081,273],{"class":219},[86,41083,41084],{"class":174,"line":37911},[86,41085,40889],{"class":182},[86,41087,41088,41091,41093,41096,41098,41101,41103,41106,41108,41111,41113,41116,41118,41121,41123,41125,41127,41130,41132,41134],{"class":174,"line":37934},[86,41089,41090],{"class":182},"    data",[86,41092,61],{"class":219},[86,41094,41095],{"class":182},"append",[86,41097,32924],{"class":219},[86,41099,41100],{"class":182},"temperatura",[86,41102,291],{"class":219},[86,41104,41105],{"class":182}," inversion_publicidad",[86,41107,291],{"class":219},[86,41109,41110],{"class":182}," eventos_cercanos",[86,41112,291],{"class":219},[86,41114,41115],{"class":182}," descuento_aplicado",[86,41117,291],{"class":219},[86,41119,41120],{"class":182}," clima",[86,41122,291],{"class":219},[86,41124,40747],{"class":812},[86,41126,243],{"class":219},[86,41128,41129],{"class":182},"ventas",[86,41131,291],{"class":219},[86,41133,624],{"class":223},[86,41135,41136],{"class":219},")])\n",[86,41138,41139],{"class":174,"line":37957},[86,41140,209],{"emptyLinePlaceholder":208},[86,41142,41143,41146,41148,41150,41152,41155,41157,41159,41161,41164,41166,41168,41170,41173,41175,41177,41179,41182,41184,41186,41188,41191,41193,41195,41197,41200,41202],{"class":174,"line":37980},[86,41144,41145],{"class":182},"columns ",[86,41147,258],{"class":219},[86,41149,726],{"class":219},[86,41151,576],{"class":575},[86,41153,41154],{"class":579},"temperatura_c",[86,41156,576],{"class":575},[86,41158,291],{"class":219},[86,41160,737],{"class":575},[86,41162,41163],{"class":579},"inversion_publicidad",[86,41165,576],{"class":575},[86,41167,291],{"class":219},[86,41169,737],{"class":575},[86,41171,41172],{"class":579},"evento_local",[86,41174,576],{"class":575},[86,41176,291],{"class":219},[86,41178,737],{"class":575},[86,41180,41181],{"class":579},"descuento",[86,41183,576],{"class":575},[86,41185,291],{"class":219},[86,41187,737],{"class":575},[86,41189,41190],{"class":579},"clima",[86,41192,576],{"class":575},[86,41194,291],{"class":219},[86,41196,737],{"class":575},[86,41198,41199],{"class":579},"ventas_diarias",[86,41201,576],{"class":575},[86,41203,752],{"class":219},[86,41205,41206,41208,41210,41212,41214,41216,41218,41220,41222,41224,41226,41228],{"class":174,"line":38008},[86,41207,13168],{"class":182},[86,41209,258],{"class":219},[86,41211,261],{"class":182},[86,41213,61],{"class":219},[86,41215,13177],{"class":182},[86,41217,243],{"class":219},[86,41219,11013],{"class":182},[86,41221,291],{"class":219},[86,41223,34015],{"class":304},[86,41225,258],{"class":219},[86,41227,33809],{"class":182},[86,41229,273],{"class":219},[86,41231,41232,41234,41236,41238],{"class":174,"line":38013},[86,41233,569],{"class":182},[86,41235,61],{"class":219},[86,41237,33285],{"class":182},[86,41239,11991],{"class":219},[323,41241,41243],{"id":41242},"paso-2-conociendo-la-data-exploración-inicial","Paso 2: Conociendo la Data (Exploración Inicial)",[12,41245,41246,41247,41250,41251,41254],{},"Con ",[145,41248,41249],{},"df.info()"," comprobamos que no haya datos faltantes (nulos) y los tipos de dato, mientras que ",[145,41252,41253],{},"df.describe()"," nos resume la media, los máximos y mínimos diarios de ventas y gastos.",[164,41256,41258],{"className":166,"code":41257,"language":168,"meta":169,"style":169},"# Un vistazo rápido a la salud de nuestra tabla\nprint(df.info())\n\n# Estadísticas descriptivas (promedios, cuartiles, mín\u002Fmáx)\nprint(df.describe())\n",[145,41259,41260,41265,41280,41284,41289],{"__ignoreMap":169},[86,41261,41262],{"class":174,"line":175},[86,41263,41264],{"class":1360},"# Un vistazo rápido a la salud de nuestra tabla\n",[86,41266,41267,41269,41271,41273,41275,41278],{"class":174,"line":192},[86,41268,13294],{"class":812},[86,41270,243],{"class":219},[86,41272,569],{"class":182},[86,41274,61],{"class":219},[86,41276,41277],{"class":182},"info",[86,41279,33288],{"class":219},[86,41281,41282],{"class":174,"line":205},[86,41283,209],{"emptyLinePlaceholder":208},[86,41285,41286],{"class":174,"line":212},[86,41287,41288],{"class":1360},"# Estadísticas descriptivas (promedios, cuartiles, mín\u002Fmáx)\n",[86,41290,41291,41293,41295,41297,41299,41301],{"class":174,"line":227},[86,41292,13294],{"class":812},[86,41294,243],{"class":219},[86,41296,569],{"class":182},[86,41298,61],{"class":219},[86,41300,34290],{"class":182},[86,41302,33288],{"class":219},[12,41304,41305],{},"Dando como resultado lo siguiente:",[164,41307,41311],{"className":41308,"code":41309,"language":41310,"meta":169,"style":169},"language-sh shiki shiki-themes vitesse-light vitesse-dark","\u003Cclass 'pandas.core.frame.DataFrame'>\nRangeIndex: 365 entries, 0 to 364\nData columns (total 6 columns):\n #   Column         Non-Null Count  Dtype  \n---  ------         --------------  -----  \n 0   temperature_c  365 non-null    float64\n 1   ad_investment  365 non-null    float64\n 2   local_event    365 non-null    int64  \n 3   discount       365 non-null    int64  \n 4   weather        365 non-null    object \n 5   daily_sales    365 non-null    float64\ndtypes: float64(3), int64(2), object(1)\nmemory usage: 17.2+ KB\nNone\n       temperature_c  ad_investment  local_event    discount  daily_sales\ncount     365.000000     365.000000   365.000000  365.000000   365.000000\nmean       24.648767      82.490247     0.561644   11.684932   735.927151\nstd         5.687482      40.828333     0.496867    7.270059   204.863687\nmin        15.100000      10.060000     0.000000    0.000000   226.620000\n25%        19.800000      48.400000     0.000000   10.000000   576.890000\n50%        24.500000      84.780000     1.000000   15.000000   729.730000\n75%        29.600000     120.280000     1.000000   20.000000   879.280000\nmax        35.000000     149.780000     1.000000   20.000000  1337.220000\n","sh",[145,41312,41313,41331,41350,41366,41371,41388,41404,41417,41434,41450,41467,41480,41516,41530,41535,41552,41570,41589,41608,41627,41645,41664,41682],{"__ignoreMap":169},[86,41314,41315,41318,41321,41323,41326,41328],{"class":174,"line":175},[86,41316,41317],{"class":235},"\u003C",[86,41319,41320],{"class":182},"class ",[86,41322,10971],{"class":575},[86,41324,41325],{"class":579},"pandas.core.frame.DataFrame",[86,41327,10971],{"class":575},[86,41329,41330],{"class":235},">\n",[86,41332,41333,41336,41339,41342,41344,41347],{"class":174,"line":192},[86,41334,41335],{"class":239},"RangeIndex:",[86,41337,41338],{"class":223}," 365",[86,41340,41341],{"class":579}," entries,",[86,41343,33979],{"class":223},[86,41345,41346],{"class":579}," to",[86,41348,41349],{"class":223}," 364\n",[86,41351,41352,41355,41357,41360,41362,41364],{"class":174,"line":205},[86,41353,41354],{"class":239},"Data",[86,41356,34015],{"class":579},[86,41358,41359],{"class":182}," (total ",[86,41361,4114],{"class":223},[86,41363,34015],{"class":579},[86,41365,249],{"class":182},[86,41367,41368],{"class":174,"line":212},[86,41369,41370],{"class":1360}," #   Column         Non-Null Count  Dtype  \n",[86,41372,41373,41376,41379,41382,41385],{"class":174,"line":227},[86,41374,41375],{"class":239},"---",[86,41377,41378],{"class":215},"  ------",[86,41380,41381],{"class":215},"         --------------",[86,41383,41384],{"class":215},"  -----",[86,41386,41387],{"class":182},"  \n",[86,41389,41390,41392,41395,41398,41401],{"class":174,"line":232},[86,41391,33979],{"class":239},[86,41393,41394],{"class":579},"   temperature_c",[86,41396,41397],{"class":223},"  365",[86,41399,41400],{"class":579}," non-null",[86,41402,41403],{"class":579},"    float64\n",[86,41405,41406,41408,41411,41413,41415],{"class":174,"line":252},[86,41407,786],{"class":239},[86,41409,41410],{"class":579},"   ad_investment",[86,41412,41397],{"class":223},[86,41414,41400],{"class":579},[86,41416,41403],{"class":579},[86,41418,41419,41421,41424,41427,41429,41432],{"class":174,"line":276},[86,41420,624],{"class":239},[86,41422,41423],{"class":579},"   local_event",[86,41425,41426],{"class":223},"    365",[86,41428,41400],{"class":579},[86,41430,41431],{"class":579},"    int64",[86,41433,41387],{"class":182},[86,41435,41436,41438,41441,41444,41446,41448],{"class":174,"line":315},[86,41437,37386],{"class":239},[86,41439,41440],{"class":579},"   discount",[86,41442,41443],{"class":223},"       365",[86,41445,41400],{"class":579},[86,41447,41431],{"class":579},[86,41449,41387],{"class":182},[86,41451,41452,41454,41457,41460,41462,41465],{"class":174,"line":3665},[86,41453,35045],{"class":239},[86,41455,41456],{"class":579},"   weather",[86,41458,41459],{"class":223},"        365",[86,41461,41400],{"class":579},[86,41463,41464],{"class":579},"    object",[86,41466,40918],{"class":182},[86,41468,41469,41471,41474,41476,41478],{"class":174,"line":13256},[86,41470,34717],{"class":239},[86,41472,41473],{"class":579},"   daily_sales",[86,41475,41426],{"class":223},[86,41477,41400],{"class":579},[86,41479,41403],{"class":579},[86,41481,41482,41485,41488,41490,41492,41494,41496,41499,41501,41503,41505,41507,41510,41512,41514],{"class":174,"line":13286},[86,41483,41484],{"class":239},"dtypes:",[86,41486,41487],{"class":579}," float64",[86,41489,243],{"class":219},[86,41491,4100],{"class":239},[86,41493,867],{"class":219},[86,41495,291],{"class":579},[86,41497,41498],{"class":579}," int64",[86,41500,243],{"class":219},[86,41502,980],{"class":239},[86,41504,867],{"class":219},[86,41506,291],{"class":579},[86,41508,41509],{"class":579}," object",[86,41511,243],{"class":219},[86,41513,802],{"class":239},[86,41515,273],{"class":219},[86,41517,41518,41521,41524,41527],{"class":174,"line":13291},[86,41519,41520],{"class":239},"memory",[86,41522,41523],{"class":579}," usage:",[86,41525,41526],{"class":579}," 17.2+",[86,41528,41529],{"class":579}," KB\n",[86,41531,41532],{"class":174,"line":13308},[86,41533,41534],{"class":239},"None\n",[86,41536,41537,41540,41543,41546,41549],{"class":174,"line":13334},[86,41538,41539],{"class":239},"       temperature_c",[86,41541,41542],{"class":579},"  ad_investment",[86,41544,41545],{"class":579},"  local_event",[86,41547,41548],{"class":579},"    discount",[86,41550,41551],{"class":579},"  daily_sales\n",[86,41553,41554,41556,41559,41561,41564,41567],{"class":174,"line":13359},[86,41555,34445],{"class":239},[86,41557,41558],{"class":223},"     365.000000",[86,41560,41558],{"class":223},[86,41562,41563],{"class":223},"   365.000000",[86,41565,41566],{"class":223},"  365.000000",[86,41568,41569],{"class":223},"   365.000000\n",[86,41571,41572,41574,41577,41580,41583,41586],{"class":174,"line":13385},[86,41573,13227],{"class":239},[86,41575,41576],{"class":223},"       24.648767",[86,41578,41579],{"class":223},"      82.490247",[86,41581,41582],{"class":223},"     0.561644",[86,41584,41585],{"class":223},"   11.684932",[86,41587,41588],{"class":223},"   735.927151\n",[86,41590,41591,41593,41596,41599,41602,41605],{"class":174,"line":13390},[86,41592,13487],{"class":239},[86,41594,41595],{"class":223},"         5.687482",[86,41597,41598],{"class":223},"      40.828333",[86,41600,41601],{"class":223},"     0.496867",[86,41603,41604],{"class":223},"    7.270059",[86,41606,41607],{"class":223},"   204.863687\n",[86,41609,41610,41612,41615,41618,41621,41624],{"class":174,"line":13396},[86,41611,13436],{"class":239},[86,41613,41614],{"class":223},"        15.100000",[86,41616,41617],{"class":223},"      10.060000",[86,41619,41620],{"class":223},"     0.000000",[86,41622,41623],{"class":223},"    0.000000",[86,41625,41626],{"class":223},"   226.620000\n",[86,41628,41629,41631,41634,41637,41639,41642],{"class":174,"line":3615},[86,41630,34454],{"class":239},[86,41632,41633],{"class":223},"        19.800000",[86,41635,41636],{"class":223},"      48.400000",[86,41638,41620],{"class":223},[86,41640,41641],{"class":223},"   10.000000",[86,41643,41644],{"class":223},"   576.890000\n",[86,41646,41647,41649,41652,41655,41658,41661],{"class":174,"line":2254},[86,41648,34457],{"class":239},[86,41650,41651],{"class":223},"        24.500000",[86,41653,41654],{"class":223},"      84.780000",[86,41656,41657],{"class":223},"     1.000000",[86,41659,41660],{"class":223},"   15.000000",[86,41662,41663],{"class":223},"   729.730000\n",[86,41665,41666,41668,41671,41674,41676,41679],{"class":174,"line":13492},[86,41667,34460],{"class":239},[86,41669,41670],{"class":223},"        29.600000",[86,41672,41673],{"class":223},"     120.280000",[86,41675,41657],{"class":223},[86,41677,41678],{"class":223},"   20.000000",[86,41680,41681],{"class":223},"   879.280000\n",[86,41683,41684,41686,41689,41692,41694,41696],{"class":174,"line":13545},[86,41685,7260],{"class":239},[86,41687,41688],{"class":223},"        35.000000",[86,41690,41691],{"class":223},"     149.780000",[86,41693,41657],{"class":223},[86,41695,41678],{"class":223},[86,41697,41698],{"class":223},"  1337.220000\n",[12,41700,41701],{},"Exploremos un poco los resultados:",[30,41703,41704,41707,41717,41720,41723],{},[33,41705,41706],{},"La temperatura promedio es de 24.65°C, con un rango entre 15.1°C y 35°C.",[33,41708,41709,41710,41713,41714,61],{},"La inversión en publicidad varía ampliamente, con un promedio de ",[145,41711,41712],{},"$82.49"," y un máximo de ",[145,41715,41716],{},"$149.78",[33,41718,41719],{},"El 56.16% de los días tuvieron un evento local.",[33,41721,41722],{},"El descuento aplicado varía, con un promedio de 11.68% y un máximo de 20%.",[33,41724,41725,41726,41729,41730,41733,41734,61],{},"Las ventas diarias tienen un promedio de ",[145,41727,41728],{},"$735.93",", con una amplia variabilidad, desde un mínimo de ",[145,41731,41732],{},"$226.62"," hasta un máximo de ",[145,41735,41736],{},"$1337.22",[12,41738,41739],{},"Además, no hay valores nulos en el dataset, lo que es una buena señal para el análisis posterior.\nLa amplia variabilidad en las ventas diarias sugiere que hay factores significativos que afectan las ventas, lo que hace que el análisis exploratorio de datos sea aún más crucial para entender estas relaciones.",[323,41741,41743],{"id":41742},"paso-3-visualización-estratégica","Paso 3: Visualización Estratégica",[12,41745,41746],{},"La mejor forma de entender nuestros datos es a través de la visualización. Vamos a construir tres gráficos clave para nuestro análisis:",[117,41748,41749,41755,41761],{},[33,41750,41751,41754],{},[122,41752,41753],{},"Histograma de Ventas:"," Nos dice si nuestras ganancias diarias siguen una curva normal (Campana de Gauss) o si están sesgadas.",[33,41756,41757,41760],{},[122,41758,41759],{},"Dispersión (Scatter) Publicidad vs. Ventas:"," Revela si meter más dinero a los Ads realmente sube las ventas o si llega a un tope (rendimiento decreciente).",[33,41762,41763,41766],{},[122,41764,41765],{},"Matriz de Correlación:"," Es el \"santo grial\" del EDA. Asignará un valor de -1 a 1 a la relación entre todas nuestras variables.",[164,41768,41770],{"className":166,"code":41769,"language":168,"meta":169,"style":169},"# 1. Distribución de las ventas (¿vendemos más en días \"buenos\" o \"malos\" estadísticamente?)\nplt.figure(figsize=(8,5))\nsns.histplot(df[\"ventas_diarias\"], bins=20, kde=True, color=\"brown\")\nplt.title(\"Distribución de las Ventas Diarias de Café\")\nplt.xlabel(\"Ventas en $\")\nplt.ylabel(\"Frecuencia (Días)\")\nplt.show()\n\n# 2. El impacto de los Ads\nplt.figure(figsize=(8,5))\nsns.scatterplot(x=\"inversion_publicidad\", y=\"ventas_diarias\", hue=\"clima\", data=df)\nplt.title(\"Inversión en Publicidad vs. Ventas (Coloreado por Clima)\")\nplt.xlabel(\"Inversión ($)\")\nplt.ylabel(\"Ventas ($)\")\nplt.show()\n\n# 3. El mapa de calor (Heatmap)\nplt.figure(figsize=(8,6))\nsns.heatmap(df.corr(numeric_only=True), annot=True, cmap=\"YlOrBr\", fmt=\".2f\")\nplt.title(\"Correlación de Variables\")\nplt.show()\n",[145,41771,41772,41777,41799,41851,41870,41889,41908,41918,41922,41927,41949,42005,42024,42043,42062,42072,42076,42081,42103,42162,42181],{"__ignoreMap":169},[86,41773,41774],{"class":174,"line":175},[86,41775,41776],{"class":1360},"# 1. Distribución de las ventas (¿vendemos más en días \"buenos\" o \"malos\" estadísticamente?)\n",[86,41778,41779,41781,41783,41785,41787,41789,41791,41793,41795,41797],{"class":174,"line":192},[86,41780,33172],{"class":182},[86,41782,61],{"class":219},[86,41784,34701],{"class":182},[86,41786,243],{"class":219},[86,41788,34706],{"class":304},[86,41790,34709],{"class":219},[86,41792,34578],{"class":223},[86,41794,291],{"class":219},[86,41796,1108],{"class":223},[86,41798,33401],{"class":219},[86,41800,41801,41803,41805,41807,41809,41811,41813,41815,41817,41819,41821,41823,41825,41828,41830,41832,41834,41836,41838,41840,41842,41844,41847,41849],{"class":174,"line":205},[86,41802,33151],{"class":182},[86,41804,61],{"class":219},[86,41806,36779],{"class":182},[86,41808,243],{"class":219},[86,41810,569],{"class":182},[86,41812,572],{"class":219},[86,41814,576],{"class":575},[86,41816,41199],{"class":579},[86,41818,576],{"class":575},[86,41820,9750],{"class":219},[86,41822,36585],{"class":304},[86,41824,258],{"class":219},[86,41826,41827],{"class":223},"20",[86,41829,291],{"class":219},[86,41831,36796],{"class":304},[86,41833,258],{"class":219},[86,41835,310],{"class":178},[86,41837,291],{"class":219},[86,41839,36817],{"class":304},[86,41841,258],{"class":219},[86,41843,576],{"class":575},[86,41845,41846],{"class":579},"brown",[86,41848,576],{"class":575},[86,41850,273],{"class":219},[86,41852,41853,41855,41857,41859,41861,41863,41866,41868],{"class":174,"line":212},[86,41854,33172],{"class":182},[86,41856,61],{"class":219},[86,41858,34801],{"class":182},[86,41860,243],{"class":219},[86,41862,576],{"class":575},[86,41864,41865],{"class":579},"Distribución de las Ventas Diarias de Café",[86,41867,576],{"class":575},[86,41869,273],{"class":219},[86,41871,41872,41874,41876,41878,41880,41882,41885,41887],{"class":174,"line":227},[86,41873,33172],{"class":182},[86,41875,61],{"class":219},[86,41877,34821],{"class":182},[86,41879,243],{"class":219},[86,41881,576],{"class":575},[86,41883,41884],{"class":579},"Ventas en $",[86,41886,576],{"class":575},[86,41888,273],{"class":219},[86,41890,41891,41893,41895,41897,41899,41901,41904,41906],{"class":174,"line":232},[86,41892,33172],{"class":182},[86,41894,61],{"class":219},[86,41896,34841],{"class":182},[86,41898,243],{"class":219},[86,41900,576],{"class":575},[86,41902,41903],{"class":579},"Frecuencia (Días)",[86,41905,576],{"class":575},[86,41907,273],{"class":219},[86,41909,41910,41912,41914,41916],{"class":174,"line":252},[86,41911,33172],{"class":182},[86,41913,61],{"class":219},[86,41915,35087],{"class":182},[86,41917,11991],{"class":219},[86,41919,41920],{"class":174,"line":276},[86,41921,209],{"emptyLinePlaceholder":208},[86,41923,41924],{"class":174,"line":315},[86,41925,41926],{"class":1360},"# 2. El impacto de los Ads\n",[86,41928,41929,41931,41933,41935,41937,41939,41941,41943,41945,41947],{"class":174,"line":3665},[86,41930,33172],{"class":182},[86,41932,61],{"class":219},[86,41934,34701],{"class":182},[86,41936,243],{"class":219},[86,41938,34706],{"class":304},[86,41940,34709],{"class":219},[86,41942,34578],{"class":223},[86,41944,291],{"class":219},[86,41946,1108],{"class":223},[86,41948,33401],{"class":219},[86,41950,41951,41953,41955,41958,41960,41962,41964,41966,41968,41970,41972,41974,41976,41978,41980,41982,41984,41986,41988,41990,41992,41994,41996,41999,42001,42003],{"class":174,"line":13256},[86,41952,33151],{"class":182},[86,41954,61],{"class":219},[86,41956,41957],{"class":182},"scatterplot",[86,41959,243],{"class":219},[86,41961,3189],{"class":304},[86,41963,258],{"class":219},[86,41965,576],{"class":575},[86,41967,41163],{"class":579},[86,41969,576],{"class":575},[86,41971,291],{"class":219},[86,41973,1098],{"class":304},[86,41975,258],{"class":219},[86,41977,576],{"class":575},[86,41979,41199],{"class":579},[86,41981,576],{"class":575},[86,41983,291],{"class":219},[86,41985,34773],{"class":304},[86,41987,258],{"class":219},[86,41989,576],{"class":575},[86,41991,41190],{"class":579},[86,41993,576],{"class":575},[86,41995,291],{"class":219},[86,41997,41998],{"class":304}," data",[86,42000,258],{"class":219},[86,42002,569],{"class":182},[86,42004,273],{"class":219},[86,42006,42007,42009,42011,42013,42015,42017,42020,42022],{"class":174,"line":13286},[86,42008,33172],{"class":182},[86,42010,61],{"class":219},[86,42012,34801],{"class":182},[86,42014,243],{"class":219},[86,42016,576],{"class":575},[86,42018,42019],{"class":579},"Inversión en Publicidad vs. Ventas (Coloreado por Clima)",[86,42021,576],{"class":575},[86,42023,273],{"class":219},[86,42025,42026,42028,42030,42032,42034,42036,42039,42041],{"class":174,"line":13291},[86,42027,33172],{"class":182},[86,42029,61],{"class":219},[86,42031,34821],{"class":182},[86,42033,243],{"class":219},[86,42035,576],{"class":575},[86,42037,42038],{"class":579},"Inversión ($)",[86,42040,576],{"class":575},[86,42042,273],{"class":219},[86,42044,42045,42047,42049,42051,42053,42055,42058,42060],{"class":174,"line":13308},[86,42046,33172],{"class":182},[86,42048,61],{"class":219},[86,42050,34841],{"class":182},[86,42052,243],{"class":219},[86,42054,576],{"class":575},[86,42056,42057],{"class":579},"Ventas ($)",[86,42059,576],{"class":575},[86,42061,273],{"class":219},[86,42063,42064,42066,42068,42070],{"class":174,"line":13334},[86,42065,33172],{"class":182},[86,42067,61],{"class":219},[86,42069,35087],{"class":182},[86,42071,11991],{"class":219},[86,42073,42074],{"class":174,"line":13359},[86,42075,209],{"emptyLinePlaceholder":208},[86,42077,42078],{"class":174,"line":13385},[86,42079,42080],{"class":1360},"# 3. El mapa de calor (Heatmap)\n",[86,42082,42083,42085,42087,42089,42091,42093,42095,42097,42099,42101],{"class":174,"line":13390},[86,42084,33172],{"class":182},[86,42086,61],{"class":219},[86,42088,34701],{"class":182},[86,42090,243],{"class":219},[86,42092,34706],{"class":304},[86,42094,34709],{"class":219},[86,42096,34578],{"class":223},[86,42098,291],{"class":219},[86,42100,4114],{"class":223},[86,42102,33401],{"class":219},[86,42104,42105,42107,42109,42111,42113,42115,42117,42119,42121,42123,42125,42127,42129,42131,42133,42135,42137,42139,42141,42143,42146,42148,42150,42152,42154,42156,42158,42160],{"class":174,"line":13396},[86,42106,33151],{"class":182},[86,42108,61],{"class":219},[86,42110,35581],{"class":182},[86,42112,243],{"class":219},[86,42114,569],{"class":182},[86,42116,61],{"class":219},[86,42118,35539],{"class":182},[86,42120,243],{"class":219},[86,42122,35544],{"class":304},[86,42124,258],{"class":219},[86,42126,310],{"class":178},[86,42128,1357],{"class":219},[86,42130,35590],{"class":304},[86,42132,258],{"class":219},[86,42134,310],{"class":178},[86,42136,291],{"class":219},[86,42138,35613],{"class":304},[86,42140,258],{"class":219},[86,42142,576],{"class":575},[86,42144,42145],{"class":579},"YlOrBr",[86,42147,576],{"class":575},[86,42149,291],{"class":219},[86,42151,35599],{"class":304},[86,42153,258],{"class":219},[86,42155,576],{"class":575},[86,42157,35606],{"class":579},[86,42159,576],{"class":575},[86,42161,273],{"class":219},[86,42163,42164,42166,42168,42170,42172,42174,42177,42179],{"class":174,"line":3615},[86,42165,33172],{"class":182},[86,42167,61],{"class":219},[86,42169,34801],{"class":182},[86,42171,243],{"class":219},[86,42173,576],{"class":575},[86,42175,42176],{"class":579},"Correlación de Variables",[86,42178,576],{"class":575},[86,42180,273],{"class":219},[86,42182,42183,42185,42187,42189],{"class":174,"line":2254},[86,42184,33172],{"class":182},[86,42186,61],{"class":219},[86,42188,35087],{"class":182},[86,42190,11991],{"class":219},[12,42192,42193,42197],{},[1945,42194],{"alt":42195,"src":42196},"Distribución de ventas diarias","\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis\u002Fshared\u002Fsales_distribution.webp",[901,42198,42199],{},"Histograma de Ventas",[12,42201,42202,42203,42206,42207,42210,42211,42214],{},"Comencemos con el ",[122,42204,42205],{},"histograma",", que nos permite visualizar cómo se distribuyen las ventas diarias a lo largo del tiempo. En este caso, observamos que las ventas siguen una ",[122,42208,42209],{},"distribución aproximadamente normal",", con una media cercana a ",[145,42212,42213],{},"$800",". Esto significa que la mayoría de los días las ventas se concentran alrededor de ese valor promedio, y que los días con ventas muy bajas o muy altas son menos frecuentes y se distribuyen de manera relativamente simétrica a ambos lados.",[30,42216,42217],{},[33,42218,42219],{},"¿Por qué es importante identificar una distribución normal?",[12,42221,42222,42223,42226],{},"Porque muchos modelos estadísticos y de machine learning, como la ",[122,42224,42225],{},"regresión lineal",", el análisis de varianza o ciertos modelos probabilísticos, funcionan mejor cuando los datos (o al menos los errores del modelo) siguen una distribución normal.",[12,42228,42229],{},"Cuando esta condición se cumple:",[30,42231,42232,42235,42238],{},[33,42233,42234],{},"Las estimaciones tienden a ser más estables.",[33,42236,42237],{},"Los intervalos de confianza y pruebas estadísticas son más confiables.",[33,42239,42240],{},"El modelo no se ve excesivamente afectado por valores extremos.",[12,42242,42243,42244,42246],{},"Si los datos ",[122,42245,33505],{}," siguen una distribución normal, puede ser necesario aplicar transformaciones matemáticas (como logaritmo, raíz cuadrada o Box-Cox) para estabilizar la varianza y reducir la asimetría.",[30,42248,42249],{},[33,42250,42251],{},"¿Qué significa \"sesgo a la derecha\" o \"sesgo a la izquierda\"?",[30,42253,42254,42260],{},[33,42255,42256,42259],{},[122,42257,42258],{},"Sesgo a la derecha (asimetría positiva):"," Hay una cola larga hacia valores altos. Esto indica que existen pocos días con ventas extremadamente altas.",[33,42261,42262,42265],{},[122,42263,42264],{},"Sesgo a la izquierda (asimetría negativa):"," Hay una cola larga hacia valores bajos. Esto indica que existen pocos días con ventas inusualmente bajas.",[12,42267,42268],{},"La asimetría es importante porque los modelos sensibles a valores extremos pueden verse distorsionados.",[12,42270,42271,42272,392,42275,42278,42279,61],{},"Supongamos que la mayoría de los días las ventas están entre ",[145,42273,42274],{},"$700",[145,42276,42277],{},"$900",", pero en tres días especiales (por ejemplo, promociones o feriados) las ventas alcanzan ",[145,42280,13687],{},[12,42282,42283],{},"Si entrenamos una regresión lineal directamente con esos datos:",[30,42285,42286,42289,42292],{},[33,42287,42288],{},"El modelo intentará ajustar una línea que también explique esos picos.",[33,42290,42291],{},"Esto puede desplazar la pendiente o el intercepto.",[33,42293,42294],{},"Como resultado, las predicciones para los días “normales” (que son la mayoría) podrían quedar ligeramente infladas.",[12,42296,42297],{},"En cambio, si aplicamos una transformación logarítmica antes de entrenar el modelo:",[30,42299,42300,42303,42306],{},[33,42301,42302],{},"Se reduce el impacto de los valores extremadamente altos.",[33,42304,42305],{},"La distribución se vuelve más simétrica.",[33,42307,42308],{},"El modelo aprende un patrón más representativo del comportamiento general.",[12,42310,42311,42315],{},[1945,42312],{"alt":42313,"src":42314},"Publicidad vs Ventas","\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis\u002Fshared\u002Fads_vs_sales.webp",[901,42316,42317],{},"Dispersión entre Inversión en Publicidad y Ventas",[12,42319,42320],{},"Los puntos según el clima son de diferentes colores: Azul-Soleado, Naranja-Nublado, Verde-Lluvioso",[30,42322,42323],{},[33,42324,42325],{},[122,42326,42327],{},"Relación principal: inversión vs. ventas",[12,42329,42330,42331,42334],{},"Lo primero que se observa es una ",[122,42332,42333],{},"tendencia positiva",":\nA medida que aumenta la inversión en publicidad, las ventas tienden a aumentar.",[12,42336,42337,42338,42341],{},"Esto indica una ",[122,42339,42340],{},"correlación positiva"," entre ambas variables. No parece una relación completamente aleatoria; los puntos muestran una pendiente ascendente general.",[12,42343,42344,42345,42348],{},"En términos de machine learning, esto sugiere que la inversión publicitaria es ",[122,42346,42347],{},"una"," variable predictora relevante para estimar ventas (no la única).",[30,42350,42351],{},[33,42352,42353],{},[122,42354,42355],{},"Variabilidad en las ventas",[12,42357,42358],{},"Aunque la tendencia es positiva, los puntos están bastante dispersos verticalmente.",[12,42360,3135],{},[12,42362,42363,42364,42367,42368,392,42371,42374],{},"Con una inversión de ",[145,42365,42366],{},"$100",", las ventas pueden variar entre aproximadamente ",[145,42369,42370],{},"$400",[145,42372,42373],{},"$1,100"," dependiendo de otros factores.",[12,42376,42377],{},"Esto nos dice algo muy importante:",[16,42379,42380],{},[12,42381,42382],{},"La inversión no explica el 100% del comportamiento de las ventas.",[12,42384,42385],{},"Existen otras variables influyendo (en este caso, sabemos que el clima es una de ellas).",[30,42387,42388],{},[33,42389,42390],{},[122,42391,42392],{},"Impacto del clima",[12,42394,42395],{},"Aquí es donde el gráfico se vuelve más interesante.",[12,42397,42398],{},"Observando los colores:",[30,42400,42401,42404,42407],{},[33,42402,42403],{},"Los puntos verdes (lluvioso) tienden a ubicarse en valores de ventas más altos.",[33,42405,42406],{},"Los puntos azules (soleado) tienden a concentrarse en valores más bajos para el mismo nivel de inversión.",[33,42408,42409],{},"Los naranjas (nublado) están en un punto intermedio.",[12,42411,42412,42413,61],{},"Esto sugiere que el clima actúa como una ",[122,42414,42415],{},"variable moderadora",[12,42417,42418,42419,162],{},"Por ejemplo:\nCon una inversión de ",[145,42420,42421],{},"$120",[30,42423,42424,42430],{},[33,42425,42426,42427],{},"Día soleado → ventas alrededor de ",[145,42428,42429],{},"$500–900",[33,42431,42432,42433],{},"Día lluvioso → ventas alrededor de ",[145,42434,42435],{},"$700–1,200",[12,42437,42438],{},"En un modelo de regresión simple que solo use inversión, estas diferencias generarían errores grandes.",[30,42440,42441],{},[33,42442,42443],{},[122,42444,42445],{},"Implicación para modelado",[12,42447,42448],{},"Si entrenamos un modelo usando solo inversión:",[86,42450,42452],{"className":42451},[3173],[86,42453,42455,42502],{"className":42454},[955],[86,42456,42458],{"className":42457},[959],[961,42459,42460],{"xmlns":963,"display":3182},[965,42461,42462,42499],{},[968,42463,42464,42467,42469,42476,42478,42484,42486],{},[3754,42465,42466],{},"Ventas",[3191,42468,258],{},[6849,42470,42471,42474],{},[974,42472,42473],{},"β",[978,42475,2553],{},[3191,42477,6565],{},[6849,42479,42480,42482],{},[974,42481,42473],{},[978,42483,802],{},[3191,42485,4975],{},[968,42487,42488,42491,42497],{},[3754,42489,42490],{},"Inversi",[3758,42492,42493,42495],{"accent":990},[3754,42494,6018],{},[3191,42496,3765],{},[3754,42498,6896],{},[982,42500,42501],{"encoding":984},"\\text{Ventas} = \\beta_0 + \\beta_1 \\cdot \\text{Inversión}",[86,42503,42505,42526,42583,42638],{"className":42504,"ariaHidden":990},[989],[86,42506,42508,42511,42517,42520,42523],{"className":42507},[994],[86,42509],{"className":42510,"style":3575},[998],[86,42512,42514],{"className":42513},[1003,3141],[86,42515,42466],{"className":42516},[1003],[86,42518],{"className":42519,"style":3222},[3221],[86,42521,258],{"className":42522},[3226],[86,42524],{"className":42525,"style":3222},[3221],[86,42527,42529,42532,42574,42577,42580],{"className":42528},[994],[86,42530],{"className":42531,"style":4888},[998],[86,42533,42535,42539],{"className":42534},[1003],[86,42536,42473],{"className":42537,"style":42538},[1003,1007],"margin-right:0.0528em;",[86,42540,42542],{"className":42541},[1012],[86,42543,42545,42566],{"className":42544},[1016,3836],[86,42546,42548,42563],{"className":42547},[1020],[86,42549,42551],{"className":42550,"style":6984},[1024],[86,42552,42554,42557],{"style":42553},"top:-2.55em;margin-left:-0.0528em;margin-right:0.05em;",[86,42555],{"className":42556,"style":1032},[1031],[86,42558,42560],{"className":42559},[1036,1037,1038,1039],[86,42561,2553],{"className":42562},[1003,1039],[86,42564,3963],{"className":42565},[3962],[86,42567,42569],{"className":42568},[1020],[86,42570,42572],{"className":42571,"style":7006},[1024],[86,42573],{},[86,42575],{"className":42576,"style":5012},[3221],[86,42578,6565],{"className":42579},[5016],[86,42581],{"className":42582,"style":5012},[3221],[86,42584,42586,42589,42629,42632,42635],{"className":42585},[994],[86,42587],{"className":42588,"style":4888},[998],[86,42590,42592,42595],{"className":42591},[1003],[86,42593,42473],{"className":42594,"style":42538},[1003,1007],[86,42596,42598],{"className":42597},[1012],[86,42599,42601,42621],{"className":42600},[1016,3836],[86,42602,42604,42618],{"className":42603},[1020],[86,42605,42607],{"className":42606,"style":6984},[1024],[86,42608,42609,42612],{"style":42553},[86,42610],{"className":42611,"style":1032},[1031],[86,42613,42615],{"className":42614},[1036,1037,1038,1039],[86,42616,802],{"className":42617},[1003,1039],[86,42619,3963],{"className":42620},[3962],[86,42622,42624],{"className":42623},[1020],[86,42625,42627],{"className":42626,"style":7006},[1024],[86,42628],{},[86,42630],{"className":42631,"style":5012},[3221],[86,42633,4975],{"className":42634},[5016],[86,42636],{"className":42637,"style":5012},[3221],[86,42639,42641,42644],{"className":42640},[994],[86,42642],{"className":42643,"style":3873},[998],[86,42645,42647,42650,42681],{"className":42646},[1003,3141],[86,42648,42490],{"className":42649},[1003],[86,42651,42653],{"className":42652},[1003,3863],[86,42654,42656],{"className":42655},[1016],[86,42657,42659],{"className":42658},[1020],[86,42660,42662,42670],{"className":42661,"style":3873},[1024],[86,42663,42664,42667],{"style":3876},[86,42665],{"className":42666,"style":3850},[1031],[86,42668,6018],{"className":42669},[1003],[86,42671,42672,42675],{"style":3876},[86,42673],{"className":42674,"style":3850},[1031],[86,42676,42678],{"className":42677,"style":3892},[3891],[86,42679,3765],{"className":42680},[1003],[86,42682,6896],{"className":42683},[1003],[12,42685,42686],{},"El modelo capturará la tendencia general, pero tendrá errores sistemáticos dependiendo del clima.",[12,42688,42689],{},"En cambio, si incluimos el clima como variable categórica (por ejemplo usando one-hot encoding):",[86,42691,42693],{"className":42692},[3173],[86,42694,42696,42753],{"className":42695},[955],[86,42697,42699],{"className":42698},[959],[961,42700,42701],{"xmlns":963,"display":3182},[965,42702,42703,42750],{},[968,42704,42705,42707,42709,42715,42717,42723,42725,42737,42739,42745,42747],{},[3754,42706,42466],{},[3191,42708,258],{},[6849,42710,42711,42713],{},[974,42712,42473],{},[978,42714,2553],{},[3191,42716,6565],{},[6849,42718,42719,42721],{},[974,42720,42473],{},[978,42722,802],{},[3191,42724,4975],{},[968,42726,42727,42729,42735],{},[3754,42728,42490],{},[3758,42730,42731,42733],{"accent":990},[3754,42732,6018],{},[3191,42734,3765],{},[3754,42736,6896],{},[3191,42738,6565],{},[6849,42740,42741,42743],{},[974,42742,42473],{},[978,42744,980],{},[3191,42746,4975],{},[3754,42748,42749],{},"Clima",[982,42751,42752],{"encoding":984},"\\text{Ventas} = \\beta_0 + \\beta_1 \\cdot \\text{Inversión} + \\beta_2 \\cdot \\text{Clima}",[86,42754,42756,42777,42832,42887,42943,42998],{"className":42755,"ariaHidden":990},[989],[86,42757,42759,42762,42768,42771,42774],{"className":42758},[994],[86,42760],{"className":42761,"style":3575},[998],[86,42763,42765],{"className":42764},[1003,3141],[86,42766,42466],{"className":42767},[1003],[86,42769],{"className":42770,"style":3222},[3221],[86,42772,258],{"className":42773},[3226],[86,42775],{"className":42776,"style":3222},[3221],[86,42778,42780,42783,42823,42826,42829],{"className":42779},[994],[86,42781],{"className":42782,"style":4888},[998],[86,42784,42786,42789],{"className":42785},[1003],[86,42787,42473],{"className":42788,"style":42538},[1003,1007],[86,42790,42792],{"className":42791},[1012],[86,42793,42795,42815],{"className":42794},[1016,3836],[86,42796,42798,42812],{"className":42797},[1020],[86,42799,42801],{"className":42800,"style":6984},[1024],[86,42802,42803,42806],{"style":42553},[86,42804],{"className":42805,"style":1032},[1031],[86,42807,42809],{"className":42808},[1036,1037,1038,1039],[86,42810,2553],{"className":42811},[1003,1039],[86,42813,3963],{"className":42814},[3962],[86,42816,42818],{"className":42817},[1020],[86,42819,42821],{"className":42820,"style":7006},[1024],[86,42822],{},[86,42824],{"className":42825,"style":5012},[3221],[86,42827,6565],{"className":42828},[5016],[86,42830],{"className":42831,"style":5012},[3221],[86,42833,42835,42838,42878,42881,42884],{"className":42834},[994],[86,42836],{"className":42837,"style":4888},[998],[86,42839,42841,42844],{"className":42840},[1003],[86,42842,42473],{"className":42843,"style":42538},[1003,1007],[86,42845,42847],{"className":42846},[1012],[86,42848,42850,42870],{"className":42849},[1016,3836],[86,42851,42853,42867],{"className":42852},[1020],[86,42854,42856],{"className":42855,"style":6984},[1024],[86,42857,42858,42861],{"style":42553},[86,42859],{"className":42860,"style":1032},[1031],[86,42862,42864],{"className":42863},[1036,1037,1038,1039],[86,42865,802],{"className":42866},[1003,1039],[86,42868,3963],{"className":42869},[3962],[86,42871,42873],{"className":42872},[1020],[86,42874,42876],{"className":42875,"style":7006},[1024],[86,42877],{},[86,42879],{"className":42880,"style":5012},[3221],[86,42882,4975],{"className":42883},[5016],[86,42885],{"className":42886,"style":5012},[3221],[86,42888,42890,42894,42934,42937,42940],{"className":42889},[994],[86,42891],{"className":42892,"style":42893},[998],"height:0.7778em;vertical-align:-0.0833em;",[86,42895,42897,42900,42931],{"className":42896},[1003,3141],[86,42898,42490],{"className":42899},[1003],[86,42901,42903],{"className":42902},[1003,3863],[86,42904,42906],{"className":42905},[1016],[86,42907,42909],{"className":42908},[1020],[86,42910,42912,42920],{"className":42911,"style":3873},[1024],[86,42913,42914,42917],{"style":3876},[86,42915],{"className":42916,"style":3850},[1031],[86,42918,6018],{"className":42919},[1003],[86,42921,42922,42925],{"style":3876},[86,42923],{"className":42924,"style":3850},[1031],[86,42926,42928],{"className":42927,"style":3892},[3891],[86,42929,3765],{"className":42930},[1003],[86,42932,6896],{"className":42933},[1003],[86,42935],{"className":42936,"style":5012},[3221],[86,42938,6565],{"className":42939},[5016],[86,42941],{"className":42942,"style":5012},[3221],[86,42944,42946,42949,42989,42992,42995],{"className":42945},[994],[86,42947],{"className":42948,"style":4888},[998],[86,42950,42952,42955],{"className":42951},[1003],[86,42953,42473],{"className":42954,"style":42538},[1003,1007],[86,42956,42958],{"className":42957},[1012],[86,42959,42961,42981],{"className":42960},[1016,3836],[86,42962,42964,42978],{"className":42963},[1020],[86,42965,42967],{"className":42966,"style":6984},[1024],[86,42968,42969,42972],{"style":42553},[86,42970],{"className":42971,"style":1032},[1031],[86,42973,42975],{"className":42974},[1036,1037,1038,1039],[86,42976,980],{"className":42977},[1003,1039],[86,42979,3963],{"className":42980},[3962],[86,42982,42984],{"className":42983},[1020],[86,42985,42987],{"className":42986,"style":7006},[1024],[86,42988],{},[86,42990],{"className":42991,"style":5012},[3221],[86,42993,4975],{"className":42994},[5016],[86,42996],{"className":42997,"style":5012},[3221],[86,42999,43001,43004],{"className":43000},[994],[86,43002],{"className":43003,"style":3873},[998],[86,43005,43007],{"className":43006},[1003,3141],[86,43008,42749],{"className":43009},[1003],[12,43011,43012],{},"El modelo podrá:",[30,43014,43015,43018,43021],{},[33,43016,43017],{},"Ajustar diferentes interceptos por clima (por ejemplo, un término extra para días lluviosos).",[33,43019,43020],{},"Mejorar precisión (ya que nos permite capturar esa variabilidad adicional).",[33,43022,43023],{},"Reducir varianza del error (porque la varianza, es decir, la dispersión de los puntos alrededor de la línea de regresión, se reduce al explicar más factores).",[12,43025,43026,43030],{},[1945,43027],{"alt":43028,"src":43029},"Matriz de Correlación Cafetería","\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis\u002Fshared\u002Fcafeteria_correlation_matrix.webp",[901,43031,43032],{},"Heatmap de Correlación",[12,43034,43035],{},"Vamos a descomponer la matriz de correlación, interpretando cada valor, pero antes recordemos qué significa cada número:",[30,43037,43038,43044,43050],{},[33,43039,43040,43043],{},[122,43041,43042],{},"1.00",": correlación positiva perfecta",[33,43045,43046,43049],{},[122,43047,43048],{},"0.00",": no hay relación lineal",[33,43051,43052,43055],{},[122,43053,43054],{},"-1.00",": correlación negativa perfecta",[12,43057,43058,43059,43062],{},"La matriz es ",[122,43060,43061],{},"simétrica",", es decir:",[164,43064,43067],{"className":43065,"code":43066,"language":3141},[3139],"Corr(A, B) = Corr(B, A)\n",[145,43068,43066],{"__ignoreMap":169},[12,43070,43071],{},"Por eso verás los mismos valores reflejados arriba y abajo de la diagonal.",[12,43073,43074,43075,43077],{},"La diagonal principal siempre es ",[122,43076,43042],{},", porque cada variable está perfectamente correlacionada consigo misma.",[12,43079,43080],{},"Las variables incluidas son:",[30,43082,43083,43088,43093,43098,43103],{},[33,43084,43085],{},[145,43086,43087],{},"temperature_c",[33,43089,43090],{},[145,43091,43092],{},"ad_investment",[33,43094,43095],{},[145,43096,43097],{},"local_event",[33,43099,43100],{},[145,43101,43102],{},"discount",[33,43104,43105],{},[145,43106,43107],{},"daily_sales",[117,43109,43110],{},[33,43111,43112,43114],{},[145,43113,43087],{},": Temperatura en grados Celsius.",[30,43116,43117,43123,43130,43137,43144],{},[33,43118,43119,43120,43122],{},"temperature_c - temperature_c = ",[122,43121,43042],{},"\nPerfecta correlación consigo misma.",[33,43124,43125,43126,43129],{},"temperature_c - ad_investment = ",[122,43127,43128],{},"-0.03","\nRelación prácticamente inexistente.\nLa temperatura no influye en cuánto se invierte en publicidad.",[33,43131,43132,43133,43136],{},"temperature_c - local_event = ",[122,43134,43135],{},"0.05","\nCorrelación muy débil positiva.\nLos eventos locales no dependen realmente del clima en este dataset.",[33,43138,43139,43140,43143],{},"temperature_c - discount = ",[122,43141,43142],{},"0.04","\nSin relación relevante.\nLos descuentos no parecen aplicarse según temperatura.",[33,43145,43146,43147,43150,43151,43154,43155,43163,43165],{},"temperature_c - daily_sales = ",[122,43148,43149],{},"-0.24","\nCorrelación negativa débil-moderada.\nCuando la temperatura aumenta, las ventas tienden a bajar ligeramente.",[43152,43153],"br",{},"Esto puede indicar:",[30,43156,43157,43160],{},[33,43158,43159],{},"El negocio vende productos que se consumen más en clima fresco.",[33,43161,43162],{},"En días muy calurosos hay menos afluencia.",[43152,43164],{},"No es una relación fuerte, pero sí consistente.",[117,43167,43168],{"start":192},[33,43169,43170,43172],{},[145,43171,43092],{},": Inversión en publicidad.",[30,43174,43175,43180,43187,43193],{},[33,43176,43177,43178],{},"ad_investment - ad_investment = ",[122,43179,43042],{},[33,43181,43182,43183,43186],{},"ad_investment - local_event = ",[122,43184,43185],{},"-0.05","\nPrácticamente independencia.\nLa inversión publicitaria no depende directamente de si hay evento.",[33,43188,43189,43190,43192],{},"ad_investment - discount = ",[122,43191,43128],{},"\nSin relación.\nInversión y descuentos parecen decisiones separadas.",[33,43194,43195,43196,43199,43200,43202,43203,43214,43216],{},"ad_investment - daily_sales = ",[122,43197,43198],{},"0.47","\nCorrelación positiva moderada.",[43152,43201],{},"Esto significa:",[30,43204,43205,43208,43211],{},[33,43206,43207],{},"A mayor inversión, mayores ventas.",[33,43209,43210],{},"La relación es significativa, pero no perfecta.",[33,43212,43213],{},"Hay otros factores influyendo.",[43152,43215],{},"Estadísticamente, es un predictor importante.",[117,43218,43219],{"start":205},[33,43220,43221,43223],{},[145,43222,43097],{},": Evento local.",[30,43225,43226,43231,43238],{},[33,43227,43228,43229],{},"local_event - local_event = ",[122,43230,43042],{},[33,43232,43233,43234,43237],{},"local_event - discount = ",[122,43235,43236],{},"-0.06","\nRelación casi nula.\nNo parece que los eventos impliquen necesariamente descuentos.",[33,43239,43240,43241,43244,43245,43247,43248,43259,43261],{},"local_event - daily_sales = ",[122,43242,43243],{},"0.57","\nEs la correlación más alta con ventas.",[43152,43246],{},"Interpretación:",[30,43249,43250,43253,43256],{},[33,43251,43252],{},"Cuando hay evento local, las ventas aumentan notablemente.",[33,43254,43255],{},"Es el factor más influyente del dataset.",[33,43257,43258],{},"Representa una variable clave para el modelo.",[43152,43260],{},"En términos prácticos:\nLos eventos generan tráfico o demanda adicional.",[117,43263,43264],{"start":212},[33,43265,43266,43268],{},[145,43267,43102],{},": Descuento.",[30,43270,43271,43276],{},[33,43272,43273,43274],{},"discount - discount = ",[122,43275,43042],{},[33,43277,43278,43279,43282,43283,43285,43286,43294,43296,43297],{},"discount - daily_sales = ",[122,43280,43281],{},"0.13","\nCorrelación positiva débil.",[43152,43284],{},"Significa:",[30,43287,43288,43291],{},[33,43289,43290],{},"Los descuentos tienen un impacto pequeño.",[33,43292,43293],{},"No parecen ser el motor principal de ventas.",[43152,43295],{},"Posibles explicaciones:",[30,43298,43299,43302,43305],{},[33,43300,43301],{},"Descuentos bajos",[33,43303,43304],{},"Mala estrategia",[33,43306,43307],{},"O efecto condicionado a otras variables",[117,43309,43310],{"start":227},[33,43311,43312,43314],{},[145,43313,43107],{},": Ventas diarias.",[12,43316,43317],{},"Ya interpretamos todas sus correlaciones con las demás variables:",[461,43319,43320,43330],{},[464,43321,43322],{},[467,43323,43324,43327],{},[470,43325,43326],{},"Variable",[470,43328,43329],{},"Correlación",[480,43331,43332,43338,43344,43350],{},[467,43333,43334,43336],{},[485,43335,43087],{},[485,43337,43149],{},[467,43339,43340,43342],{},[485,43341,43092],{},[485,43343,43198],{},[467,43345,43346,43348],{},[485,43347,43097],{},[485,43349,43243],{},[467,43351,43352,43354],{},[485,43353,43102],{},[485,43355,43281],{},[12,43357,43358],{},"Ordenadas por impacto lineal:",[117,43360,43361,43364,43367,43370],{},[33,43362,43363],{},"local_event (0.57)",[33,43365,43366],{},"ad_investment (0.47)",[33,43368,43369],{},"temperature_c (-0.24)",[33,43371,43372],{},"discount (0.13)",[12,43374,43375],{},[122,43376,43377],{},"¿Qué nos dice esto a nivel de modelado?",[12,43379,43380],{},"Lo primero es que las variables más predictivas para estimar ventas son:",[30,43382,43383,43385],{},[33,43384,43097],{},[33,43386,43092],{},[12,43388,43389],{},"Ambas deberían incluirse en el modelo.",[12,43391,43392],{},"Luego tenemos la multicolinealidad",[12,43394,43395],{},"Observamos que:",[30,43397,43398,43401],{},[33,43399,43400],{},"Ninguna variable independiente tiene correlación alta con otra.",[33,43402,43403],{},"Todos los valores entre predictores están cerca de 0.",[12,43405,43406],{},"Esto es excelente porque significa que no hay redundancia fuerte y que cada variable aporta información distinta.",[12,43408,43409],{},"Si tuviesemos valores cercanos a 1 o -1 entre predictores (por ejemplo, ad_investment y local_event), tendríamos que considerar eliminar o combinar variables para evitar problemas de multicolinealidad.",[12,43411,43412],{},"Asi que con todo esto podemos concluir:",[30,43414,43415,43418,43421,43424,43427,43430],{},[33,43416,43417],{},"El principal motor de ventas son los eventos locales.",[33,43419,43420],{},"La inversión publicitaria tiene un impacto claro y consistente.",[33,43422,43423],{},"La temperatura afecta ligeramente de forma negativa.",[33,43425,43426],{},"Los descuentos tienen impacto bajo.",[33,43428,43429],{},"No hay multicolinealidad problemática.",[33,43431,43432],{},"El dataset es apto para un modelo de regresión múltiple.",[16,43434,43435,43438],{},[12,43436,43437],{},"Con esta información, un gerente de la cafetería podría tomar decisiones estratégicas como:",[30,43439,43440,43443,43446,43449],{},[33,43441,43442],{},"Prioriza campañas durante eventos locales.",[33,43444,43445],{},"Mantén inversión publicitaria constante.",[33,43447,43448],{},"Reevaluar estrategia de descuentos.",[33,43450,43451],{},"Considerar estrategias específicas para días calurosos.",[323,43453,43455],{"id":43454},"paso-4-de-los-datos-a-la-predicción-modelado","Paso 4: De los Datos a la Predicción (Modelado)",[12,43457,43458,43459,61],{},"Con el EDA completado, transformamos el clima a un formato binario y alimentamos a un modelo de ",[901,43460,43461],{},"Regresión Lineal Simple",[164,43463,43465],{"className":166,"code":43464,"language":168,"meta":169,"style":169},"from sklearn.model_selection import train_test_split\nfrom sklearn.linear_model import LinearRegression\nfrom sklearn.metrics import mean_absolute_error, mean_squared_error, r2_score\n\n# One-Hot Encoding: Convierte \"Soleado\" o \"Lluvioso\" en columnas de 0s y 1s\ndf_encoded = pd.get_dummies(df, columns=[\"clima\"])\nX = df_encoded.drop(\"ventas_diarias\", axis=1)\ny = df_encoded[\"ventas_diarias\"]\n\n# Dividimos: 80% para que el modelo aprenda, 20% para examinarlo después\nX_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)\n\nmodelo_cafeteria = LinearRegression()\nmodelo_cafeteria.fit(X_train, y_train)\n\n# Hacemos predicciones con el modelo entrenado\npredicciones = modelo_cafeteria.predict(X_test)\n",[145,43466,43467,43482,43497,43522,43526,43531,43562,43594,43612,43616,43621,43667,43671,43683,43702,43706,43711],{"__ignoreMap":169},[86,43468,43469,43471,43473,43475,43477,43479],{"class":174,"line":175},[86,43470,1053],{"class":178},[86,43472,1056],{"class":182},[86,43474,61],{"class":219},[86,43476,1061],{"class":182},[86,43478,179],{"class":178},[86,43480,43481],{"class":182}," train_test_split\n",[86,43483,43484,43486,43488,43490,43492,43494],{"class":174,"line":192},[86,43485,1053],{"class":178},[86,43487,1056],{"class":182},[86,43489,61],{"class":219},[86,43491,38794],{"class":182},[86,43493,179],{"class":178},[86,43495,43496],{"class":182}," LinearRegression\n",[86,43498,43499,43501,43503,43505,43507,43509,43512,43514,43517,43519],{"class":174,"line":205},[86,43500,1053],{"class":178},[86,43502,1056],{"class":182},[86,43504,61],{"class":219},[86,43506,39123],{"class":182},[86,43508,179],{"class":178},[86,43510,43511],{"class":182}," mean_absolute_error",[86,43513,291],{"class":219},[86,43515,43516],{"class":182}," mean_squared_error",[86,43518,291],{"class":219},[86,43520,43521],{"class":182}," r2_score\n",[86,43523,43524],{"class":174,"line":212},[86,43525,209],{"emptyLinePlaceholder":208},[86,43527,43528],{"class":174,"line":227},[86,43529,43530],{"class":1360},"# One-Hot Encoding: Convierte \"Soleado\" o \"Lluvioso\" en columnas de 0s y 1s\n",[86,43532,43533,43536,43538,43540,43542,43544,43546,43548,43550,43552,43554,43556,43558,43560],{"class":174,"line":232},[86,43534,43535],{"class":182},"df_encoded ",[86,43537,258],{"class":219},[86,43539,261],{"class":182},[86,43541,61],{"class":219},[86,43543,34006],{"class":182},[86,43545,243],{"class":219},[86,43547,569],{"class":182},[86,43549,291],{"class":219},[86,43551,34015],{"class":304},[86,43553,1119],{"class":219},[86,43555,576],{"class":575},[86,43557,41190],{"class":579},[86,43559,576],{"class":575},[86,43561,1417],{"class":219},[86,43563,43564,43566,43568,43571,43573,43575,43577,43579,43581,43583,43585,43588,43590,43592],{"class":174,"line":252},[86,43565,12095],{"class":182},[86,43567,258],{"class":219},[86,43569,43570],{"class":182}," df_encoded",[86,43572,61],{"class":219},[86,43574,33804],{"class":182},[86,43576,243],{"class":219},[86,43578,576],{"class":575},[86,43580,41199],{"class":579},[86,43582,576],{"class":575},[86,43584,291],{"class":219},[86,43586,43587],{"class":304}," axis",[86,43589,258],{"class":219},[86,43591,802],{"class":223},[86,43593,273],{"class":219},[86,43595,43596,43598,43600,43602,43604,43606,43608,43610],{"class":174,"line":276},[86,43597,38411],{"class":182},[86,43599,258],{"class":219},[86,43601,43570],{"class":182},[86,43603,572],{"class":219},[86,43605,576],{"class":575},[86,43607,41199],{"class":579},[86,43609,576],{"class":575},[86,43611,752],{"class":219},[86,43613,43614],{"class":174,"line":315},[86,43615,209],{"emptyLinePlaceholder":208},[86,43617,43618],{"class":174,"line":3665},[86,43619,43620],{"class":1360},"# Dividimos: 80% para que el modelo aprenda, 20% para examinarlo después\n",[86,43622,43623,43625,43627,43629,43631,43633,43635,43637,43639,43641,43643,43645,43647,43649,43651,43653,43655,43657,43659,43661,43663,43665],{"class":174,"line":13256},[86,43624,9710],{"class":182},[86,43626,291],{"class":219},[86,43628,38443],{"class":182},[86,43630,291],{"class":219},[86,43632,38448],{"class":182},[86,43634,291],{"class":219},[86,43636,38453],{"class":182},[86,43638,258],{"class":219},[86,43640,38345],{"class":182},[86,43642,243],{"class":219},[86,43644,4624],{"class":182},[86,43646,291],{"class":219},[86,43648,1098],{"class":182},[86,43650,291],{"class":219},[86,43652,38473],{"class":304},[86,43654,258],{"class":219},[86,43656,38478],{"class":223},[86,43658,291],{"class":219},[86,43660,38483],{"class":304},[86,43662,258],{"class":219},[86,43664,1387],{"class":223},[86,43666,273],{"class":219},[86,43668,43669],{"class":174,"line":13286},[86,43670,209],{"emptyLinePlaceholder":208},[86,43672,43673,43676,43678,43681],{"class":174,"line":13291},[86,43674,43675],{"class":182},"modelo_cafeteria ",[86,43677,258],{"class":219},[86,43679,43680],{"class":182}," LinearRegression",[86,43682,11991],{"class":219},[86,43684,43685,43688,43690,43692,43694,43696,43698,43700],{"class":174,"line":13308},[86,43686,43687],{"class":182},"modelo_cafeteria",[86,43689,61],{"class":219},[86,43691,11051],{"class":182},[86,43693,243],{"class":219},[86,43695,9710],{"class":182},[86,43697,291],{"class":219},[86,43699,38448],{"class":182},[86,43701,273],{"class":219},[86,43703,43704],{"class":174,"line":13334},[86,43705,209],{"emptyLinePlaceholder":208},[86,43707,43708],{"class":174,"line":13359},[86,43709,43710],{"class":1360},"# Hacemos predicciones con el modelo entrenado\n",[86,43712,43713,43716,43718,43721,43723,43725,43727,43729],{"class":174,"line":13385},[86,43714,43715],{"class":182},"predicciones ",[86,43717,258],{"class":219},[86,43719,43720],{"class":182}," modelo_cafeteria",[86,43722,61],{"class":219},[86,43724,38883],{"class":182},[86,43726,243],{"class":219},[86,43728,38708],{"class":182},[86,43730,273],{"class":219},[323,43732,43734],{"id":43733},"paso-5-calificando-al-modelo","Paso 5: Calificando al Modelo",[12,43736,43737],{},"Ahora evaluemos que tan \"certero\" es nuestro algoritmo comparando las ventas contra sus predicciones.",[164,43739,43741],{"className":166,"code":43740,"language":168,"meta":169,"style":169},"mae = mean_absolute_error(y_test, predicciones)\nrmse = np.sqrt(mean_squared_error(y_test, predicciones))\nr2 = r2_score(y_test, predicciones)\n\nprint(f\"MAE: ${mae:.2f}\")\nprint(f\"RMSE: ${rmse:.2f}\")\nprint(f\"R^2: {r2:.2f}\")\n",[145,43742,43743,43763,43791,43811,43815,43839,43863],{"__ignoreMap":169},[86,43744,43745,43748,43750,43752,43754,43756,43758,43761],{"class":174,"line":175},[86,43746,43747],{"class":182},"mae ",[86,43749,258],{"class":219},[86,43751,43511],{"class":182},[86,43753,243],{"class":219},[86,43755,39232],{"class":182},[86,43757,291],{"class":219},[86,43759,43760],{"class":182}," predicciones",[86,43762,273],{"class":219},[86,43764,43765,43768,43770,43772,43774,43776,43778,43781,43783,43785,43787,43789],{"class":174,"line":192},[86,43766,43767],{"class":182},"rmse ",[86,43769,258],{"class":219},[86,43771,294],{"class":182},[86,43773,61],{"class":219},[86,43775,10044],{"class":182},[86,43777,243],{"class":219},[86,43779,43780],{"class":182},"mean_squared_error",[86,43782,243],{"class":219},[86,43784,39232],{"class":182},[86,43786,291],{"class":219},[86,43788,43760],{"class":182},[86,43790,33401],{"class":219},[86,43792,43793,43796,43798,43801,43803,43805,43807,43809],{"class":174,"line":205},[86,43794,43795],{"class":182},"r2 ",[86,43797,258],{"class":219},[86,43799,43800],{"class":182}," r2_score",[86,43802,243],{"class":219},[86,43804,39232],{"class":182},[86,43806,291],{"class":219},[86,43808,43760],{"class":182},[86,43810,273],{"class":219},[86,43812,43813],{"class":174,"line":212},[86,43814,209],{"emptyLinePlaceholder":208},[86,43816,43817,43819,43821,43823,43826,43828,43831,43833,43835,43837],{"class":174,"line":227},[86,43818,13294],{"class":812},[86,43820,243],{"class":219},[86,43822,6178],{"class":235},[86,43824,43825],{"class":579},"\"MAE: $",[86,43827,4089],{"class":215},[86,43829,43830],{"class":182},"mae",[86,43832,13325],{"class":235},[86,43834,4117],{"class":215},[86,43836,576],{"class":579},[86,43838,273],{"class":219},[86,43840,43841,43843,43845,43847,43850,43852,43855,43857,43859,43861],{"class":174,"line":232},[86,43842,13294],{"class":812},[86,43844,243],{"class":219},[86,43846,6178],{"class":235},[86,43848,43849],{"class":579},"\"RMSE: $",[86,43851,4089],{"class":215},[86,43853,43854],{"class":182},"rmse",[86,43856,13325],{"class":235},[86,43858,4117],{"class":215},[86,43860,576],{"class":579},[86,43862,273],{"class":219},[86,43864,43865,43867,43869,43871,43874,43876,43878,43880,43882,43884],{"class":174,"line":252},[86,43866,13294],{"class":812},[86,43868,243],{"class":219},[86,43870,6178],{"class":235},[86,43872,43873],{"class":579},"\"R^2: ",[86,43875,4089],{"class":215},[86,43877,1124],{"class":182},[86,43879,13325],{"class":235},[86,43881,4117],{"class":215},[86,43883,576],{"class":579},[86,43885,273],{"class":219},[12,43887,39062],{},[12,43889,43890,43891],{},"MAE: ",[145,43892,43893],{},"$55.39",[12,43895,43896,43897],{},"RMSE: ",[145,43898,43899],{},"$74.51",[12,43901,43902,43960],{},[86,43903,43905,43922],{"className":43904},[955],[86,43906,43908],{"className":43907},[959],[961,43909,43910],{"xmlns":963},[965,43911,43912,43920],{},[968,43913,43914],{},[971,43915,43916,43918],{},[974,43917,976],{},[978,43919,980],{},[982,43921,985],{"encoding":984},[86,43923,43925],{"className":43924,"ariaHidden":990},[989],[86,43926,43928,43931],{"className":43927},[994],[86,43929],{"className":43930,"style":999},[998],[86,43932,43934,43937],{"className":43933},[1003],[86,43935,976],{"className":43936,"style":1008},[1003,1007],[86,43938,43940],{"className":43939},[1012],[86,43941,43943],{"className":43942},[1016],[86,43944,43946],{"className":43945},[1020],[86,43947,43949],{"className":43948,"style":999},[1024],[86,43950,43951,43954],{"style":1027},[86,43952],{"className":43953,"style":1032},[1031],[86,43955,43957],{"className":43956},[1036,1037,1038,1039],[86,43958,980],{"className":43959},[1003,1039],": 0.88",[12,43962,43963],{},"¿Qué significan estos números?",[30,43965,43966,43975,43984],{},[33,43967,43968,43971,43972,43974],{},[122,43969,43970],{},"MAE (Error Absoluto Medio)",": En promedio, nuestras predicciones se desvían de las ventas reales por aproximadamente ",[145,43973,43893],{},". Esto nos da una idea de la magnitud del error en términos monetarios.",[33,43976,43977,43980,43981,43983],{},[122,43978,43979],{},"RMSE (Error Cuadrático Medio)",": Al penalizar más los errores grandeses, el RMSE de ",[145,43982,43899],{}," indica que, aunque la mayoría de las predicciones están cerca, hay algunos casos donde el modelo se equivoca más significativamente.",[33,43985,43986,44047,44048,44106],{},[122,43987,43988,44046],{},[86,43989,43991,44008],{"className":43990},[955],[86,43992,43994],{"className":43993},[959],[961,43995,43996],{"xmlns":963},[965,43997,43998,44006],{},[968,43999,44000],{},[971,44001,44002,44004],{},[974,44003,976],{},[978,44005,980],{},[982,44007,985],{"encoding":984},[86,44009,44011],{"className":44010,"ariaHidden":990},[989],[86,44012,44014,44017],{"className":44013},[994],[86,44015],{"className":44016,"style":999},[998],[86,44018,44020,44023],{"className":44019},[1003],[86,44021,976],{"className":44022,"style":1008},[1003,1007],[86,44024,44026],{"className":44025},[1012],[86,44027,44029],{"className":44028},[1016],[86,44030,44032],{"className":44031},[1020],[86,44033,44035],{"className":44034,"style":999},[1024],[86,44036,44037,44040],{"style":1027},[86,44038],{"className":44039,"style":1032},[1031],[86,44041,44043],{"className":44042},[1036,1037,1038,1039],[86,44044,980],{"className":44045},[1003,1039]," (Puntuación de Determinación)",": Un ",[86,44049,44051,44068],{"className":44050},[955],[86,44052,44054],{"className":44053},[959],[961,44055,44056],{"xmlns":963},[965,44057,44058,44066],{},[968,44059,44060],{},[971,44061,44062,44064],{},[974,44063,976],{},[978,44065,980],{},[982,44067,985],{"encoding":984},[86,44069,44071],{"className":44070,"ariaHidden":990},[989],[86,44072,44074,44077],{"className":44073},[994],[86,44075],{"className":44076,"style":999},[998],[86,44078,44080,44083],{"className":44079},[1003],[86,44081,976],{"className":44082,"style":1008},[1003,1007],[86,44084,44086],{"className":44085},[1012],[86,44087,44089],{"className":44088},[1016],[86,44090,44092],{"className":44091},[1020],[86,44093,44095],{"className":44094,"style":999},[1024],[86,44096,44097,44100],{"style":1027},[86,44098],{"className":44099,"style":1032},[1031],[86,44101,44103],{"className":44102},[1036,1037,1038,1039],[86,44104,980],{"className":44105},[1003,1039]," de 0.88 significa que el modelo explica el 88% de la variabilidad en las ventas diarias. Esto es un resultado bastante bueno, indicando que el modelo captura la mayoría de los patrones presentes en los datos.",[12,44108,44109],{},[122,44110,44111],{},"Grafico de Predicciones vs Realidad",[164,44113,44115],{"className":166,"code":44114,"language":168,"meta":169,"style":169},"plt.figure(figsize=(8,5))\nsns.scatterplot(x=y_test, y=predictions)\nplt.plot([y.min(), y.max()], [y.min(), y.max()], 'r--')  # Perfect reference line\nplt.title(\"Predictions vs Actual Sales\")\nplt.xlabel(\"Actual Sales ($)\")\nplt.ylabel(\"Model Predictions ($)\")\nplt.show()\n",[145,44116,44117,44139,44166,44224,44243,44262,44281],{"__ignoreMap":169},[86,44118,44119,44121,44123,44125,44127,44129,44131,44133,44135,44137],{"class":174,"line":175},[86,44120,33172],{"class":182},[86,44122,61],{"class":219},[86,44124,34701],{"class":182},[86,44126,243],{"class":219},[86,44128,34706],{"class":304},[86,44130,34709],{"class":219},[86,44132,34578],{"class":223},[86,44134,291],{"class":219},[86,44136,1108],{"class":223},[86,44138,33401],{"class":219},[86,44140,44141,44143,44145,44147,44149,44151,44153,44155,44157,44159,44161,44164],{"class":174,"line":192},[86,44142,33151],{"class":182},[86,44144,61],{"class":219},[86,44146,41957],{"class":182},[86,44148,243],{"class":219},[86,44150,3189],{"class":304},[86,44152,258],{"class":219},[86,44154,39232],{"class":182},[86,44156,291],{"class":219},[86,44158,1098],{"class":304},[86,44160,258],{"class":219},[86,44162,44163],{"class":182},"predictions",[86,44165,273],{"class":219},[86,44167,44168,44170,44172,44174,44176,44178,44180,44182,44185,44187,44189,44191,44194,44196,44198,44200,44202,44204,44206,44208,44210,44212,44214,44217,44219,44221],{"class":174,"line":205},[86,44169,33172],{"class":182},[86,44171,61],{"class":219},[86,44173,39676],{"class":182},[86,44175,32924],{"class":219},[86,44177,5464],{"class":182},[86,44179,61],{"class":219},[86,44181,13436],{"class":182},[86,44183,44184],{"class":219},"(),",[86,44186,1098],{"class":182},[86,44188,61],{"class":219},[86,44190,7260],{"class":182},[86,44192,44193],{"class":219},"()],",[86,44195,726],{"class":219},[86,44197,5464],{"class":182},[86,44199,61],{"class":219},[86,44201,13436],{"class":182},[86,44203,44184],{"class":219},[86,44205,1098],{"class":182},[86,44207,61],{"class":219},[86,44209,7260],{"class":182},[86,44211,44193],{"class":219},[86,44213,11970],{"class":575},[86,44215,44216],{"class":579},"r--",[86,44218,10971],{"class":575},[86,44220,867],{"class":219},[86,44222,44223],{"class":1360},"  # Perfect reference line\n",[86,44225,44226,44228,44230,44232,44234,44236,44239,44241],{"class":174,"line":212},[86,44227,33172],{"class":182},[86,44229,61],{"class":219},[86,44231,34801],{"class":182},[86,44233,243],{"class":219},[86,44235,576],{"class":575},[86,44237,44238],{"class":579},"Predictions vs Actual Sales",[86,44240,576],{"class":575},[86,44242,273],{"class":219},[86,44244,44245,44247,44249,44251,44253,44255,44258,44260],{"class":174,"line":227},[86,44246,33172],{"class":182},[86,44248,61],{"class":219},[86,44250,34821],{"class":182},[86,44252,243],{"class":219},[86,44254,576],{"class":575},[86,44256,44257],{"class":579},"Actual Sales ($)",[86,44259,576],{"class":575},[86,44261,273],{"class":219},[86,44263,44264,44266,44268,44270,44272,44274,44277,44279],{"class":174,"line":232},[86,44265,33172],{"class":182},[86,44267,61],{"class":219},[86,44269,34841],{"class":182},[86,44271,243],{"class":219},[86,44273,576],{"class":575},[86,44275,44276],{"class":579},"Model Predictions ($)",[86,44278,576],{"class":575},[86,44280,273],{"class":219},[86,44282,44283,44285,44287,44289],{"class":174,"line":252},[86,44284,33172],{"class":182},[86,44286,61],{"class":219},[86,44288,35087],{"class":182},[86,44290,11991],{"class":219},[12,44292,44293,44297],{},[1945,44294],{"alt":44295,"src":44296},"Predicciones vs Realidad","\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis\u002Fshared\u002Fpredictions_vs_actual_sales.webp",[901,44298,44299],{},"Gráfico de Predicciones vs Ventas Reales",[12,44301,44302],{},"Como se observa, tenemos una línea de referencia (en rojo) que representa la perfección: si todas las ventas estuvieran exactamente en esa línea, el modelo sería perfecto, pero la realidad nunca será asi de ideal. Aún así, la mayoría de los puntos se agrupan alrededor de esa línea, lo que indica que el modelo tiene un buen desempeño general. Algunos puntos se alejan más, lo que refleja los casos donde el modelo no predice tan bien, posiblemente debido a factores no capturados en el dataset o a la variabilidad inherente en las ventas diarias.",[12,44304,44305],{},"Podemos también obtener los coeficientes del modelo para entender la importancia de cada variable:",[164,44307,44309],{"className":166,"code":44308,"language":168,"meta":169,"style":169},"coeficientes = pd.DataFrame({\n    'Variable': X.columns,\n    'Coeficiente': modelo_cafeteria.coef_\n})\ndisplay(coeficientes.sort_values(by='Coeficiente', ascending=False))\n",[145,44310,44311,44327,44346,44364,44368],{"__ignoreMap":169},[86,44312,44313,44316,44318,44320,44322,44324],{"class":174,"line":175},[86,44314,44315],{"class":182},"coeficientes ",[86,44317,258],{"class":219},[86,44319,261],{"class":182},[86,44321,61],{"class":219},[86,44323,13177],{"class":182},[86,44325,44326],{"class":219},"({\n",[86,44328,44329,44332,44334,44336,44338,44340,44342,44344],{"class":174,"line":192},[86,44330,44331],{"class":575},"    '",[86,44333,43326],{"class":579},[86,44335,10971],{"class":575},[86,44337,162],{"class":219},[86,44339,1093],{"class":182},[86,44341,61],{"class":219},[86,44343,33809],{"class":182},[86,44345,1111],{"class":219},[86,44347,44348,44350,44353,44355,44357,44359,44361],{"class":174,"line":205},[86,44349,44331],{"class":575},[86,44351,44352],{"class":579},"Coeficiente",[86,44354,10971],{"class":575},[86,44356,162],{"class":219},[86,44358,43720],{"class":182},[86,44360,61],{"class":219},[86,44362,44363],{"class":182},"coef_\n",[86,44365,44366],{"class":174,"line":212},[86,44367,13195],{"class":219},[86,44369,44370,44372,44374,44377,44379,44381,44383,44386,44388,44390,44392,44394,44396,44399,44401,44403],{"class":174,"line":227},[86,44371,33276],{"class":182},[86,44373,243],{"class":219},[86,44375,44376],{"class":182},"coeficientes",[86,44378,61],{"class":219},[86,44380,33714],{"class":182},[86,44382,243],{"class":219},[86,44384,44385],{"class":304},"by",[86,44387,258],{"class":219},[86,44389,10971],{"class":575},[86,44391,44352],{"class":579},[86,44393,10971],{"class":575},[86,44395,291],{"class":219},[86,44397,44398],{"class":304}," ascending",[86,44400,258],{"class":219},[86,44402,33508],{"class":178},[86,44404,33401],{"class":219},[12,44406,44407],{},"Esto nos arroja el siguiente resultado:",[461,44409,44410,44420],{},[464,44411,44412],{},[467,44413,44414,44417],{},[470,44415,44416],{},"Feature",[470,44418,44419],{},"Coefficient",[480,44421,44422,44429,44437,44444,44451,44458,44466],{},[467,44423,44424,44426],{},[485,44425,43097],{},[485,44427,44428],{},"261.839739",[467,44430,44431,44434],{},[485,44432,44433],{},"weather_Rainy",[485,44435,44436],{},"124.573377",[467,44438,44439,44441],{},[485,44440,43102],{},[485,44442,44443],{},"4.837618",[467,44445,44446,44448],{},[485,44447,43092],{},[485,44449,44450],{},"2.482678",[467,44452,44453,44455],{},[485,44454,43087],{},[485,44456,44457],{},"-8.578684",[467,44459,44460,44463],{},[485,44461,44462],{},"weather_Cloudy",[485,44464,44465],{},"-28.151991",[467,44467,44468,44471],{},[485,44469,44470],{},"weather_Sunny",[485,44472,44473],{},"-96.421386",[12,44475,44476],{},"Lo que nos dice cada coeficiente es el impacto que tiene esa variable en las ventas diarias, manteniendo las demás constantes. Por ejemplo:",[30,44478,44479,44485,44491,44498,44504,44510,44516],{},[33,44480,44481,44482,61],{},"Un evento local (local_event) aumenta las ventas en aproximadamente ",[145,44483,44484],{},"$261.84",[33,44486,44487,44488,61],{},"Un día lluvioso (weather_Rainy) aumenta las ventas en aproximadamente ",[145,44489,44490],{},"$124.57",[33,44492,44493,44494,44497],{},"Un descuento (discount) aumenta las ventas en aproximadamente ",[145,44495,44496],{},"$4.84"," por cada punto porcentual de descuento.",[33,44499,44500,44501,61],{},"Cada dólar adicional invertido en publicidad (ad_investment) aumenta las ventas en aproximadamente ",[145,44502,44503],{},"$2.48",[33,44505,44506,44507],{},"Cada grado Celsius adicional (temperature_c) disminuye las ventas en aproximadamente ",[145,44508,44509],{},"$8.58",[33,44511,44512,44513,61],{},"Un día nublado (weather_Cloudy) disminuye las ventas en aproximadamente ",[145,44514,44515],{},"$28.15",[33,44517,44518,44519,61],{},"Un día soleado (weather_Sunny) disminuye las ventas en aproximadamente ",[145,44520,44521],{},"$96.42",[12,44523,44524],{},"¿Qué mejoras podemos hacer al modelo?",[30,44526,44527,44544,44550,44559,44565],{},[33,44528,44529,44532,44533,392,44535,44537,44538,392,44540,44543],{},[122,44530,44531],{},"Feature Engineering",": Explorar la creación de nuevas características a partir de las existentes. Por ejemplo, los términos de interacción entre ",[145,44534,43092],{},[145,44536,43102],{},", o ",[145,44539,43087],{},[145,44541,44542],{},"weather",", podrían capturar relaciones más complejas.",[33,44545,44546,44549],{},[122,44547,44548],{},"Relaciones no lineales",": El modelo actual es lineal. Si los diagramas de dispersión sugieren relaciones no lineales (p. ej., ventas que alcanzan su máximo a cierta temperatura y luego disminuyen), las características polinómicas u otros modelos no lineales (como Random Forest o Gradient Boosting) podrían capturarlas mejor.",[33,44551,44552,44555,44556,44558],{},[122,44553,44554],{},"Aspectos de series temporales",": Dado que los datos son de ventas diarias, podría haber patrones temporales (p. ej., efectos del día de la semana, estacionalidad no capturada completamente por ",[145,44557,44542],{},"). Incorporar características como el día de la semana, el mes o utilizar modelos específicos para series temporales podría ser beneficioso.",[33,44560,44561,44564],{},[122,44562,44563],{},"Detección de valores atípicos",": Investigar cualquier valor atípico potencial en los datos que pueda estar influyendo desproporcionadamente en los coeficientes y predicciones del modelo.",[33,44566,44567,44570],{},[122,44568,44569],{},"Más datos",": Si bien no siempre es factible, contar con puntos de datos más diversos (por ejemplo, de diferentes cafeterías, durante un período más prolongado y con condiciones más variadas) podría ayudar a que el modelo se generalice mejor.",[2218,44572,44573],{},"html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}html pre.shiki code .scnC2, html code.shiki .scnC2{--shiki-default:#B5695977;--shiki-dark:#C98A7D77}html pre.shiki code .spP0B, html code.shiki .spP0B{--shiki-default:#B56959;--shiki-dark:#C98A7D}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html pre.shiki code .s5TCs, html code.shiki .s5TCs{--shiki-default:#AB5959;--shiki-dark:#CB7676}html pre.shiki code .s9nN2, html code.shiki .s9nN2{--shiki-default:#B07D48;--shiki-dark:#BD976A}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .s_xSY, html code.shiki .s_xSY{--shiki-default:#59873A;--shiki-dark:#80A665}html pre.shiki code .sfsYZ, html code.shiki .sfsYZ{--shiki-default:#A65E2B;--shiki-dark:#C99076}",{"title":169,"searchDepth":205,"depth":205,"links":44575},[44576],{"id":40519,"depth":192,"text":40520,"children":44577},[44578,44579,44580,44581,44582],{"id":40538,"depth":205,"text":40539},{"id":41242,"depth":205,"text":41243},{"id":41742,"depth":205,"text":41743},{"id":43454,"depth":205,"text":43455},{"id":43733,"depth":205,"text":43734},"2026-04-19","\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis\u002Fshared\u002Feda.webp",{},"\u002Fblog\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis",{"title":33028,"description":40505},{"loc":44589,"priority":2259,"lastmod":44583},"\u002Fes\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis","experimenting-with-exploratory-data-analysis","blog\u002Fblog\u002Fexperimenting-with-exploratory-data-analysis","En este artículo, exploraremos el proceso de análisis exploratorio de datos (EDA) en el contexto de proyectos de aprendizaje automático.",[3625,3675,40495,40496,40497],"OkZVPl-PFaVX7ahJmiC3RapiWh12DIEW2GXTz6cT5-Q",{"id":44596,"title":40512,"author":7,"body":44597,"date":46276,"description":44601,"extension":2250,"image":46277,"lastmod":32998,"meta":46278,"navigation":208,"order":212,"path":46279,"seo":46280,"sitemap":46281,"slug":46283,"stem":46284,"summary":46285,"tags":46286,"__hash__":46289},"content_es\u002Fblog\u002Fblog\u002Fworkflow-machine-learning-projects.md",{"type":9,"value":44598,"toc":46239},[44599,44602,44609,44611,44613,44616,44642,44656,44665,44667,44671,44674,44700,44703,44706,44728,44730,44734,44737,44763,44766,44770,44773,44776,44780,44783,44839,44842,44867,44872,44876,44905,44909,44912,44938,44941,44945,45001,45005,45013,45016,45022,45030,45036,45044,45050,45058,45062,45065,45091,45099,45105,45108,45112,45115,45153,45156,45160,45163,45180,45182,45188,45192,45217,45221,45224,45226,45240,45244,45247,45263,45266,45270,45273,45276,45279,45299,45304,45307,45345,45349,45352,45355,45358,45383,45386,45406,45409,45412,45454,45457,45460,45463,45466,45470,45473,45505,45509,45512,45532,45535,45573,45576,45608,45611,45637,45639,45643,45646,45651,45654,45679,45682,45688,45691,45697,45704,45710,45717,45721,45727,45730,45736,45741,45747,45753,45756,45763,45766,45772,45775,45779,45782,45789,45795,45802,45808,45812,45815,45821,45824,45830,45836,45839,45842,45849,45852,45858,45865,45868,45874,45881,45884,45890,45893,45896,45899,45944,45947,45953,45960,45964,45967,45978,45981,46037,46043,46054,46060,46064,46067,46078,46081,46084,46087,46090,46098,46101,46107,46110,46116,46119,46125,46128,46134,46137,46141,46144,46158,46161,46165,46168,46171,46174,46182,46189,46192,46195,46203,46205,46212,46223,46230,46237],[12,44600,44601],{},"Continuamos aprendiendo sobre el mundo del aprendizaje automático, y en esta ocasión, nos adentraremos en el flujo típico de un proyecto de aprendizaje automático.",[12,44603,19786,44604],{},[22,44605,44608],{"href":44606,"rel":44607},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations",[26],"Paradigmas de aprendizaje automático y fundamentos matemáticos",[40,44610],{},[43,44612],{},[12,44614,44615],{},"¿Por qué es importante entender el flujo de un proyecto de aprendizaje automático?",[30,44617,44618,44624,44630,44636],{},[33,44619,44620,44623],{},[122,44621,44622],{},"El proceso es más importante que el resultado",": Los modelos exitosos no dependen únicamente de algoritmos sofisticados, sino de un\nproceso bien estructurado. Un Random Forest con datos limpios y bien preparados supera consistentemente a una red neuronal profunda con datos de mala calidad.",[33,44625,44626,44629],{},[122,44627,44628],{},"Reproducibilidad",": Un flujo de trabajo claro y documentado permite que otros científicos de datos puedan reproducir tus resultados, lo cual es fundamental para la validación y el avance del conocimiento en el campo.",[33,44631,44632,44635],{},[122,44633,44634],{},"Colaboración",": En proyectos de aprendizaje automático, a menudo hay múltiples personas involucradas, desde científicos de datos hasta ingenieros de datos y stakeholders. Un flujo de trabajo bien definido facilita la comunicación y la colaboración entre todos los miembros del equipo.",[33,44637,44638,44641],{},[122,44639,44640],{},"Reduce el riesgo de errores",": Un proceso estructurado ayuda a identificar y corregir errores en las etapas tempranas del proyecto, lo que puede ahorrar tiempo y recursos a largo plazo.",[12,44643,44644,44645,44648,44649,392,44652,44655],{},"De forma general el aprendizaje automático es un proceso que es ",[122,44646,44647],{},"parte de un sistema",", con un ",[122,44650,44651],{},"ciclo iterativo",[122,44653,44654],{},"orientado a generar valor"," que consta de varias etapas, cada una con sus propias tareas y desafíos.",[12,44657,44658,44662],{},[1945,44659],{"alt":44660,"src":44661},"Visión integradora del ciclo en Machine Learning","\u002Fblog\u002Fworkflow-machine-learning-projects\u002Fshared\u002Fmachine-learning-cycle.webp",[901,44663,44664],{},"Ciclo en Machine Learning",[43,44666],{},[46,44668,44670],{"id":44669},"_1-definición-del-problema","1. Definición del problema",[12,44672,44673],{},"La primera etapa de cualquier proyecto de aprendizaje automático es la definición del problema:",[30,44675,44676,44682,44688,44694],{},[33,44677,44678,44681],{},[122,44679,44680],{},"Identificación del problema",": ¿Que queremos lograr con el proyecto? ¿Qué decisiones queremos apoyar con el modelo? Es crucial entender el contexto del negocio o la aplicación para definir claramente el problema.",[33,44683,44684,44687],{},[122,44685,44686],{},"Variable objetivo",": ¿Cuál es la variable que queremos predecir o clasificar? Esta variable, también conocida como variable dependiente, es el foco del proyecto y debe ser claramente definida.",[33,44689,44690,44693],{},[122,44691,44692],{},"Tipo de problema",": ¿Es un problema de clasificación, regresión, clustering, o algo más? La naturaleza del problema influirá en la elección de los algoritmos y técnicas a utilizar.",[33,44695,44696,44699],{},[122,44697,44698],{},"Métricas de evaluación",": ¿Cómo vamos a medir el éxito del modelo? Es importante definir las métricas de evaluación desde el principio, ya que estas guiarán el desarrollo del modelo y la toma de decisiones a lo largo del proyecto.",[12,44701,44702],{},"Esta etapa es el cimiento de todo el proyecto. Un problema mal definido puede llevar a esfuerzos desperdiciados y resultados insatisfactorios. Es fundamental dedicar tiempo a entender el problema y establecer objetivos claros antes de avanzar a las siguientes etapas.",[12,44704,44705],{},"Veámos un ejemplo práctico:\nSupongamos que una empresa de comercio electrónico quiere predecir si un cliente realizará una compra en su sitio web. En este caso:",[30,44707,44708,44713,44718,44723],{},[33,44709,44710,44712],{},[122,44711,44680],{},": Predecir la probabilidad de que un cliente realice una compra.",[33,44714,44715,44717],{},[122,44716,44686],{},": La variable objetivo podría ser una variable binaria que indique si el cliente realizó una compra (1) o no (0).",[33,44719,44720,44722],{},[122,44721,44692],{},": Este es un problema de clasificación binaria.",[33,44724,44725,44727],{},[122,44726,44698],{},": Las métricas de evaluación podrían incluir la precisión, el recall y el F1-score, dependiendo de la importancia relativa de los falsos positivos y los falsos negativos en el contexto del negocio.",[43,44729],{},[46,44731,44733],{"id":44732},"_2-recopilación-de-datos","2. Recopilación de datos",[12,44735,44736],{},"Una vez que el problema está claramente definido, el siguiente paso es la recopilación de datos, aquí se deben identificar y acceder a las fuentes de datos relevantes. Esto puede incluir:",[30,44738,44739,44745,44751,44757],{},[33,44740,44741,44744],{},[122,44742,44743],{},"Bases de datos internas\u002Fempresariales",": Datos almacenados en sistemas internos de la empresa, como bases de datos relacionales, data warehouses o data lakes. Algunos ejemplos incluyen registros de ventas, datos de clientes, datos provenientes de CRM o ERP, entre otros.",[33,44746,44747,44750],{},[122,44748,44749],{},"APIs y servicios web",": Datos externos de proveedores de datos, redes sociales, servicios de geolocalización, etc. Por ejemplo, una empresa de análisis de sentimientos podría utilizar la API de Twitter para recopilar tweets relacionados con un tema específico.",[33,44752,44753,44756],{},[122,44754,44755],{},"Logs y registros de eventos de sistemas",": Datos generados por aplicaciones, servidores, dispositivos IoT, etc. Por ejemplo, una empresa de monitoreo de infraestructura podría recopilar logs de servidores para detectar patrones de fallos.",[33,44758,44759,44762],{},[122,44760,44761],{},"Datos públicos\u002Fexternos",": Datos disponibles públicamente, como conjuntos de datos de Kaggle, datos gubernamentales, datos de investigación académica, etc. Por ejemplo, un investigador podría utilizar el conjunto de datos de imágenes de MNIST para entrenar un modelo de reconocimiento de dígitos manuscritos.",[12,44764,44765],{},"Es importante tener en cuenta que la calidad de los datos recopilados es crucial para el éxito del proyecto. Los datos deben ser relevantes, completos, precisos y actualizados. Además, es fundamental considerar aspectos éticos y legales relacionados con la recopilación y el uso de datos, como la privacidad de los usuarios y el cumplimiento de regulaciones como GDPR.",[46,44767,44769],{"id":44768},"_3-preprocesamiento-de-datos","3. Preprocesamiento de datos",[12,44771,44772],{},"Esta es la fase de preparación y limpieza de datos,  es un paso crucial y a menudo es el mayor cuello de botella. Los prefesionales de datos suelen dedicar entre el 70% y el 80% de su tiempo a preparar datos y no a construir modelos.",[12,44774,44775],{},"La calidad del modelos depende directamente de la calidad de los datos, si están desordenados o incompletos, el modelo no podrá aprender patrones útiles. Incluso el algoritmo más sofisticado no puede compensar por datos de mala calidad.",[46,44777,44779],{"id":44778},"_4-análisis-exploratorio-de-datos-eda","4. Análisis exploratorio de datos (EDA)",[12,44781,44782],{},"Durante esta etapa, se realiza un análisis detallado de los datos para comprender su estructura, distribución y relaciones entre variables. Esto incluye:",[30,44784,44785,44805,44822],{},[33,44786,44787,44790,44791],{},[122,44788,44789],{},"Analisis univariado",": Examinar la distribución de cada variable individualmente, utilizando estadísticas descriptivas y visualizaciones como:\n",[30,44792,44793,44796,44799,44802],{},[33,44794,44795],{},"Histogramas",[33,44797,44798],{},"Diagramas de caja (boxplots)",[33,44800,44801],{},"Gráficos de barras",[33,44803,44804],{},"Estadísticas de tendencia central (media, mediana) y dispersión (desviación estándar, rango intercuartílico)",[33,44806,44807,44810,44811],{},[122,44808,44809],{},"Analisis bivariado",": Explorar las relaciones entre pares de variables, utilizando visualizaciones como:\n",[30,44812,44813,44816,44819],{},[33,44814,44815],{},"Diagramas de dispersión (scatter plots)",[33,44817,44818],{},"Mapas de calor (heatmaps) para visualizar correlaciones",[33,44820,44821],{},"Gráficos de barras apiladas para variables categóricas",[33,44823,44824,44827,44828],{},[122,44825,44826],{},"Analisis multivariado",": Examinar las relaciones entre múltiples variables simultáneamente, utilizando técnicas como:\n",[30,44829,44830,44833,44836],{},[33,44831,44832],{},"Análisis de componentes principales (PCA)",[33,44834,44835],{},"Análisis de clústeres",[33,44837,44838],{},"Gráficos de pares (pair plots)\nEl EDA es fundamental para detectar problemas en los datos, como valores atípicos, distribuciones sesgadas o relaciones no lineales entre variables. Además, el EDA puede proporcionar insights valiosos que guiarán la selección de características y la elección de algoritmos en las etapas posteriores del proyecto.",[12,44840,44841],{},"Las herramientas comunes para realizar EDA incluye:",[30,44843,44844,44850,44855,44861],{},[33,44845,44846,44849],{},[122,44847,44848],{},"Python",": Bibliotecas como Pandas, Matplotlib, Seaborn y Plotly son ampliamente utilizadas para el análisis exploratorio de datos en Python.",[33,44851,44852,44854],{},[122,44853,976],{},": Paquetes como ggplot2, dplyr y tidyr son populares para realizar EDA en R.",[33,44856,44857,44860],{},[122,44858,44859],{},"Herramientas de visualización",": Herramientas como Tableau, Power BI o QlikView también pueden ser utilizadas para realizar análisis exploratorio de datos de manera interactiva.",[33,44862,44863,44866],{},[122,44864,44865],{},"Jupyter Notebooks",": Los notebooks de Jupyter son una herramienta común para realizar EDA, ya que permiten combinar código, visualizaciones y texto explicativo en un solo documento.",[16,44868,44869],{},[12,44870,44871],{},"El EDA no es un paso lineal, a menudo se realiza de manera iterativa a medida que se descubren nuevos insights o se identifican problemas en los datos. Es importante documentar los hallazgos del EDA, ya que estos pueden ser útiles para la toma de decisiones en las etapas posteriores del proyecto.",[323,44873,44875],{"id":44874},"principios-para-un-eda-efectivo","Principios para un EDA efectivo",[30,44877,44878,44884,44890,44899],{},[33,44879,44880,44883],{},[122,44881,44882],{},"Comenzar simple",": Iniciar con visualizaciones y estadísticas básicas para obtener una comprensión general de los datos antes de profundizar en análisis más complejos.",[33,44885,44886,44889],{},[122,44887,44888],{},"Colores con propósito",": Utilizar colores de manera estratégica para resaltar patrones o diferencias importantes en los datos, evitando el uso excesivo de colores que pueda distraer.",[33,44891,44892,44895,44898],{},[122,44893,44894],{},"Proceso iterativo",[44896,44897],"iterar",{}," continuamente a medida que se descubren nuevos insights o se identifican problemas en los datos, ajustando el enfoque del EDA según sea necesario.",[33,44900,44901,44904],{},[122,44902,44903],{},"Documentar hallazgos",": Registrar los insights y descubrimientos del EDA para facilitar la toma de decisiones en las etapas posteriores del proyecto y para compartir con otros miembros del equipo.",[46,44906,44908],{"id":44907},"_5-feature-engineering","5. Feature engineering",[12,44910,44911],{},"El feature engineering es el proceso de crear nuevas características a partir de los datos originales para mejorar el rendimiento del modelo. Es el puente entre datos crudos sin estructurar y entradas listas para modelar. Esta etapa es crucial porque nos ayuda a:",[30,44913,44914,44920,44926,44932],{},[33,44915,44916,44919],{},[122,44917,44918],{},"Mejorar precisión",": Las características bien diseñadas pueden capturar patrones complejos en los datos que los modelos pueden aprovechar para hacer mejores predicciones.",[33,44921,44922,44925],{},[122,44923,44924],{},"Reducir sobreajuste",": Al crear características más relevantes, podemos ayudar a los modelos a generalizar mejor a datos no vistos, reduciendo el riesgo de sobreajuste.",[33,44927,44928,44931],{},[122,44929,44930],{},"Facilitar la interpretación",": Las características bien diseñadas pueden hacer que los modelos sean más interpretables, lo que es especialmente importante en aplicaciones donde la explicabilidad es crucial.",[33,44933,44934,44937],{},[122,44935,44936],{},"Aumentar la eficiencia",": Al reducir la dimensionalidad de los datos o crear características más informativas, podemos mejorar la eficiencia del entrenamiento del modelo.",[12,44939,44940],{},"Algunas técnicas fundamentales de feature engineering incluyen:",[323,44942,44944],{"id":44943},"transformaciones-numéricas","Transformaciones Numéricas",[30,44946,44947,44967],{},[33,44948,44949,44952,44953],{},[122,44950,44951],{},"Escalado",": Útil para modelos sensibles a magnitudes (Regresión, SVM, KNN, redes neuronales).",[30,44954,44955,44961,44964],{},[33,44956,44957,44958],{},"Min-Max Scaling: Lleva valores a rango ",[86,44959,44960],{},"0,1",[33,44962,44963],{},"Standardization (Z-score): media 0, desviación 1",[33,44965,44966],{},"Robust Scaling: usa mediana y rango intercuartílico (mejor con outliers)",[33,44968,44969,44972,44973],{},[122,44970,44971],{},"Transformaciones no lineales",": Cuando la relación no es lineal.",[30,44974,44975,44981,44987,44998],{},[33,44976,44977,44978],{},"Log transform: ",[145,44979,44980],{},"log(x)",[33,44982,44983,44984],{},"Raíz cuadrada: ",[145,44985,44986],{},"sqrt(x)",[33,44988,44989,44990,44993,44994,44997],{},"Box-Cox: ",[145,44991,44992],{},"((x + 1)^λ - 1) \u002F λ"," (para λ ≠ 0) o ",[145,44995,44996],{},"log(x + 1)"," (para λ = 0)",[33,44999,45000],{},"Yeo-Johnson: Similar a Box-Cox pero para datos con valores negativos\nMuy útil cuando hay distribuciones muy sesgadas.",[323,45002,45004],{"id":45003},"variables-categóricas","Variables Categóricas",[30,45006,45007],{},[33,45008,45009,45012],{},[122,45010,45011],{},"One-Hot Encoding",": Convierte categorías en columnas binarias.",[12,45014,45015],{},"Ejemplo:",[164,45017,45020],{"className":45018,"code":45019,"language":3141},[3139],"Color: [Rojo, Azul, Verde]\n\nPasan a ser:\n\nRojo  Azul  Verde\n1     0     0\n",[145,45021,45019],{"__ignoreMap":169},[30,45023,45024],{},[33,45025,45026,45029],{},[122,45027,45028],{},"Ordinal Encoding",": Cuando hay orden:",[164,45031,45034],{"className":45032,"code":45033,"language":3141},[3139],"Bajo \u003C Medio \u003C Alto\n",[145,45035,45033],{"__ignoreMap":169},[30,45037,45038],{},[33,45039,45040,45043],{},[122,45041,45042],{},"Target Encoding",": Reemplaza categoría por promedio del target:",[164,45045,45048],{"className":45046,"code":45047,"language":3141},[3139],"Ciudad → promedio de ventas\n",[145,45049,45047],{"__ignoreMap":169},[30,45051,45052],{},[33,45053,45054,45057],{},[122,45055,45056],{},"Frequency Encoding",": Reemplaza categoría por frecuencia de aparición.",[323,45059,45061],{"id":45060},"features-temporales","Features Temporales",[12,45063,45064],{},"Si se trabaja con fechas:",[30,45066,45067,45070,45073,45076,45079,45082,45085,45088],{},[33,45068,45069],{},"Año",[33,45071,45072],{},"Mes",[33,45074,45075],{},"Día",[33,45077,45078],{},"Día de la semana",[33,45080,45081],{},"Es fin de semana",[33,45083,45084],{},"Trimestre",[33,45086,45087],{},"Diferencia entre fechas",[33,45089,45090],{},"Tiempo desde último evento",[30,45092,45093],{},[33,45094,45095,45098],{},[122,45096,45097],{},"Codificación cíclica",": Para variables como hora o mes:",[164,45100,45103],{"className":45101,"code":45102,"language":3141},[3139],"sin(2π * hora \u002F 24)\ncos(2π * hora \u002F 24)\n",[145,45104,45102],{"__ignoreMap":169},[12,45106,45107],{},"Evita que 23 y 0 parezcan \"lejanos\".",[323,45109,45111],{"id":45110},"interacciones-entre-variables","Interacciones entre Variables",[12,45113,45114],{},"A veces la combinación importa más que la variable sola.",[30,45116,45117,45126,45137,45145],{},[33,45118,45119,45122,45123],{},[122,45120,45121],{},"Producto de variables",": ",[145,45124,45125],{},"x1 * x2",[33,45127,45128,45122,45131,93,45134],{},[122,45129,45130],{},"Polinomios",[145,45132,45133],{},"x^2",[145,45135,45136],{},"x^3",[33,45138,45139,45122,45142],{},[122,45140,45141],{},"Ratios",[145,45143,45144],{},"precio \u002F tamaño",[33,45146,45147,45122,45150],{},[122,45148,45149],{},"Diferencias",[145,45151,45152],{},"fecha_pago - fecha_registro",[12,45154,45155],{},"Muy usado en modelos lineales.",[323,45157,45159],{"id":45158},"binning-discretización","Binning (Discretización)",[12,45161,45162],{},"Convertir numéricos en categorías:",[30,45164,45165,45170,45175],{},[33,45166,45167],{},[122,45168,45169],{},"Binning uniforme",[33,45171,45172],{},[122,45173,45174],{},"Binning por cuantiles",[33,45176,45177],{},[122,45178,45179],{},"Binning basado en negocio",[12,45181,45015],{},[164,45183,45186],{"className":45184,"code":45185,"language":3141},[3139],"Edad → [0-18], [19-35], [36-60], 60+\n",[145,45187,45185],{"__ignoreMap":169},[323,45189,45191],{"id":45190},"manejo-de-outliers","Manejo de Outliers",[30,45193,45194,45199,45204,45209],{},[33,45195,45196],{},[122,45197,45198],{},"Clipping",[33,45200,45201],{},[122,45202,45203],{},"Winsorizing",[33,45205,45206],{},[122,45207,45208],{},"Log transform",[33,45210,45211,45122,45214],{},[122,45212,45213],{},"Crear feature binaria",[145,45215,45216],{},"es_outlier",[323,45218,45220],{"id":45219},"features-basadas-en-agrupaciones","Features basadas en agrupaciones",[12,45222,45223],{},"Muy potente en datasets transaccionales.",[12,45225,45015],{},[30,45227,45228,45231,45234,45237],{},[33,45229,45230],{},"Promedio de compras por usuario",[33,45232,45233],{},"Número de pedidos",[33,45235,45236],{},"Tiempo desde última compra",[33,45238,45239],{},"Máximo \u002F mínimo histórico",[323,45241,45243],{"id":45242},"feature-selection","Feature Selection",[12,45245,45246],{},"No todo es crear - también eliminar.",[30,45248,45249,45251,45254,45257,45260],{},[33,45250,43329],{},[33,45252,45253],{},"Mutual information",[33,45255,45256],{},"RFE",[33,45258,45259],{},"Lasso (L1)",[33,45261,45262],{},"Feature importance (árboles)",[12,45264,45265],{},"El feature engineering es una de las habilidades más valiosas en la ciencia de datos, ya que puede marcar la diferencia entre un modelo mediocre y uno excepcional.",[46,45267,45269],{"id":45268},"_6-entrenamiento-de-modelos","6. Entrenamiento de modelos",[12,45271,45272],{},"Una vez que los datos están preparados y las características han sido diseñadas, el siguiente paso es entrenar un modelo de aprendizaje automático.",[12,45274,45275],{},"En esta etapa, se selecciona un algoritmo de aprendizaje automático adecuado para el problema definido y se ajusta a los datos de entrenamiento. El proceso de entrenamiento implica alimentar el modelo con los datos y permitir que aprenda patrones y relaciones para hacer predicciones.",[12,45277,45278],{},"Lo primero que debemos tener en cuenta antes de empezar es la división de los datos (datasets) en conjuntos de entrenamiento, validación y prueba. Esto es crucial para evaluar el rendimiento del modelo de manera justa y evitar el sobreajuste:",[30,45280,45281,45287,45293],{},[33,45282,45283,45286],{},[122,45284,45285],{},"Conjunto de entrenamiento (Training Set) - (70-80%)",": Es el conjunto de datos que se utiliza para entrenar el modelo. El modelo aprende a partir de estos datos, ajustando sus parámetros para minimizar el error en las predicciones.",[33,45288,45289,45292],{},[122,45290,45291],{},"Conjunto de validación (Validation Set) - (10-15%)",": Es un conjunto de datos separado que se utiliza para ajustar los hiperparámetros del modelo y tomar decisiones sobre la arquitectura del modelo. El modelo no se entrena directamente con estos datos, pero se utilizan para evaluar su rendimiento durante el proceso de entrenamiento.",[33,45294,45295,45298],{},[122,45296,45297],{},"Conjunto de prueba (Test Set) - (10-15%)",": Es un conjunto de datos completamente separado que se utiliza para evaluar el rendimiento final del modelo después de que se ha completado el entrenamiento y la selección de hiperparámetros. Este conjunto no se utiliza en absoluto durante el proceso de entrenamiento o validación, lo que permite obtener una evaluación imparcial del modelo.",[16,45300,45301],{},[12,45302,45303],{},"Como dato, si utilizas agentes de IA para el desarrollo de software, una buena práctica es utilizar distintas sesiones o agentes para cada etapa del desarrollo, un agente para la generación de código, otro para la revisión y otro para las pruebas. En este otro caso ayuda a que la IA no sea autoreferencial y pueda detectar errores que un mismo agente podría pasar por alto.",[12,45305,45306],{},"Para el entrenamiento del modelo, se selecciona un algoritmo de aprendizaje automático adecuado para el tipo de problema que se está abordando (clasificación, regresión, clustering, etc.). Algunos ejemplos de algoritmos comunes, como ya los vimos son:",[30,45308,45309,45315,45321,45327,45333,45339],{},[33,45310,45311,45314],{},[122,45312,45313],{},"Regresión lineal",": Modelo simple para relaciones lineales, rápido, interpretable, pero limitado a relaciones lineales.",[33,45316,45317,45320],{},[122,45318,45319],{},"Árboles de decisión",": Modelos basados en reglas, fáciles de interpretar, pero propensos a sobreajuste.",[33,45322,45323,45326],{},[122,45324,45325],{},"Random Forest",": Conjunto de árboles de decisión, reduce sobreajuste, pero menos interpretable.",[33,45328,45329,45332],{},[122,45330,45331],{},"Gradient Boosting (XGBoost, LightGBM)",": Potente para datos tabulares, pero puede ser lento y propenso a sobreajuste si no se ajusta correctamente.",[33,45334,45335,45338],{},[122,45336,45337],{},"Redes neuronales",": Modelos inspirados en el cerebro, capaces de capturar relaciones complejas, pero requieren grandes cantidades de datos y son menos interpretables.",[33,45340,45341,45344],{},[122,45342,45343],{},"Support Vector Machines (SVM)",": Efectivo para problemas de clasificación, pero puede ser lento con grandes conjuntos de datos.",[46,45346,45348],{"id":45347},"_7-evaluación-del-modelo","7. Evaluación del modelo",[12,45350,45351],{},"Una vez que el modelo ha sido entrenado, es crucial evaluar su rendimiento utilizando el conjunto de validación y el conjunto de prueba. La evaluación del modelo implica medir su capacidad para hacer predicciones precisas y generalizar a datos no vistos.",[12,45353,45354],{},"Las métricas de evaluación varían según el tipo de problema que se esté abordando.",[12,45356,45357],{},"Para problemas de clasificación, algunas métricas comunes incluyen:",[30,45359,45360,45366,45372,45378],{},[33,45361,45362,45365],{},[122,45363,45364],{},"Precisión",": Proporción de predicciones correctas sobre el total de predicciones realizadas.",[33,45367,45368,45371],{},[122,45369,45370],{},"Recall (Sensibilidad)",": Proporción de verdaderos positivos sobre el total de positivos reales.",[33,45373,45374,45377],{},[122,45375,45376],{},"F1-score",": La media armónica de la precisión y el recall, útil cuando hay un desequilibrio entre clases.",[33,45379,45380,45382],{},[122,45381,1252],{},": Área bajo la curva ROC, que mide la capacidad del modelo para distinguir entre clases.",[12,45384,45385],{},"Para problemas de regresión, algunas métricas comunes incluyen:",[30,45387,45388,45394,45400],{},[33,45389,45390,45393],{},[122,45391,45392],{},"Error cuadrático medio (MSE)",": Promedio de los cuadrados de los errores entre las predicciones y los valores reales.",[33,45395,45396,45399],{},[122,45397,45398],{},"Error absoluto medio (MAE)",": Promedio de los valores absolutos de los errores entre las predicciones y los valores reales.",[33,45401,45402,45405],{},[122,45403,45404],{},"R² (Coeficiente de determinación)",": Proporción de la varianza en la variable dependiente que es predecible a partir de las variables independientes.",[323,45407,1951],{"id":45408},"matriz-de-confusión",[12,45410,45411],{},"Una herramienta útil para evaluar modelos de clasificación es la matriz de confusión, que muestra el número de verdaderos positivos, falsos positivos, verdaderos negativos y falsos negativos. Esto permite entender mejor el rendimiento del modelo y las áreas donde puede estar cometiendo errores.",[461,45413,45414,45426],{},[464,45415,45416],{},[467,45417,45418,45420,45423],{},[470,45419],{},[470,45421,45422],{},"Predicción Positiva",[470,45424,45425],{},"Predicción Negativa",[480,45427,45428,45441],{},[467,45429,45430,45435,45438],{},[485,45431,45432],{},[122,45433,45434],{},"Real Positivo",[485,45436,45437],{},"Verdaderos Positivos (TP)",[485,45439,45440],{},"Falsos Negativos (FN)",[467,45442,45443,45448,45451],{},[485,45444,45445],{},[122,45446,45447],{},"Real Negativo",[485,45449,45450],{},"Falsos Positivos (FP)",[485,45452,45453],{},"Verdaderos Negativos (TN)",[323,45455,40397],{"id":45456},"curva-roc",[12,45458,45459],{},"La curva ROC (Receiver Operating Characteristic) es una herramienta gráfica que muestra la relación entre la tasa de verdaderos positivos (TPR) y la tasa de falsos positivos (FPR) a medida que se varía el umbral de clasificación. El área bajo la curva ROC (AUC-ROC) es una métrica que mide la capacidad del modelo para distinguir entre clases, con un valor de 1 indicando un modelo perfecto y un valor de 0.5 indicando un modelo sin capacidad de discriminación.",[323,45461,40405],{"id":45462},"curva-precision-recall",[12,45464,45465],{},"La curva Precision-Recall es otra herramienta gráfica que muestra la relación entre la precisión y el recall a medida que se varía el umbral de clasificación. Esta curva es especialmente útil cuando hay un desequilibrio entre clases, ya que se enfoca en la capacidad del modelo para identificar correctamente la clase minoritaria.",[46,45467,45469],{"id":45468},"_8-implementación-y-despliegue","8. Implementación y despliegue",[12,45471,45472],{},"Una vez que el modelo ha sido entrenado y evaluado, el siguiente paso es implementarlo en un entorno de producción para que pueda ser utilizado por los usuarios finales o integrado en sistemas existentes. La implementación y el despliegue de modelos de aprendizaje automático pueden ser desafiantes debido a la necesidad de garantizar la escalabilidad, la seguridad y la mantenibilidad del modelo en un entorno de producción. Algunas consideraciones clave para la implementación y el despliegue de modelos de aprendizaje automático incluyen:",[30,45474,45475,45481,45487,45493,45499],{},[33,45476,45477,45480],{},[122,45478,45479],{},"APIs",": Exponer el modelo a través de una API RESTful o gRPC para que pueda ser consumido por otras aplicaciones o servicios.",[33,45482,45483,45486],{},[122,45484,45485],{},"Aplicaciones web",": Integrar el modelo en una aplicación web para que los usuarios puedan interactuar con él a través de una interfaz gráfica.",[33,45488,45489,45492],{},[122,45490,45491],{},"Integraciones con sistemas existentes",": Integrar el modelo en sistemas empresariales existentes, como CRM, ERP o sistemas de recomendación.",[33,45494,45495,45498],{},[122,45496,45497],{},"Contenedores y orquestación",": Utilizar contenedores (Docker) y herramientas de orquestación (Kubernetes) para facilitar el despliegue, la escalabilidad y la gestión del modelo en producción.",[33,45500,45501,45504],{},[122,45502,45503],{},"Monitoreo y mantenimiento",": Implementar sistemas de monitoreo para rastrear el rendimiento del modelo en producción, detectar posibles problemas y realizar actualizaciones o retrainings según sea necesario.",[46,45506,45508],{"id":45507},"_9-monitoreo-y-mantenimiento","9. Monitoreo y mantenimiento",[12,45510,45511],{},"Una vez que el modelo está en producción, es crucial monitorear su rendimiento de manera continua para asegurarse de que sigue siendo efectivo y relevante. El monitoreo del modelo implica rastrear métricas clave, detectar posibles problemas y realizar ajustes o retrainings según sea necesario. Algunos problemas que pueden surgir en esta etapa incluyen:",[30,45513,45514,45520,45526],{},[33,45515,45516,45519],{},[122,45517,45518],{},"Deriva de datos (Data Drift)",": Ocurre cuando la distribución de los datos de entrada cambia con el tiempo, lo que puede afectar negativamente el rendimiento del modelo. Es importante monitorear la distribución de los datos y realizar retrainings si se detecta una deriva significativa.",[33,45521,45522,45525],{},[122,45523,45524],{},"Deriva de concepto (Concept Drift)",": Ocurre cuando la relación entre las características y la variable objetivo cambia con el tiempo, lo que puede hacer que el modelo sea menos efectivo. Es importante monitorear el rendimiento del modelo y realizar ajustes o retrainings si se detecta una deriva de concepto.",[33,45527,45528,45531],{},[122,45529,45530],{},"Training-serving skew",": Ocurre cuando hay diferencias entre los datos utilizados para entrenar el modelo y los datos que se encuentran en producción, lo que puede afectar negativamente el rendimiento del modelo. Es importante asegurarse de que los datos de entrenamiento sean representativos de los datos en producción y realizar ajustes si se detecta un skew significativo.",[12,45533,45534],{},"Para lograr un buen monitoreo se pueden tomar algunas buenas prácticas, como:",[30,45536,45537,45543,45549,45555,45561,45567],{},[33,45538,45539,45542],{},[122,45540,45541],{},"Definir KPIs claros",": Establecer métricas clave de rendimiento (KPIs) para monitorear el modelo, como precisión, recall, F1-score, AUC-ROC, etc.",[33,45544,45545,45548],{},[122,45546,45547],{},"Implementar alertas",": Configurar alertas para notificar al equipo cuando el rendimiento del modelo cae por debajo de un umbral predefinido o cuando se detecta una deriva significativa.",[33,45550,45551,45554],{},[122,45552,45553],{},"Diversificar metricas",": Monitorear múltiples métricas para obtener una visión completa del rendimiento del modelo y detectar posibles problemas desde diferentes ángulos.",[33,45556,45557,45560],{},[122,45558,45559],{},"Automatizar retrainings",": Configurar procesos automatizados para realizar retrainings del modelo cuando se detecta una deriva significativa o cuando el rendimiento cae por debajo de un umbral predefinido.",[33,45562,45563,45566],{},[122,45564,45565],{},"Documentar cambios",": Mantener un registro de los cambios realizados en el modelo, como ajustes de hiperparámetros, cambios en los datos de entrenamiento, etc., para facilitar la trazabilidad y la comprensión de las decisiones tomadas.",[33,45568,45569,45572],{},[122,45570,45571],{},"Versionar modelos",": Utilizar herramientas de versionado de modelos para mantener un historial de las diferentes versiones del modelo y facilitar la gestión de cambios y actualizaciones.",[12,45574,45575],{},"Normalmente el proceso de mantenimiento lleva un proceso como el siguiente:",[117,45577,45578,45584,45590,45596,45602],{},[33,45579,45580,45583],{},[122,45581,45582],{},"Monitoreo continuo",": Rastrear el rendimiento del modelo en producción utilizando las métricas clave definidas.",[33,45585,45586,45589],{},[122,45587,45588],{},"Detección de problemas",": Identificar posibles problemas, como deriva de datos, deriva de concepto o training-serving skew, a través del monitoreo de métricas y alertas.",[33,45591,45592,45595],{},[122,45593,45594],{},"Análisis de causas",": Investigar las causas subyacentes de los problemas detectados, como cambios en la distribución de los datos, cambios en el comportamiento de los usuarios, etc.",[33,45597,45598,45601],{},[122,45599,45600],{},"Ajustes o retrainings",": Realizar ajustes en el modelo o realizar retrainings utilizando nuevos datos para abordar los problemas detectados y mejorar el rendimiento del modelo.",[33,45603,45604,45607],{},[122,45605,45606],{},"Validar y desplegar",": Validar el rendimiento del modelo ajustado o retrained utilizando el conjunto de validación y luego desplegar la nueva versión del modelo en producción.",[12,45609,45610],{},"Algunas herramientas populares para el monitoreo y mantenimiento de modelos de aprendizaje automático incluyen:",[30,45612,45613,45619,45625,45631],{},[33,45614,45615,45618],{},[122,45616,45617],{},"Prometheus",": Sistema de monitoreo y alerta de código abierto que se puede utilizar para rastrear métricas de rendimiento del modelo en producción.",[33,45620,45621,45624],{},[122,45622,45623],{},"Grafana",": Plataforma de visualización de datos que se puede integrar con Prometheus para crear paneles de control personalizados para monitorear el rendimiento del modelo.",[33,45626,45627,45630],{},[122,45628,45629],{},"MLflow",": Plataforma de código abierto para la gestión del ciclo de vida de los modelos de aprendizaje automático, que incluye funcionalidades para el monitoreo y mantenimiento de modelos en producción.",[33,45632,45633,45636],{},[122,45634,45635],{},"Evidently AI",": Evidently AI es una plataforma de código abierto y basada en la nube para evaluar, probar y supervisar sistemas de IA y aprendizaje automático.",[43,45638],{},[46,45640,45642],{"id":45641},"caso-práctico-predicción-de-abandono-churn-en-una-fintech","Caso práctico: Predicción de abandono (churn) en una fintech",[12,45644,45645],{},"Haremos un recorrido por un caso práctico simulado de un proyecto de aprendizaje automático para predecir el abandono (churn) en una fintech de suscripciones digitales. En este caso ilustraremos el conocimiento que tenemos hasta ahora sobre el flujo de un proyecto de aprendizaje automático.",[12,45647,45648],{},[122,45649,45650],{},"Contexto del negocio",[12,45652,45653],{},"Una fintech de suscripciones digitales tiene:",[30,45655,45656,45661,45667,45673],{},[33,45657,45658],{},[122,45659,45660],{},"120,000 usuarios activos",[33,45662,45663,45664],{},"Suscripción mensual promedio: ",[122,45665,45666],{},"$25",[33,45668,45669,45670],{},"Ingreso mensual recurrente (MRR): ",[122,45671,45672],{},"$3,000,000",[33,45674,45675,45676],{},"Tasa de abandono mensual (churn): ",[122,45677,45678],{},"8%",[12,45680,45681],{},"Eso significa que cada mes:",[164,45683,45686],{"className":45684,"code":45685,"language":3141},[3139],"120,000 x 8% = 9,600 usuarios cancelan\n",[145,45687,45685],{"__ignoreMap":169},[12,45689,45690],{},"Pérdida mensual estimada:",[164,45692,45695],{"className":45693,"code":45694,"language":3141},[3139],"9,600 x $25 = $240,000\n",[145,45696,45694],{"__ignoreMap":169},[12,45698,45699,45700,45703],{},"La empresa quiere reducir el churn al ",[122,45701,45702],{},"6%",", lo que implicaría ahorrar:",[164,45705,45708],{"className":45706,"code":45707,"language":3141},[3139],"2% x 120,000 x $25 = $60,000 mensuales\n",[145,45709,45707],{"__ignoreMap":169},[12,45711,45712,45713,45716],{},"El objetivo del proyecto de Machine Learning es ",[122,45714,45715],{},"identificar usuarios con alta probabilidad de cancelar en los próximos 30 días",", para enviarles una campaña de retención personalizada.",[323,45718,45720],{"id":45719},"definición-del-problema","Definición del problema",[30,45722,45723],{},[33,45724,45725],{},[122,45726,44680],{},[12,45728,45729],{},"Reducir la tasa de abandono mensual del 8% al 6%.",[30,45731,45732],{},[33,45733,45734],{},[122,45735,44686],{},[12,45737,45738,162],{},[145,45739,45740],{},"churn_30d",[164,45742,45745],{"className":45743,"code":45744,"language":3141},[3139],"1 - Cancela en los próximos 30 días\n0 - No cancela\n",[145,45746,45744],{"__ignoreMap":169},[30,45748,45749],{},[33,45750,45751],{},[122,45752,44692],{},[12,45754,45755],{},"Clasificación binaria.",[30,45757,45758],{},[33,45759,45760],{},[122,45761,45762],{},"Métrica de negocio clave",[12,45764,45765],{},"No basta con accuracy (es decir , la tasa de acierto general). Lo importante es:",[164,45767,45770],{"className":45768,"code":45769,"language":3141},[3139],"Recall de la clase churn\nROI de la campaña de retención\n",[145,45771,45769],{"__ignoreMap":169},[12,45773,45774],{},"¿Por qué? Porque queremos identificar correctamente a los usuarios que van a cancelar (recall) y asegurarnos de que la campaña de retención sea rentable (ROI).",[323,45776,45778],{"id":45777},"recopilación-de-datos","Recopilación de datos",[12,45780,45781],{},"Se recopilaron datos de:",[30,45783,45784],{},[33,45785,45786],{},[122,45787,45788],{},"Fuentes internas",[164,45790,45793],{"className":45791,"code":45792,"language":3141},[3139],"* Historial de pagos\n* Frecuencia de uso de la app\n* Tiempo desde último login\n* Tickets de soporte\n* Tipo de plan\n* Método de pago\n* Historial de fallos de pago\n",[145,45794,45792],{"__ignoreMap":169},[30,45796,45797],{},[33,45798,45799],{},[122,45800,45801],{},"Volumen de datos",[164,45803,45806],{"className":45804,"code":45805,"language":3141},[3139],"* 18 meses de histórico\n* 1.5 millones de registros mensuales\n* Dataset final: **95,000 usuarios únicos** con historial completo\n",[145,45807,45805],{"__ignoreMap":169},[323,45809,45811],{"id":45810},"preprocesamiento","Preprocesamiento",[12,45813,45814],{},"Problemas detectados:",[164,45816,45819],{"className":45817,"code":45818,"language":3141},[3139],"* 7% valores nulos en \"último login\"\n* 3% registros duplicados\n* Variables categóricas con alta cardinalidad (ciudades)\n",[145,45820,45818],{"__ignoreMap":169},[12,45822,45823],{},"Acciones tomadas:",[164,45825,45828],{"className":45826,"code":45827,"language":3141},[3139],"* Imputación con mediana para variables numéricas\n* Eliminación de duplicados\n* Agrupación de ciudades poco frecuentes como \"Otras\"\n",[145,45829,45827],{"__ignoreMap":169},[12,45831,45832,45833],{},"Tiempo invertido en esta etapa: ",[122,45834,45835],{},"72% del proyecto",[323,45837,45838],{"id":325},"Análisis Exploratorio",[12,45840,45841],{},"Hallazgos clave:",[30,45843,45844],{},[33,45845,45846],{},[122,45847,45848],{},"Insight 1",[12,45850,45851],{},"Usuarios que no inician sesión en 14 días tienen:",[164,45853,45856],{"className":45854,"code":45855,"language":3141},[3139],"* 22% probabilidad de churn\n  vs\n* 4% en usuarios activos recientes\n",[145,45857,45855],{"__ignoreMap":169},[30,45859,45860],{},[33,45861,45862],{},[122,45863,45864],{},"Insight 2",[12,45866,45867],{},"Usuarios con más de 2 fallos de pago en 60 días:",[164,45869,45872],{"className":45870,"code":45871,"language":3141},[3139],"* 35% probabilidad de churn\n",[145,45873,45871],{"__ignoreMap":169},[30,45875,45876],{},[33,45877,45878],{},[122,45879,45880],{},"Insight 3",[12,45882,45883],{},"Usuarios que abrieron más de 3 tickets de soporte:",[164,45885,45888],{"className":45886,"code":45887,"language":3141},[3139],"* 18% churn\n* Principal causa: problemas técnicos\n",[145,45889,45887],{"__ignoreMap":169},[12,45891,45892],{},"Esto nos cambia el enfoque: no solo es un problema de retención, sino también de experiencia del usuario y soporte técnico. Estos datos nos están diciendo que los usuarios que tienen problemas técnicos o dificultades para usar la app son mucho más propensos a cancelar, lo que sugiere que una campaña de retención efectiva también debería abordar estos problemas y mejorar la experiencia del usuario.",[323,45894,44531],{"id":45895},"feature-engineering",[12,45897,45898],{},"Se crearon variables como:",[30,45900,45901,45907,45913,45919,45925,45931,45937],{},[33,45902,45903,45906],{},[145,45904,45905],{},"dias_desde_ultimo_login",": Es la cantidad de días desde la última vez que el usuario inició sesión en la aplicación. Esta variable es importante porque, como se descubrió en el análisis exploratorio, los usuarios que no inician sesión en un período prolongado tienen una mayor probabilidad de cancelar su suscripción.",[33,45908,45909,45912],{},[145,45910,45911],{},"numero_fallos_pago_60d",": Es el número de fallos de pago que un usuario ha tenido en los últimos 60 días. Como se descubrió en el EDA, los usuarios con más de 2 fallos de pago en este período tienen una probabilidad significativamente mayor de cancelar su suscripción.",[33,45914,45915,45918],{},[145,45916,45917],{},"promedio_uso_semanal",": Es el promedio de uso de la aplicación por semana. Esta variable puede ayudar a capturar el nivel de compromiso del usuario con la aplicación, lo que puede ser un indicador importante de su probabilidad de cancelar.",[33,45920,45921,45924],{},[145,45922,45923],{},"tiempo_cliente_meses",": Usuarios que han sido clientes por más tiempo pueden tener una menor probabilidad de cancelar.",[33,45926,45927,45930],{},[145,45928,45929],{},"tickets_soporte_90d",": Es el número de tickets de soporte que un usuario ha abierto en los últimos 90 días. Dado que se descubrió que los usuarios que abren más de 3 tickets de soporte tienen una mayor probabilidad de cancelar, esta variable puede ser un indicador importante del riesgo de churn.",[33,45932,45933,45936],{},[145,45934,45935],{},"ratio_fallos_pago = fallos \u002F intentos",": Este ratio puede ser un indicador más preciso del riesgo de churn relacionado con los problemas de pago, ya que tiene en cuenta tanto el número de fallos como el número total de intentos de pago.",[33,45938,45939,45940,45943],{},"Variable binaria: ",[145,45941,45942],{},"es_usuario_nuevo (\u003C3 meses)",": Los usuarios nuevos pueden tener un riesgo diferente de churn en comparación con los usuarios más antiguos, por lo que esta variable puede ayudar a capturar esa diferencia.",[12,45945,45946],{},"También se creó:",[164,45948,45951],{"className":45949,"code":45950,"language":3141},[3139],"riesgo_inactividad = dias_desde_ultimo_login x (1 \u002F promedio_uso)\n",[145,45952,45950],{"__ignoreMap":169},[12,45954,45955,45956,45959],{},"Esta variable compuesta puede ser un indicador poderoso del riesgo de churn, ya que combina la información sobre la inactividad del usuario (días desde el último login) con su nivel de compromiso (promedio de uso semanal). Un valor alto de ",[145,45957,45958],{},"riesgo_inactividad"," indicaría que un usuario no ha iniciado sesión en mucho tiempo y tiene un bajo nivel de uso, lo que podría ser un fuerte indicador de que está en riesgo de cancelar su suscripción.",[323,45961,45963],{"id":45962},"entrenamiento-de-modelos","Entrenamiento de modelos",[12,45965,45966],{},"Se dividieron datos:",[30,45968,45969,45972,45975],{},[33,45970,45971],{},"75% entrenamiento",[33,45973,45974],{},"15% validación",[33,45976,45977],{},"10% prueba",[12,45979,45980],{},"Se probaron:",[461,45982,45983,45994],{},[464,45984,45985],{},[467,45986,45987,45989,45991],{},[470,45988,472],{},[470,45990,1252],{},[470,45992,45993],{},"Recall churn",[480,45995,45996,46006,46016,46026],{},[467,45997,45998,46000,46003],{},[485,45999,1439],{},[485,46001,46002],{},"0.76",[485,46004,46005],{},"0.58",[467,46007,46008,46010,46013],{},[485,46009,45325],{},[485,46011,46012],{},"0.84",[485,46014,46015],{},"0.71",[467,46017,46018,46021,46024],{},[485,46019,46020],{},"XGBoost",[485,46022,46023],{},"0.87",[485,46025,1894],{},[467,46027,46028,46031,46034],{},[485,46029,46030],{},"Red neuronal",[485,46032,46033],{},"0.85",[485,46035,46036],{},"0.73",[12,46038,46039,46040,46042],{},"Aunque XGBoost tenía mejor métrica, se eligió ",[122,46041,45325],{}," inicialmente porque:",[30,46044,46045,46048,46051],{},[33,46046,46047],{},"Era más interpretable",[33,46049,46050],{},"Menor riesgo de sobreajuste",[33,46052,46053],{},"Más fácil de mantener",[12,46055,46056,46057,61],{},"Esto es clave: ",[122,46058,46059],{},"la mejor métrica no siempre es la mejor decisión de negocio",[323,46061,46063],{"id":46062},"evaluación","Evaluación",[12,46065,46066],{},"En el conjunto de prueba:",[30,46068,46069,46072,46075],{},[33,46070,46071],{},"9% churn real",[33,46073,46074],{},"Modelo detectó 76% de los churners",[33,46076,46077],{},"Falsos positivos: 18%",[12,46079,46080],{},"Simulación:",[12,46082,46083],{},"Se decide intervenir solo en usuarios con probabilidad > 0.65.",[12,46085,46086],{},"Usuarios marcados como \"riesgo alto\": 11,000",[12,46088,46089],{},"De esos:",[30,46091,46092,46095],{},[33,46093,46094],{},"6,800 realmente iban a cancelar",[33,46096,46097],{},"4,200 eran falsos positivos",[12,46099,46100],{},"Costo campaña:",[164,46102,46105],{"className":46103,"code":46104,"language":3141},[3139],"11,000 x $2 = $22,000\n",[145,46106,46104],{"__ignoreMap":169},[12,46108,46109],{},"Clientes salvados (tasa de éxito campaña 40%):",[164,46111,46114],{"className":46112,"code":46113,"language":3141},[3139],"6,800 x 40% = 2,720 clientes retenidos\n",[145,46115,46113],{"__ignoreMap":169},[12,46117,46118],{},"Ingreso recuperado mensual:",[164,46120,46123],{"className":46121,"code":46122,"language":3141},[3139],"2,720 x $25 = $68,000\n",[145,46124,46122],{"__ignoreMap":169},[12,46126,46127],{},"ROI mensual:",[164,46129,46132],{"className":46130,"code":46131,"language":3141},[3139],"$68,000 - $22,000 = $46,000 beneficio neto\n",[145,46133,46131],{"__ignoreMap":169},[12,46135,46136],{},"Objetivo cumplido.",[323,46138,46140],{"id":46139},"implementación","Implementación",[12,46142,46143],{},"El modelo se desplegó como:",[30,46145,46146,46149,46152,46155],{},[33,46147,46148],{},"API REST en FastAPI",[33,46150,46151],{},"Contenedor Docker",[33,46153,46154],{},"Job nocturno que recalcula riesgo diario",[33,46156,46157],{},"Integración con CRM para disparar campañas automáticas",[12,46159,46160],{},"Tiempo de inferencia por usuario: 12 ms.",[323,46162,46164],{"id":46163},"monitoreo-en-producción","Monitoreo en producción",[12,46166,46167],{},"Después de 4 meses:",[12,46169,46170],{},"La tasa de churn volvió a subir a 7.4%.",[12,46172,46173],{},"Se detectó:",[30,46175,46176,46179],{},[33,46177,46178],{},"Nuevo competidor con descuento agresivo",[33,46180,46181],{},"Cambio en comportamiento de usuarios jóvenes",[12,46183,46184,46185,46188],{},"Se identificó ",[122,46186,46187],{},"concept drift",", es decir, el modelo ya no estaba capturando correctamente los patrones de churn debido a cambios en el mercado y en el comportamiento de los usuarios.",[12,46190,46191],{},"Se hizo retraining con datos recientes.",[12,46193,46194],{},"Nuevo modelo:",[30,46196,46197,46200],{},[33,46198,46199],{},"Mejoró recall a 81%",[33,46201,46202],{},"Redujo churn nuevamente a 6.2%",[43,46204],{},[12,46206,46207,46208,46211],{},"¿Que podemos aprender de este caso? Primero, ",[122,46209,46210],{},"el modelo no era el centro - el proceso sí",". El éxito no vino de un algoritmo sofisticado, sino de un proceso bien ejecutado que incluyó:",[30,46213,46214,46217,46220],{},[33,46215,46216],{},"Buen EDA",[33,46218,46219],{},"Buen feature engineering",[33,46221,46222],{},"Definir correctamente la métrica de negocio",[12,46224,46225,46226,46229],{},"Segundo, accuracy no era la métrica correcta, aqui ya nos importaba ponerle ojo al ROI, porque no solo queríamos un modelo que fuera bueno en métricas técnicas, sino que también generara un impacto positivo en el negocio.\nY es que como ya hemos dicho, ",[122,46227,46228],{},"el modelo es parte de un sistema"," que incluye otros componentes como marketing, CRM, infraestructura, monitoreo y retraining. El éxito del proyecto depende de la integración efectiva de todos estos componentes, no solo del modelo en sí.",[12,46231,46232,46233,46236],{},"Tercero, el proyecto nunca termina, ",[122,46234,46235],{},"es un ciclo continuo",", el monitoreo y mantenimiento son tan importantes como el entrenamiento inicial, porque el entorno cambia, los usuarios cambian, el mercado cambia, y el modelo debe adaptarse para seguir siendo efectivo.",[43,46238],{},{"title":169,"searchDepth":205,"depth":205,"links":46240},[46241,46242,46243,46244,46247,46257,46258,46263,46264,46265],{"id":44669,"depth":192,"text":44670},{"id":44732,"depth":192,"text":44733},{"id":44768,"depth":192,"text":44769},{"id":44778,"depth":192,"text":44779,"children":46245},[46246],{"id":44874,"depth":205,"text":44875},{"id":44907,"depth":192,"text":44908,"children":46248},[46249,46250,46251,46252,46253,46254,46255,46256],{"id":44943,"depth":205,"text":44944},{"id":45003,"depth":205,"text":45004},{"id":45060,"depth":205,"text":45061},{"id":45110,"depth":205,"text":45111},{"id":45158,"depth":205,"text":45159},{"id":45190,"depth":205,"text":45191},{"id":45219,"depth":205,"text":45220},{"id":45242,"depth":205,"text":45243},{"id":45268,"depth":192,"text":45269},{"id":45347,"depth":192,"text":45348,"children":46259},[46260,46261,46262],{"id":45408,"depth":205,"text":1951},{"id":45456,"depth":205,"text":40397},{"id":45462,"depth":205,"text":40405},{"id":45468,"depth":192,"text":45469},{"id":45507,"depth":192,"text":45508},{"id":45641,"depth":192,"text":45642,"children":46266},[46267,46268,46269,46270,46271,46272,46273,46274,46275],{"id":45719,"depth":205,"text":45720},{"id":45777,"depth":205,"text":45778},{"id":45810,"depth":205,"text":45811},{"id":325,"depth":205,"text":45838},{"id":45895,"depth":205,"text":44531},{"id":45962,"depth":205,"text":45963},{"id":46062,"depth":205,"text":46063},{"id":46139,"depth":205,"text":46140},{"id":46163,"depth":205,"text":46164},"2026-04-18","\u002Fblog\u002Fworkflow-machine-learning-projects\u002Fshared\u002Fworkflow.webp",{},"\u002Fblog\u002Fblog\u002Fworkflow-machine-learning-projects",{"title":40512,"description":44601},{"loc":46282,"priority":2259,"lastmod":32998},"\u002Fes\u002Fblog\u002Fworkflow-machine-learning-projects","workflow-machine-learning-projects","blog\u002Fblog\u002Fworkflow-machine-learning-projects","Descubre el flujo típico de un proyecto de aprendizaje automático, desde la recopilación de datos hasta la implementación del modelo, y aprende sobre las mejores prácticas y desafíos comunes en el campo de la ciencia de datos.",[2264,2265,46287,46288],"proyectos de ml","flujo de trabajo","xv9kRIO15qctzwjUxpyUFEGm9xbXKBLn-h5OM8xxsJM",{"id":46291,"title":44608,"author":7,"body":46292,"date":63535,"description":46296,"extension":2250,"image":63536,"lastmod":63535,"meta":63537,"navigation":208,"order":205,"path":63538,"seo":63539,"sitemap":63540,"slug":63542,"stem":63543,"summary":63544,"tags":63545,"__hash__":63550},"content_es\u002Fblog\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations.md",{"type":9,"value":46293,"toc":63519},[46294,46297,46304,46306,46308,46312,46315,46335,46339,46342,46879,46955,46958,46972,46975,46980,46982,46986,47195,47209,47214,47216,47220,47223,47249,47252,47257,47259,47263,47273,47276,47284,47287,47290,47762,47764,48386,48448,48553,48652,48661,48664,48735,48774,49026,49029,49367,49370,49776,49778,50057,50060,50360,50363,50739,50781,50786,50964,51548,51786,51788,52097,52100,52136,52143,52328,52330,52569,52711,53286,53523,53525,53833,53836,54437,54794,54982,55106,55208,55211,55369,55376,55778,55780,55999,56004,56593,56598,56840,57259,57264,57563,57599,57607,57609,57612,57618,57621,57624,57644,57649,57652,57771,57896,57903,57912,58362,58371,58564,58569,59190,59192,59732,59735,59740,59743,59932,59934,60489,60543,60546,60689,60696,60838,61139,61151,61154,61468,61471,62099,62101,62378,62381,62392,62395,62404,62407,62412,62687,62692,62987,62990,62994,62998,63004,63030,63034,63059,63064,63068,63075,63078,63181,63183,63300,63303,63401,63404,63413,63427,63430,63457,63461,63464],[12,46295,46296],{},"Continuamos aprendiendo sobre Machine Learning, en esta ocasión nos adentraremos en los diferentes paradigmas de aprendizaje automático y los fundamentos matemáticos que sustentan estos modelos.",[12,46298,19786,46299],{},[22,46300,46303],{"href":46301,"rel":46302},"https:\u002F\u002Fderas.dev\u002Fes\u002Fblog\u002Fmachine-learning-fundamentals",[26],"Fundamentos de Aprendizaje Automático",[40,46305],{},[43,46307],{},[46,46309,46311],{"id":46310},"paradigmas-de-aprendizaje-automático","Paradigmas de Aprendizaje Automático",[12,46313,46314],{},"El machine learning NO comienza con algoritmos. EL proceso comienza con una comprension profunda del problema antes de seleccionar cualquier técnica o modelo, además de tres criterios fundamentales para determinar que enfoque  y técnicas podemos usar:",[30,46316,46317,46323,46329],{},[33,46318,46319,46322],{},[122,46320,46321],{},"Naturaleza de los datos",": Analizar el tipo de datos disponibles (etiquetados o no etiquetados) y su estructura.",[33,46324,46325,46328],{},[122,46326,46327],{},"Tipo de salida esperada",": ¿Qué tipo de resultado esperamos obtener? ¿Una\ncategoría, un número continuo, o una estructura oculta?",[33,46330,46331,46334],{},[122,46332,46333],{},"Interacción con el entorno",": ¿El modelo necesita aprender a través de la interacción con un entorno dinámico?",[323,46336,46338],{"id":46337},"aprendizaje-supervisado","Aprendizaje Supervisado",[12,46340,46341],{},"El aprendizaje supervisado requiere un conjunto de datos donde cada ejemplo de entrada X está asociado con una etiqueta o salida Y. El objetivo del modelo es aprender una función que mapee las entradas a las salidas correctas.",[12,46343,46344,46345,46736,46737,46807,46808,46878],{},"En función de esto, el conjunto de datos de entrenamiento se representa como un conjunto de pares ",[86,46346,46348,46430],{"className":46347},[955],[86,46349,46351],{"className":46350},[959],[961,46352,46353],{"xmlns":963},[965,46354,46355,46427],{},[968,46356,46357,46359,46361,46367,46369,46375,46377,46379,46381,46387,46389,46395,46397,46399,46401,46403,46405,46407,46409,46415,46417,46423,46425],{},[3191,46358,4089],{"stretchy":3295},[3191,46360,243],{"stretchy":3295},[6849,46362,46363,46365],{},[974,46364,3189],{},[978,46366,802],{},[3191,46368,291],{"separator":990},[6849,46370,46371,46373],{},[974,46372,5464],{},[978,46374,802],{},[3191,46376,867],{"stretchy":3295},[3191,46378,291],{"separator":990},[3191,46380,243],{"stretchy":3295},[6849,46382,46383,46385],{},[974,46384,3189],{},[978,46386,980],{},[3191,46388,291],{"separator":990},[6849,46390,46391,46393],{},[974,46392,5464],{},[978,46394,980],{},[3191,46396,867],{"stretchy":3295},[3191,46398,291],{"separator":990},[974,46400,61],{"mathvariant":4327},[974,46402,61],{"mathvariant":4327},[974,46404,61],{"mathvariant":4327},[3191,46406,291],{"separator":990},[3191,46408,243],{"stretchy":3295},[6849,46410,46411,46413],{},[974,46412,3189],{},[974,46414,6896],{},[3191,46416,291],{"separator":990},[6849,46418,46419,46421],{},[974,46420,5464],{},[974,46422,6896],{},[3191,46424,867],{"stretchy":3295},[3191,46426,4117],{"stretchy":3295},[982,46428,46429],{"encoding":984},"\\{(x_1, y_1), (x_2, y_2), ..., (x_n, y_n)\\}",[86,46431,46433],{"className":46432,"ariaHidden":990},[989],[86,46434,46436,46439,46442,46482,46485,46488,46528,46531,46534,46537,46540,46580,46583,46586,46626,46629,46632,46635,46638,46641,46644,46647,46687,46690,46693,46733],{"className":46435},[994],[86,46437],{"className":46438,"style":3794},[998],[86,46440,4379],{"className":46441},[3320],[86,46443,46445,46448],{"className":46444},[1003],[86,46446,3189],{"className":46447},[1003,1007],[86,46449,46451],{"className":46450},[1012],[86,46452,46454,46474],{"className":46453},[1016,3836],[86,46455,46457,46471],{"className":46456},[1020],[86,46458,46460],{"className":46459,"style":6984},[1024],[86,46461,46462,46465],{"style":6987},[86,46463],{"className":46464,"style":1032},[1031],[86,46466,46468],{"className":46467},[1036,1037,1038,1039],[86,46469,802],{"className":46470},[1003,1039],[86,46472,3963],{"className":46473},[3962],[86,46475,46477],{"className":46476},[1020],[86,46478,46480],{"className":46479,"style":7006},[1024],[86,46481],{},[86,46483,291],{"className":46484},[4158],[86,46486],{"className":46487,"style":4162},[3221],[86,46489,46491,46494],{"className":46490},[1003],[86,46492,5464],{"className":46493,"style":8109},[1003,1007],[86,46495,46497],{"className":46496},[1012],[86,46498,46500,46520],{"className":46499},[1016,3836],[86,46501,46503,46517],{"className":46502},[1020],[86,46504,46506],{"className":46505,"style":6984},[1024],[86,46507,46508,46511],{"style":20440},[86,46509],{"className":46510,"style":1032},[1031],[86,46512,46514],{"className":46513},[1036,1037,1038,1039],[86,46515,802],{"className":46516},[1003,1039],[86,46518,3963],{"className":46519},[3962],[86,46521,46523],{"className":46522},[1020],[86,46524,46526],{"className":46525,"style":7006},[1024],[86,46527],{},[86,46529,867],{"className":46530},[3356],[86,46532,291],{"className":46533},[4158],[86,46535],{"className":46536,"style":4162},[3221],[86,46538,243],{"className":46539},[3320],[86,46541,46543,46546],{"className":46542},[1003],[86,46544,3189],{"className":46545},[1003,1007],[86,46547,46549],{"className":46548},[1012],[86,46550,46552,46572],{"className":46551},[1016,3836],[86,46553,46555,46569],{"className":46554},[1020],[86,46556,46558],{"className":46557,"style":6984},[1024],[86,46559,46560,46563],{"style":6987},[86,46561],{"className":46562,"style":1032},[1031],[86,46564,46566],{"className":46565},[1036,1037,1038,1039],[86,46567,980],{"className":46568},[1003,1039],[86,46570,3963],{"className":46571},[3962],[86,46573,46575],{"className":46574},[1020],[86,46576,46578],{"className":46577,"style":7006},[1024],[86,46579],{},[86,46581,291],{"className":46582},[4158],[86,46584],{"className":46585,"style":4162},[3221],[86,46587,46589,46592],{"className":46588},[1003],[86,46590,5464],{"className":46591,"style":8109},[1003,1007],[86,46593,46595],{"className":46594},[1012],[86,46596,46598,46618],{"className":46597},[1016,3836],[86,46599,46601,46615],{"className":46600},[1020],[86,46602,46604],{"className":46603,"style":6984},[1024],[86,46605,46606,46609],{"style":20440},[86,46607],{"className":46608,"style":1032},[1031],[86,46610,46612],{"className":46611},[1036,1037,1038,1039],[86,46613,980],{"className":46614},[1003,1039],[86,46616,3963],{"className":46617},[3962],[86,46619,46621],{"className":46620},[1020],[86,46622,46624],{"className":46623,"style":7006},[1024],[86,46625],{},[86,46627,867],{"className":46628},[3356],[86,46630,291],{"className":46631},[4158],[86,46633],{"className":46634,"style":4162},[3221],[86,46636,4572],{"className":46637},[1003],[86,46639,291],{"className":46640},[4158],[86,46642],{"className":46643,"style":4162},[3221],[86,46645,243],{"className":46646},[3320],[86,46648,46650,46653],{"className":46649},[1003],[86,46651,3189],{"className":46652},[1003,1007],[86,46654,46656],{"className":46655},[1012],[86,46657,46659,46679],{"className":46658},[1016,3836],[86,46660,46662,46676],{"className":46661},[1020],[86,46663,46665],{"className":46664,"style":7171},[1024],[86,46666,46667,46670],{"style":6987},[86,46668],{"className":46669,"style":1032},[1031],[86,46671,46673],{"className":46672},[1036,1037,1038,1039],[86,46674,6896],{"className":46675},[1003,1007,1039],[86,46677,3963],{"className":46678},[3962],[86,46680,46682],{"className":46681},[1020],[86,46683,46685],{"className":46684,"style":7006},[1024],[86,46686],{},[86,46688,291],{"className":46689},[4158],[86,46691],{"className":46692,"style":4162},[3221],[86,46694,46696,46699],{"className":46695},[1003],[86,46697,5464],{"className":46698,"style":8109},[1003,1007],[86,46700,46702],{"className":46701},[1012],[86,46703,46705,46725],{"className":46704},[1016,3836],[86,46706,46708,46722],{"className":46707},[1020],[86,46709,46711],{"className":46710,"style":7171},[1024],[86,46712,46713,46716],{"style":20440},[86,46714],{"className":46715,"style":1032},[1031],[86,46717,46719],{"className":46718},[1036,1037,1038,1039],[86,46720,6896],{"className":46721},[1003,1007,1039],[86,46723,3963],{"className":46724},[3962],[86,46726,46728],{"className":46727},[1020],[86,46729,46731],{"className":46730,"style":7006},[1024],[86,46732],{},[86,46734,4597],{"className":46735},[3356],", donde ",[86,46738,46740,46758],{"className":46739},[955],[86,46741,46743],{"className":46742},[959],[961,46744,46745],{"xmlns":963},[965,46746,46747,46755],{},[968,46748,46749],{},[6849,46750,46751,46753],{},[974,46752,3189],{},[974,46754,7285],{},[982,46756,46757],{"encoding":984},"x_i",[86,46759,46761],{"className":46760,"ariaHidden":990},[989],[86,46762,46764,46767],{"className":46763},[994],[86,46765],{"className":46766,"style":21327},[998],[86,46768,46770,46773],{"className":46769},[1003],[86,46771,3189],{"className":46772},[1003,1007],[86,46774,46776],{"className":46775},[1012],[86,46777,46779,46799],{"className":46778},[1016,3836],[86,46780,46782,46796],{"className":46781},[1020],[86,46783,46785],{"className":46784,"style":7559},[1024],[86,46786,46787,46790],{"style":6987},[86,46788],{"className":46789,"style":1032},[1031],[86,46791,46793],{"className":46792},[1036,1037,1038,1039],[86,46794,7285],{"className":46795},[1003,1007,1039],[86,46797,3963],{"className":46798},[3962],[86,46800,46802],{"className":46801},[1020],[86,46803,46805],{"className":46804,"style":7006},[1024],[86,46806],{}," es la entrada y ",[86,46809,46811,46829],{"className":46810},[955],[86,46812,46814],{"className":46813},[959],[961,46815,46816],{"xmlns":963},[965,46817,46818,46826],{},[968,46819,46820],{},[6849,46821,46822,46824],{},[974,46823,5464],{},[974,46825,7285],{},[982,46827,46828],{"encoding":984},"y_i",[86,46830,46832],{"className":46831,"ariaHidden":990},[989],[86,46833,46835,46838],{"className":46834},[994],[86,46836],{"className":46837,"style":16339},[998],[86,46839,46841,46844],{"className":46840},[1003],[86,46842,5464],{"className":46843,"style":8109},[1003,1007],[86,46845,46847],{"className":46846},[1012],[86,46848,46850,46870],{"className":46849},[1016,3836],[86,46851,46853,46867],{"className":46852},[1020],[86,46854,46856],{"className":46855,"style":7559},[1024],[86,46857,46858,46861],{"style":20440},[86,46859],{"className":46860,"style":1032},[1031],[86,46862,46864],{"className":46863},[1036,1037,1038,1039],[86,46865,7285],{"className":46866},[1003,1007,1039],[86,46868,3963],{"className":46869},[3962],[86,46871,46873],{"className":46872},[1020],[86,46874,46876],{"className":46875,"style":7006},[1024],[86,46877],{}," es la etiqueta correspondiente. El modelo de aprendizaje supervisado intenta encontrar una función f que pueda predecir la salida Y a partir de la entrada X:",[86,46880,46882],{"className":46881},[3173],[86,46883,46885,46907],{"className":46884},[955],[86,46886,46888],{"className":46887},[959],[961,46889,46890],{"xmlns":963,"display":3182},[965,46891,46892,46904],{},[968,46893,46894,46896,46898,46900,46902],{},[974,46895,6178],{},[3191,46897,162],{},[974,46899,4624],{},[3191,46901,4667],{},[974,46903,4631],{},[982,46905,46906],{"encoding":984},"f: X \\rightarrow Y",[86,46908,46910,46928,46946],{"className":46909,"ariaHidden":990},[989],[86,46911,46913,46916,46919,46922,46925],{"className":46912},[994],[86,46914],{"className":46915,"style":4888},[998],[86,46917,6178],{"className":46918,"style":6231},[1003,1007],[86,46920],{"className":46921,"style":3222},[3221],[86,46923,162],{"className":46924},[3226],[86,46926],{"className":46927,"style":3222},[3221],[86,46929,46931,46934,46937,46940,46943],{"className":46930},[994],[86,46932],{"className":46933,"style":3575},[998],[86,46935,4624],{"className":46936,"style":4685},[1003,1007],[86,46938],{"className":46939,"style":3222},[3221],[86,46941,4667],{"className":46942},[3226],[86,46944],{"className":46945,"style":3222},[3221],[86,46947,46949,46952],{"className":46948},[994],[86,46950],{"className":46951,"style":3575},[998],[86,46953,4631],{"className":46954,"style":5012},[1003,1007],[12,46956,46957],{},"Dependiendo del tipo de salida, el aprendizaje supervisado se puede dividir en:",[30,46959,46960,46966],{},[33,46961,46962,46965],{},[122,46963,46964],{},"Clasificación",": Cuando la salida Y es una categoría discreta (es decir, un valor categórico). Por ejemplo, clasificar si una imagen contiene un gato o un perro, si un número es par o impar, o si un correo electrónico es spam o no spam.",[33,46967,46968,46971],{},[122,46969,46970],{},"Regresión",": Cuando la salida Y es un valor continuo (es decir, un número real). Por ejemplo, hacer una predicción de las ventas futuras basándose en datos históricos, predecir el precio de una casa basándose en sus características, o estimar la temperatura de una ciudad en función de factores climáticos.",[12,46973,46974],{},"Una regla que nos puede servir para detectar si un problema es de clasificación o regresión es, si la respuesta es \"¿Cuánto?\" entonces es un problema de regresión, pero si la respuesta es \"¿Cuál?\" entonces es un problema de clasificación.",[16,46976,46977],{},[12,46978,46979],{},"Objetivo: Aprender una función que mapee las entradas a las salidas correctas, minimizando el error entre las predicciones del modelo.",[43,46981],{},[323,46983,46985],{"id":46984},"aprendizaje-no-supervisado","Aprendizaje No Supervisado",[12,46987,46988,46989,47194],{},"En el aprendizaje no supervisado, el modelo recibe solo las entradas X sin etiquetas asociadas: ",[86,46990,46992,47038],{"className":46991},[955],[86,46993,46995],{"className":46994},[959],[961,46996,46997],{"xmlns":963},[965,46998,46999,47035],{},[968,47000,47001,47003,47009,47011,47017,47019,47021,47023,47025,47027,47033],{},[3191,47002,4089],{"stretchy":3295},[6849,47004,47005,47007],{},[974,47006,3189],{},[978,47008,802],{},[3191,47010,291],{"separator":990},[6849,47012,47013,47015],{},[974,47014,3189],{},[978,47016,980],{},[3191,47018,291],{"separator":990},[974,47020,61],{"mathvariant":4327},[974,47022,61],{"mathvariant":4327},[974,47024,61],{"mathvariant":4327},[3191,47026,291],{"separator":990},[6849,47028,47029,47031],{},[974,47030,3189],{},[974,47032,6896],{},[3191,47034,4117],{"stretchy":3295},[982,47036,47037],{"encoding":984},"\\{x_1, x_2, ..., x_n\\}",[86,47039,47041],{"className":47040,"ariaHidden":990},[989],[86,47042,47044,47047,47050,47090,47093,47096,47136,47139,47142,47145,47148,47151,47191],{"className":47043},[994],[86,47045],{"className":47046,"style":3794},[998],[86,47048,4089],{"className":47049},[3320],[86,47051,47053,47056],{"className":47052},[1003],[86,47054,3189],{"className":47055},[1003,1007],[86,47057,47059],{"className":47058},[1012],[86,47060,47062,47082],{"className":47061},[1016,3836],[86,47063,47065,47079],{"className":47064},[1020],[86,47066,47068],{"className":47067,"style":6984},[1024],[86,47069,47070,47073],{"style":6987},[86,47071],{"className":47072,"style":1032},[1031],[86,47074,47076],{"className":47075},[1036,1037,1038,1039],[86,47077,802],{"className":47078},[1003,1039],[86,47080,3963],{"className":47081},[3962],[86,47083,47085],{"className":47084},[1020],[86,47086,47088],{"className":47087,"style":7006},[1024],[86,47089],{},[86,47091,291],{"className":47092},[4158],[86,47094],{"className":47095,"style":4162},[3221],[86,47097,47099,47102],{"className":47098},[1003],[86,47100,3189],{"className":47101},[1003,1007],[86,47103,47105],{"className":47104},[1012],[86,47106,47108,47128],{"className":47107},[1016,3836],[86,47109,47111,47125],{"className":47110},[1020],[86,47112,47114],{"className":47113,"style":6984},[1024],[86,47115,47116,47119],{"style":6987},[86,47117],{"className":47118,"style":1032},[1031],[86,47120,47122],{"className":47121},[1036,1037,1038,1039],[86,47123,980],{"className":47124},[1003,1039],[86,47126,3963],{"className":47127},[3962],[86,47129,47131],{"className":47130},[1020],[86,47132,47134],{"className":47133,"style":7006},[1024],[86,47135],{},[86,47137,291],{"className":47138},[4158],[86,47140],{"className":47141,"style":4162},[3221],[86,47143,4572],{"className":47144},[1003],[86,47146,291],{"className":47147},[4158],[86,47149],{"className":47150,"style":4162},[3221],[86,47152,47154,47157],{"className":47153},[1003],[86,47155,3189],{"className":47156},[1003,1007],[86,47158,47160],{"className":47159},[1012],[86,47161,47163,47183],{"className":47162},[1016,3836],[86,47164,47166,47180],{"className":47165},[1020],[86,47167,47169],{"className":47168,"style":7171},[1024],[86,47170,47171,47174],{"style":6987},[86,47172],{"className":47173,"style":1032},[1031],[86,47175,47177],{"className":47176},[1036,1037,1038,1039],[86,47178,6896],{"className":47179},[1003,1007,1039],[86,47181,3963],{"className":47182},[3962],[86,47184,47186],{"className":47185},[1020],[86,47187,47189],{"className":47188,"style":7006},[1024],[86,47190],{},[86,47192,4117],{"className":47193},[3356],". Lo que se busca es encontrar patrones o estructuras subyacentes en los datos.\nAlgunos ejemplos de técnicas de aprendizaje no supervisado incluyen:",[30,47196,47197,47203],{},[33,47198,47199,47202],{},[122,47200,47201],{},"Clustering",": Agrupar datos similares en clusters. Por ejemplo, segmentar clientes en grupos basados en sus comportamientos de compra.",[33,47204,47205,47208],{},[122,47206,47207],{},"Reducción de Dimensionalidad",": Reducir el número de variables en un conjunto de datos mientras se conserva la mayor cantidad de información posible. Por ejemplo, usar PCA (Análisis de Componentes Principales) para visualizar datos en 2D o 3D.",[16,47210,47211],{},[12,47212,47213],{},"Objetivo: Encontrar patrones o estructuras subyacentes en los datos sin etiquetas, como agrupamientos o representaciones más compactas.",[43,47215],{},[323,47217,47219],{"id":47218},"aprendizaje-por-refuerzo","Aprendizaje por Refuerzo",[12,47221,47222],{},"El aprendizaje por refuerzo se basa en la idea de que un agente aprende a tomar decisiones mediante la interacción con un entorno. El agente recibe recompensas o castigos en función de las acciones que toma, y su objetivo es maximizar la recompensa acumulada a lo largo del tiempo.\nEn este paradigma, el agente aprende una política de acción que le permite tomar decisiones óptimas en función del estado actual del entorno. Un ejemplo clásico de aprendizaje por refuerzo es el juego de ajedrez, donde el agente aprende a jugar mejor a medida que juega más partidas y recibe retroalimentación sobre sus movimientos.",[117,47224,47225,47231,47237,47243],{},[33,47226,47227,47230],{},[122,47228,47229],{},"Agente",": El sistema que toma decisiones.",[33,47232,47233,47236],{},[122,47234,47235],{},"Entorno",": El mundo con el que el agente interactúa.",[33,47238,47239,47242],{},[122,47240,47241],{},"Recompensa",": La retroalimentación que el agente recibe después de tomar una acción.",[33,47244,47245,47248],{},[122,47246,47247],{},"Política",": La estrategia que el agente sigue para tomar decisiones.",[12,47250,47251],{},"Sus aplicaciones incluyen juegos, robótica y sistemas de recomendación.",[16,47253,47254],{},[12,47255,47256],{},"Objetivo: Aprender a tomar decisiones óptimas mediante la interacción con un entorno, maximizando la recompensa acumulada a lo largo del tiempo.",[43,47258],{},[46,47260,47262],{"id":47261},"fundamentos-matemáticos","Fundamentos Matemáticos",[12,47264,47265,47266,47269,47270,61],{},"Es importante entender que el aprendizaje automático se basa en conceptos de álgebra lineal, cálculo, probabilidad y estadística. Estos fundamentos son esenciales para comprender cómo ",[122,47267,47268],{},"funcionan"," los modelos y cómo se ",[122,47271,47272],{},"optimizan",[323,47274,46970],{"id":47275},"regresión",[16,47277,47278],{},[12,47279,47280,47281,61],{},"Utilizado en el ",[122,47282,47283],{},"aprendizaje supervisado",[12,47285,47286],{},"¿Qué es un problema de regresión? Es un tipo de problema donde el objetivo es predecir un valor continuo encontrando la mejor línea (o plano) que se ajuste a los datos. Ya hablamos de ejemplos de aplicación como el cálculo de precios, ventas, etc.",[12,47288,47289],{},"La forma mas simple de regresión es la regresión lineal, que se puede expresar matemáticamente como:",[86,47291,47293],{"className":47292},[3173],[86,47294,47296,47373],{"className":47295},[955],[86,47297,47299],{"className":47298},[959],[961,47300,47301],{"xmlns":963,"display":3182},[965,47302,47303,47370],{},[968,47304,47305,47307,47309,47315,47317,47323,47329,47331,47337,47343,47345,47347,47349,47351,47353,47359,47365,47367],{},[974,47306,5464],{},[3191,47308,258],{},[6849,47310,47311,47313],{},[974,47312,42473],{},[978,47314,2553],{},[3191,47316,6565],{},[6849,47318,47319,47321],{},[974,47320,42473],{},[978,47322,802],{},[6849,47324,47325,47327],{},[974,47326,3189],{},[978,47328,802],{},[3191,47330,6565],{},[6849,47332,47333,47335],{},[974,47334,42473],{},[978,47336,980],{},[6849,47338,47339,47341],{},[974,47340,3189],{},[978,47342,980],{},[3191,47344,6565],{},[974,47346,61],{"mathvariant":4327},[974,47348,61],{"mathvariant":4327},[974,47350,61],{"mathvariant":4327},[3191,47352,6565],{},[6849,47354,47355,47357],{},[974,47356,42473],{},[974,47358,12],{},[6849,47360,47361,47363],{},[974,47362,3189],{},[974,47364,12],{},[3191,47366,6565],{},[974,47368,47369],{},"ϵ",[982,47371,47372],{"encoding":984},"y = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_p x_p + \\epsilon",[86,47374,47376,47394,47449,47544,47639,47657,47753],{"className":47375,"ariaHidden":990},[989],[86,47377,47379,47382,47385,47388,47391],{"className":47378},[994],[86,47380],{"className":47381,"style":16339},[998],[86,47383,5464],{"className":47384,"style":8109},[1003,1007],[86,47386],{"className":47387,"style":3222},[3221],[86,47389,258],{"className":47390},[3226],[86,47392],{"className":47393,"style":3222},[3221],[86,47395,47397,47400,47440,47443,47446],{"className":47396},[994],[86,47398],{"className":47399,"style":4888},[998],[86,47401,47403,47406],{"className":47402},[1003],[86,47404,42473],{"className":47405,"style":42538},[1003,1007],[86,47407,47409],{"className":47408},[1012],[86,47410,47412,47432],{"className":47411},[1016,3836],[86,47413,47415,47429],{"className":47414},[1020],[86,47416,47418],{"className":47417,"style":6984},[1024],[86,47419,47420,47423],{"style":42553},[86,47421],{"className":47422,"style":1032},[1031],[86,47424,47426],{"className":47425},[1036,1037,1038,1039],[86,47427,2553],{"className":47428},[1003,1039],[86,47430,3963],{"className":47431},[3962],[86,47433,47435],{"className":47434},[1020],[86,47436,47438],{"className":47437,"style":7006},[1024],[86,47439],{},[86,47441],{"className":47442,"style":5012},[3221],[86,47444,6565],{"className":47445},[5016],[86,47447],{"className":47448,"style":5012},[3221],[86,47450,47452,47455,47495,47535,47538,47541],{"className":47451},[994],[86,47453],{"className":47454,"style":4888},[998],[86,47456,47458,47461],{"className":47457},[1003],[86,47459,42473],{"className":47460,"style":42538},[1003,1007],[86,47462,47464],{"className":47463},[1012],[86,47465,47467,47487],{"className":47466},[1016,3836],[86,47468,47470,47484],{"className":47469},[1020],[86,47471,47473],{"className":47472,"style":6984},[1024],[86,47474,47475,47478],{"style":42553},[86,47476],{"className":47477,"style":1032},[1031],[86,47479,47481],{"className":47480},[1036,1037,1038,1039],[86,47482,802],{"className":47483},[1003,1039],[86,47485,3963],{"className":47486},[3962],[86,47488,47490],{"className":47489},[1020],[86,47491,47493],{"className":47492,"style":7006},[1024],[86,47494],{},[86,47496,47498,47501],{"className":47497},[1003],[86,47499,3189],{"className":47500},[1003,1007],[86,47502,47504],{"className":47503},[1012],[86,47505,47507,47527],{"className":47506},[1016,3836],[86,47508,47510,47524],{"className":47509},[1020],[86,47511,47513],{"className":47512,"style":6984},[1024],[86,47514,47515,47518],{"style":6987},[86,47516],{"className":47517,"style":1032},[1031],[86,47519,47521],{"className":47520},[1036,1037,1038,1039],[86,47522,802],{"className":47523},[1003,1039],[86,47525,3963],{"className":47526},[3962],[86,47528,47530],{"className":47529},[1020],[86,47531,47533],{"className":47532,"style":7006},[1024],[86,47534],{},[86,47536],{"className":47537,"style":5012},[3221],[86,47539,6565],{"className":47540},[5016],[86,47542],{"className":47543,"style":5012},[3221],[86,47545,47547,47550,47590,47630,47633,47636],{"className":47546},[994],[86,47548],{"className":47549,"style":4888},[998],[86,47551,47553,47556],{"className":47552},[1003],[86,47554,42473],{"className":47555,"style":42538},[1003,1007],[86,47557,47559],{"className":47558},[1012],[86,47560,47562,47582],{"className":47561},[1016,3836],[86,47563,47565,47579],{"className":47564},[1020],[86,47566,47568],{"className":47567,"style":6984},[1024],[86,47569,47570,47573],{"style":42553},[86,47571],{"className":47572,"style":1032},[1031],[86,47574,47576],{"className":47575},[1036,1037,1038,1039],[86,47577,980],{"className":47578},[1003,1039],[86,47580,3963],{"className":47581},[3962],[86,47583,47585],{"className":47584},[1020],[86,47586,47588],{"className":47587,"style":7006},[1024],[86,47589],{},[86,47591,47593,47596],{"className":47592},[1003],[86,47594,3189],{"className":47595},[1003,1007],[86,47597,47599],{"className":47598},[1012],[86,47600,47602,47622],{"className":47601},[1016,3836],[86,47603,47605,47619],{"className":47604},[1020],[86,47606,47608],{"className":47607,"style":6984},[1024],[86,47609,47610,47613],{"style":6987},[86,47611],{"className":47612,"style":1032},[1031],[86,47614,47616],{"className":47615},[1036,1037,1038,1039],[86,47617,980],{"className":47618},[1003,1039],[86,47620,3963],{"className":47621},[3962],[86,47623,47625],{"className":47624},[1020],[86,47626,47628],{"className":47627,"style":7006},[1024],[86,47629],{},[86,47631],{"className":47632,"style":5012},[3221],[86,47634,6565],{"className":47635},[5016],[86,47637],{"className":47638,"style":5012},[3221],[86,47640,47642,47645,47648,47651,47654],{"className":47641},[994],[86,47643],{"className":47644,"style":14141},[998],[86,47646,4572],{"className":47647},[1003],[86,47649],{"className":47650,"style":5012},[3221],[86,47652,6565],{"className":47653},[5016],[86,47655],{"className":47656,"style":5012},[3221],[86,47658,47660,47664,47704,47744,47747,47750],{"className":47659},[994],[86,47661],{"className":47662,"style":47663},[998],"height:0.9805em;vertical-align:-0.2861em;",[86,47665,47667,47670],{"className":47666},[1003],[86,47668,42473],{"className":47669,"style":42538},[1003,1007],[86,47671,47673],{"className":47672},[1012],[86,47674,47676,47696],{"className":47675},[1016,3836],[86,47677,47679,47693],{"className":47678},[1020],[86,47680,47682],{"className":47681,"style":7171},[1024],[86,47683,47684,47687],{"style":42553},[86,47685],{"className":47686,"style":1032},[1031],[86,47688,47690],{"className":47689},[1036,1037,1038,1039],[86,47691,12],{"className":47692},[1003,1007,1039],[86,47694,3963],{"className":47695},[3962],[86,47697,47699],{"className":47698},[1020],[86,47700,47702],{"className":47701,"style":10443},[1024],[86,47703],{},[86,47705,47707,47710],{"className":47706},[1003],[86,47708,3189],{"className":47709},[1003,1007],[86,47711,47713],{"className":47712},[1012],[86,47714,47716,47736],{"className":47715},[1016,3836],[86,47717,47719,47733],{"className":47718},[1020],[86,47720,47722],{"className":47721,"style":7171},[1024],[86,47723,47724,47727],{"style":6987},[86,47725],{"className":47726,"style":1032},[1031],[86,47728,47730],{"className":47729},[1036,1037,1038,1039],[86,47731,12],{"className":47732},[1003,1007,1039],[86,47734,3963],{"className":47735},[3962],[86,47737,47739],{"className":47738},[1020],[86,47740,47742],{"className":47741,"style":10443},[1024],[86,47743],{},[86,47745],{"className":47746,"style":5012},[3221],[86,47748,6565],{"className":47749},[5016],[86,47751],{"className":47752,"style":5012},[3221],[86,47754,47756,47759],{"className":47755},[994],[86,47757],{"className":47758,"style":7401},[998],[86,47760,47369],{"className":47761},[1003,1007],[12,47763,3273],{},[30,47765,47766,47797,47996,48127,48325],{},[33,47767,47768,47796],{},[86,47769,47771,47784],{"className":47770},[955],[86,47772,47774],{"className":47773},[959],[961,47775,47776],{"xmlns":963},[965,47777,47778,47782],{},[968,47779,47780],{},[974,47781,5464],{},[982,47783,5464],{"encoding":984},[86,47785,47787],{"className":47786,"ariaHidden":990},[989],[86,47788,47790,47793],{"className":47789},[994],[86,47791],{"className":47792,"style":16339},[998],[86,47794,5464],{"className":47795,"style":8109},[1003,1007]," es la variable dependiente (lo que queremos predecir).",[33,47798,47799,47995],{},[86,47800,47802,47844],{"className":47801},[955],[86,47803,47805],{"className":47804},[959],[961,47806,47807],{"xmlns":963},[965,47808,47809,47841],{},[968,47810,47811,47817,47819,47825,47827,47829,47831,47833,47835],{},[6849,47812,47813,47815],{},[974,47814,3189],{},[978,47816,802],{},[3191,47818,291],{"separator":990},[6849,47820,47821,47823],{},[974,47822,3189],{},[978,47824,980],{},[3191,47826,291],{"separator":990},[974,47828,61],{"mathvariant":4327},[974,47830,61],{"mathvariant":4327},[974,47832,61],{"mathvariant":4327},[3191,47834,291],{"separator":990},[6849,47836,47837,47839],{},[974,47838,3189],{},[974,47840,12],{},[982,47842,47843],{"encoding":984},"x_1, x_2, ..., x_p",[86,47845,47847],{"className":47846,"ariaHidden":990},[989],[86,47848,47850,47854,47894,47897,47900,47940,47943,47946,47949,47952,47955],{"className":47849},[994],[86,47851],{"className":47852,"style":47853},[998],"height:0.7167em;vertical-align:-0.2861em;",[86,47855,47857,47860],{"className":47856},[1003],[86,47858,3189],{"className":47859},[1003,1007],[86,47861,47863],{"className":47862},[1012],[86,47864,47866,47886],{"className":47865},[1016,3836],[86,47867,47869,47883],{"className":47868},[1020],[86,47870,47872],{"className":47871,"style":6984},[1024],[86,47873,47874,47877],{"style":6987},[86,47875],{"className":47876,"style":1032},[1031],[86,47878,47880],{"className":47879},[1036,1037,1038,1039],[86,47881,802],{"className":47882},[1003,1039],[86,47884,3963],{"className":47885},[3962],[86,47887,47889],{"className":47888},[1020],[86,47890,47892],{"className":47891,"style":7006},[1024],[86,47893],{},[86,47895,291],{"className":47896},[4158],[86,47898],{"className":47899,"style":4162},[3221],[86,47901,47903,47906],{"className":47902},[1003],[86,47904,3189],{"className":47905},[1003,1007],[86,47907,47909],{"className":47908},[1012],[86,47910,47912,47932],{"className":47911},[1016,3836],[86,47913,47915,47929],{"className":47914},[1020],[86,47916,47918],{"className":47917,"style":6984},[1024],[86,47919,47920,47923],{"style":6987},[86,47921],{"className":47922,"style":1032},[1031],[86,47924,47926],{"className":47925},[1036,1037,1038,1039],[86,47927,980],{"className":47928},[1003,1039],[86,47930,3963],{"className":47931},[3962],[86,47933,47935],{"className":47934},[1020],[86,47936,47938],{"className":47937,"style":7006},[1024],[86,47939],{},[86,47941,291],{"className":47942},[4158],[86,47944],{"className":47945,"style":4162},[3221],[86,47947,4572],{"className":47948},[1003],[86,47950,291],{"className":47951},[4158],[86,47953],{"className":47954,"style":4162},[3221],[86,47956,47958,47961],{"className":47957},[1003],[86,47959,3189],{"className":47960},[1003,1007],[86,47962,47964],{"className":47963},[1012],[86,47965,47967,47987],{"className":47966},[1016,3836],[86,47968,47970,47984],{"className":47969},[1020],[86,47971,47973],{"className":47972,"style":7171},[1024],[86,47974,47975,47978],{"style":6987},[86,47976],{"className":47977,"style":1032},[1031],[86,47979,47981],{"className":47980},[1036,1037,1038,1039],[86,47982,12],{"className":47983},[1003,1007,1039],[86,47985,3963],{"className":47986},[3962],[86,47988,47990],{"className":47989},[1020],[86,47991,47993],{"className":47992,"style":10443},[1024],[86,47994],{}," son las variables independientes (las características).",[33,47997,47998,48068,48069,48097,48098,48126],{},[86,47999,48001,48019],{"className":48000},[955],[86,48002,48004],{"className":48003},[959],[961,48005,48006],{"xmlns":963},[965,48007,48008,48016],{},[968,48009,48010],{},[6849,48011,48012,48014],{},[974,48013,42473],{},[978,48015,2553],{},[982,48017,48018],{"encoding":984},"\\beta_0",[86,48020,48022],{"className":48021,"ariaHidden":990},[989],[86,48023,48025,48028],{"className":48024},[994],[86,48026],{"className":48027,"style":4888},[998],[86,48029,48031,48034],{"className":48030},[1003],[86,48032,42473],{"className":48033,"style":42538},[1003,1007],[86,48035,48037],{"className":48036},[1012],[86,48038,48040,48060],{"className":48039},[1016,3836],[86,48041,48043,48057],{"className":48042},[1020],[86,48044,48046],{"className":48045,"style":6984},[1024],[86,48047,48048,48051],{"style":42553},[86,48049],{"className":48050,"style":1032},[1031],[86,48052,48054],{"className":48053},[1036,1037,1038,1039],[86,48055,2553],{"className":48056},[1003,1039],[86,48058,3963],{"className":48059},[3962],[86,48061,48063],{"className":48062},[1020],[86,48064,48066],{"className":48065,"style":7006},[1024],[86,48067],{}," es la intersección (el valor de ",[86,48070,48072,48085],{"className":48071},[955],[86,48073,48075],{"className":48074},[959],[961,48076,48077],{"xmlns":963},[965,48078,48079,48083],{},[968,48080,48081],{},[974,48082,5464],{},[982,48084,5464],{"encoding":984},[86,48086,48088],{"className":48087,"ariaHidden":990},[989],[86,48089,48091,48094],{"className":48090},[994],[86,48092],{"className":48093,"style":16339},[998],[86,48095,5464],{"className":48096,"style":8109},[1003,1007]," cuando todas las ",[86,48099,48101,48114],{"className":48100},[955],[86,48102,48104],{"className":48103},[959],[961,48105,48106],{"xmlns":963},[965,48107,48108,48112],{},[968,48109,48110],{},[974,48111,3189],{},[982,48113,3189],{"encoding":984},[86,48115,48117],{"className":48116,"ariaHidden":990},[989],[86,48118,48120,48123],{"className":48119},[994],[86,48121],{"className":48122,"style":7401},[998],[86,48124,3189],{"className":48125},[1003,1007]," son 0).",[33,48128,48129,48324],{},[86,48130,48132,48174],{"className":48131},[955],[86,48133,48135],{"className":48134},[959],[961,48136,48137],{"xmlns":963},[965,48138,48139,48171],{},[968,48140,48141,48147,48149,48155,48157,48159,48161,48163,48165],{},[6849,48142,48143,48145],{},[974,48144,42473],{},[978,48146,802],{},[3191,48148,291],{"separator":990},[6849,48150,48151,48153],{},[974,48152,42473],{},[978,48154,980],{},[3191,48156,291],{"separator":990},[974,48158,61],{"mathvariant":4327},[974,48160,61],{"mathvariant":4327},[974,48162,61],{"mathvariant":4327},[3191,48164,291],{"separator":990},[6849,48166,48167,48169],{},[974,48168,42473],{},[974,48170,12],{},[982,48172,48173],{"encoding":984},"\\beta_1, \\beta_2, ..., \\beta_p",[86,48175,48177],{"className":48176,"ariaHidden":990},[989],[86,48178,48180,48183,48223,48226,48229,48269,48272,48275,48278,48281,48284],{"className":48179},[994],[86,48181],{"className":48182,"style":47663},[998],[86,48184,48186,48189],{"className":48185},[1003],[86,48187,42473],{"className":48188,"style":42538},[1003,1007],[86,48190,48192],{"className":48191},[1012],[86,48193,48195,48215],{"className":48194},[1016,3836],[86,48196,48198,48212],{"className":48197},[1020],[86,48199,48201],{"className":48200,"style":6984},[1024],[86,48202,48203,48206],{"style":42553},[86,48204],{"className":48205,"style":1032},[1031],[86,48207,48209],{"className":48208},[1036,1037,1038,1039],[86,48210,802],{"className":48211},[1003,1039],[86,48213,3963],{"className":48214},[3962],[86,48216,48218],{"className":48217},[1020],[86,48219,48221],{"className":48220,"style":7006},[1024],[86,48222],{},[86,48224,291],{"className":48225},[4158],[86,48227],{"className":48228,"style":4162},[3221],[86,48230,48232,48235],{"className":48231},[1003],[86,48233,42473],{"className":48234,"style":42538},[1003,1007],[86,48236,48238],{"className":48237},[1012],[86,48239,48241,48261],{"className":48240},[1016,3836],[86,48242,48244,48258],{"className":48243},[1020],[86,48245,48247],{"className":48246,"style":6984},[1024],[86,48248,48249,48252],{"style":42553},[86,48250],{"className":48251,"style":1032},[1031],[86,48253,48255],{"className":48254},[1036,1037,1038,1039],[86,48256,980],{"className":48257},[1003,1039],[86,48259,3963],{"className":48260},[3962],[86,48262,48264],{"className":48263},[1020],[86,48265,48267],{"className":48266,"style":7006},[1024],[86,48268],{},[86,48270,291],{"className":48271},[4158],[86,48273],{"className":48274,"style":4162},[3221],[86,48276,4572],{"className":48277},[1003],[86,48279,291],{"className":48280},[4158],[86,48282],{"className":48283,"style":4162},[3221],[86,48285,48287,48290],{"className":48286},[1003],[86,48288,42473],{"className":48289,"style":42538},[1003,1007],[86,48291,48293],{"className":48292},[1012],[86,48294,48296,48316],{"className":48295},[1016,3836],[86,48297,48299,48313],{"className":48298},[1020],[86,48300,48302],{"className":48301,"style":7171},[1024],[86,48303,48304,48307],{"style":42553},[86,48305],{"className":48306,"style":1032},[1031],[86,48308,48310],{"className":48309},[1036,1037,1038,1039],[86,48311,12],{"className":48312},[1003,1007,1039],[86,48314,3963],{"className":48315},[3962],[86,48317,48319],{"className":48318},[1020],[86,48320,48322],{"className":48321,"style":10443},[1024],[86,48323],{}," son los coeficientes que representan la influencia de cada característica en la variable dependiente.",[33,48326,48327,48356,48357,48385],{},[86,48328,48330,48344],{"className":48329},[955],[86,48331,48333],{"className":48332},[959],[961,48334,48335],{"xmlns":963},[965,48336,48337,48341],{},[968,48338,48339],{},[974,48340,47369],{},[982,48342,48343],{"encoding":984},"\\epsilon",[86,48345,48347],{"className":48346,"ariaHidden":990},[989],[86,48348,48350,48353],{"className":48349},[994],[86,48351],{"className":48352,"style":7401},[998],[86,48354,47369],{"className":48355},[1003,1007]," es el valor de error o ruido, que representa la variabilidad no explicada por el modelo, es decir, lo que afecta a ",[86,48358,48360,48373],{"className":48359},[955],[86,48361,48363],{"className":48362},[959],[961,48364,48365],{"xmlns":963},[965,48366,48367,48371],{},[968,48368,48369],{},[974,48370,5464],{},[982,48372,5464],{"encoding":984},[86,48374,48376],{"className":48375,"ariaHidden":990},[989],[86,48377,48379,48382],{"className":48378},[994],[86,48380],{"className":48381,"style":16339},[998],[86,48383,5464],{"className":48384,"style":8109},[1003,1007]," pero no está incluido en las variables independientes.",[12,48387,48388,48389,48418,48419,48447],{},"El objetivo del modelo de regresión es encontrar los valores de los coeficientes ",[86,48390,48392,48406],{"className":48391},[955],[86,48393,48395],{"className":48394},[959],[961,48396,48397],{"xmlns":963},[965,48398,48399,48403],{},[968,48400,48401],{},[974,48402,42473],{},[982,48404,48405],{"encoding":984},"\\beta",[86,48407,48409],{"className":48408,"ariaHidden":990},[989],[86,48410,48412,48415],{"className":48411},[994],[86,48413],{"className":48414,"style":4888},[998],[86,48416,42473],{"className":48417,"style":42538},[1003,1007]," que minimicen la diferencia entre las predicciones del modelo y los valores reales de ",[86,48420,48422,48435],{"className":48421},[955],[86,48423,48425],{"className":48424},[959],[961,48426,48427],{"xmlns":963},[965,48428,48429,48433],{},[968,48430,48431],{},[974,48432,5464],{},[982,48434,5464],{"encoding":984},[86,48436,48438],{"className":48437,"ariaHidden":990},[989],[86,48439,48441,48444],{"className":48440},[994],[86,48442],{"className":48443,"style":16339},[998],[86,48445,5464],{"className":48446,"style":8109},[1003,1007],". Esto se puede lograr utilizando técnicas como el método de mínimos cuadrados.",[12,48449,1243,48450,48453,48454,48492,48493,48522,48523,48552],{},[122,48451,48452],{},"intercepto"," se representa como el primer elemento del vector de coeficientes ",[86,48455,48457,48472],{"className":48456},[955],[86,48458,48460],{"className":48459},[959],[961,48461,48462],{"xmlns":963},[965,48463,48464,48469],{},[968,48465,48466],{},[974,48467,42473],{"mathvariant":48468},"bold-italic",[982,48470,48471],{"encoding":984},"\\boldsymbol{\\beta}",[86,48473,48475],{"className":48474,"ariaHidden":990},[989],[86,48476,48478,48481],{"className":48477},[994],[86,48479],{"className":48480,"style":4888},[998],[86,48482,48484],{"className":48483},[1003],[86,48485,48487],{"className":48486},[1003],[86,48488,42473],{"className":48489,"style":48491},[1003,48490],"boldsymbol","margin-right:0.034em;",", y es el valor de ",[86,48494,48496,48510],{"className":48495},[955],[86,48497,48499],{"className":48498},[959],[961,48500,48501],{"xmlns":963},[965,48502,48503,48507],{},[968,48504,48505],{},[974,48506,5464],{"mathvariant":19893},[982,48508,48509],{"encoding":984},"\\mathbf{y}",[86,48511,48513],{"className":48512,"ariaHidden":990},[989],[86,48514,48516,48519],{"className":48515},[994],[86,48517],{"className":48518,"style":22105},[998],[86,48520,5464],{"className":48521,"style":20401},[1003,20010]," cuando todas las variables independientes en ",[86,48524,48526,48540],{"className":48525},[955],[86,48527,48529],{"className":48528},[959],[961,48530,48531],{"xmlns":963},[965,48532,48533,48537],{},[968,48534,48535],{},[974,48536,4624],{"mathvariant":19893},[982,48538,48539],{"encoding":984},"\\mathbf{X}",[86,48541,48543],{"className":48542,"ariaHidden":990},[989],[86,48544,48546,48549],{"className":48545},[994],[86,48547],{"className":48548,"style":20006},[998],[86,48550,4624],{"className":48551},[1003,20010]," son cero, es decir, representa el punto de la línea de regresión donde cruza el eje Y.",[12,48554,1938,48555,48558,48559,48593,48594,48622,48623,48651],{},[122,48556,48557],{},"pendiente"," se representa por los coeficientes restantes en el vector ",[86,48560,48562,48575],{"className":48561},[955],[86,48563,48565],{"className":48564},[959],[961,48566,48567],{"xmlns":963},[965,48568,48569,48573],{},[968,48570,48571],{},[974,48572,42473],{"mathvariant":48468},[982,48574,48471],{"encoding":984},[86,48576,48578],{"className":48577,"ariaHidden":990},[989],[86,48579,48581,48584],{"className":48580},[994],[86,48582],{"className":48583,"style":4888},[998],[86,48585,48587],{"className":48586},[1003],[86,48588,48590],{"className":48589},[1003],[86,48591,42473],{"className":48592,"style":48491},[1003,48490],", y cada coeficiente indica la cantidad de cambio en la variable dependiente ",[86,48595,48597,48610],{"className":48596},[955],[86,48598,48600],{"className":48599},[959],[961,48601,48602],{"xmlns":963},[965,48603,48604,48608],{},[968,48605,48606],{},[974,48607,5464],{"mathvariant":19893},[982,48609,48509],{"encoding":984},[86,48611,48613],{"className":48612,"ariaHidden":990},[989],[86,48614,48616,48619],{"className":48615},[994],[86,48617],{"className":48618,"style":22105},[998],[86,48620,5464],{"className":48621,"style":20401},[1003,20010]," por cada unidad de cambio en la variable independiente correspondiente en ",[86,48624,48626,48639],{"className":48625},[955],[86,48627,48629],{"className":48628},[959],[961,48630,48631],{"xmlns":963},[965,48632,48633,48637],{},[968,48634,48635],{},[974,48636,4624],{"mathvariant":19893},[982,48638,48539],{"encoding":984},[86,48640,48642],{"className":48641,"ariaHidden":990},[989],[86,48643,48645,48648],{"className":48644},[994],[86,48646],{"className":48647,"style":20006},[998],[86,48649,4624],{"className":48650},[1003,20010],", manteniendo constantes las demás variables independientes.\nGráficamente podemos verlo de la siguiente manera:",[12,48653,48654,48658],{},[1945,48655],{"alt":48656,"src":48657},"Gráfico de regresión lineal","\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations\u002Fshared\u002Fregression-model.webp",[901,48659,48660],{},"Gráfico de Regresión Lineal",[12,48662,48663],{},"Cada punto negro representa un dato de entrenamiento, y la línea roja el modelo.",[12,48665,48666,48667,48670,48671,48705,48706,48734],{},"Lo importante aquí es entender que ",[122,48668,48669],{},"el objetivo principal"," es encontrar los valores de los coeficientes ",[86,48672,48674,48687],{"className":48673},[955],[86,48675,48677],{"className":48676},[959],[961,48678,48679],{"xmlns":963},[965,48680,48681,48685],{},[968,48682,48683],{},[974,48684,42473],{"mathvariant":48468},[982,48686,48471],{"encoding":984},[86,48688,48690],{"className":48689,"ariaHidden":990},[989],[86,48691,48693,48696],{"className":48692},[994],[86,48694],{"className":48695,"style":4888},[998],[86,48697,48699],{"className":48698},[1003],[86,48700,48702],{"className":48701},[1003],[86,48703,42473],{"className":48704,"style":48491},[1003,48490]," que hagan que las predicciones ",[86,48707,48709,48722],{"className":48708},[955],[86,48710,48712],{"className":48711},[959],[961,48713,48714],{"xmlns":963},[965,48715,48716,48720],{},[968,48717,48718],{},[974,48719,5464],{"mathvariant":19893},[982,48721,48509],{"encoding":984},[86,48723,48725],{"className":48724,"ariaHidden":990},[989],[86,48726,48728,48731],{"className":48727},[994],[86,48729],{"className":48730,"style":22105},[998],[86,48732,5464],{"className":48733,"style":20401},[1003,20010]," (la línea roja) sean lo más cercanas a los valores reales.",[12,48736,48737,48738,48773],{},"Es decir, no se busca predecir con exactitud, siempre (en la realidad) habrá un error o diferencia entre lo que el modelo predice y lo que realmente ocurre. EL término ",[86,48739,48741,48755],{"className":48740},[955],[86,48742,48744],{"className":48743},[959],[961,48745,48746],{"xmlns":963},[965,48747,48748,48752],{},[968,48749,48750],{},[974,48751,47369],{"mathvariant":48468},[982,48753,48754],{"encoding":984},"\\boldsymbol{\\epsilon}",[86,48756,48758],{"className":48757,"ariaHidden":990},[989],[86,48759,48761,48764],{"className":48760},[994],[86,48762],{"className":48763,"style":20397},[998],[86,48765,48767],{"className":48766},[1003],[86,48768,48770],{"className":48769},[1003],[86,48771,47369],{"className":48772},[1003,48490]," es la diferencia entre los valores predichos por el modelo y los valores reales:",[86,48775,48777],{"className":48776},[3173],[86,48778,48780,48820],{"className":48779},[955],[86,48781,48783],{"className":48782},[959],[961,48784,48785],{"xmlns":963,"display":3182},[965,48786,48787,48817],{},[968,48788,48789,48797,48799,48805,48807],{},[974,48790,48791],{},[6849,48792,48793,48795],{},[974,48794,47369],{"mathvariant":48468},[974,48796,7285],{"mathvariant":48468},[3191,48798,258],{},[6849,48800,48801,48803],{},[974,48802,5464],{"mathvariant":19893},[974,48804,7285],{"mathvariant":19893},[3191,48806,9864],{},[3758,48808,48809,48815],{"accent":990},[6849,48810,48811,48813],{},[974,48812,5464],{"mathvariant":19893},[974,48814,7285],{"mathvariant":19893},[3191,48816,7242],{},[982,48818,48819],{"encoding":984},"\\boldsymbol{\\epsilon _i} = \\mathbf{y_i} - \\hat{\\mathbf{y_i}}",[86,48821,48823,48885,48941],{"className":48822,"ariaHidden":990},[989],[86,48824,48826,48829,48876,48879,48882],{"className":48825},[994],[86,48827],{"className":48828,"style":21792},[998],[86,48830,48832],{"className":48831},[1003],[86,48833,48835],{"className":48834},[1003],[86,48836,48838,48841],{"className":48837},[1003],[86,48839,47369],{"className":48840},[1003,48490],[86,48842,48844],{"className":48843},[1012],[86,48845,48847,48868],{"className":48846},[1016,3836],[86,48848,48850,48865],{"className":48849},[1020],[86,48851,48854],{"className":48852,"style":48853},[1024],"height:0.3353em;",[86,48855,48856,48859],{"style":6987},[86,48857],{"className":48858,"style":1032},[1031],[86,48860,48862],{"className":48861},[1036,1037,1038,1039],[86,48863,7285],{"className":48864},[1003,48490,1039],[86,48866,3963],{"className":48867},[3962],[86,48869,48871],{"className":48870},[1020],[86,48872,48874],{"className":48873,"style":7006},[1024],[86,48875],{},[86,48877],{"className":48878,"style":3222},[3221],[86,48880,258],{"className":48881},[3226],[86,48883],{"className":48884,"style":3222},[3221],[86,48886,48888,48891,48932,48935,48938],{"className":48887},[994],[86,48889],{"className":48890,"style":20769},[998],[86,48892,48894,48897],{"className":48893},[1003],[86,48895,5464],{"className":48896,"style":20401},[1003,20010],[86,48898,48900],{"className":48899},[1012],[86,48901,48903,48924],{"className":48902},[1016,3836],[86,48904,48906,48921],{"className":48905},[1020],[86,48907,48910],{"className":48908,"style":48909},[1024],"height:0.3361em;",[86,48911,48912,48915],{"style":21813},[86,48913],{"className":48914,"style":1032},[1031],[86,48916,48918],{"className":48917},[1036,1037,1038,1039],[86,48919,7285],{"className":48920},[1003,20010,1039],[86,48922,3963],{"className":48923},[3962],[86,48925,48927],{"className":48926},[1020],[86,48928,48930],{"className":48929,"style":7006},[1024],[86,48931],{},[86,48933],{"className":48934,"style":5012},[3221],[86,48936,9864],{"className":48937},[5016],[86,48939],{"className":48940,"style":5012},[3221],[86,48942,48944,48947],{"className":48943},[994],[86,48945],{"className":48946,"style":30660},[998],[86,48948,48950],{"className":48949},[1003,3863],[86,48951,48953,49018],{"className":48952},[1016,3836],[86,48954,48956,49015],{"className":48955},[1020],[86,48957,48959,49004],{"className":48958,"style":30673},[1024],[86,48960,48961,48964],{"style":3876},[86,48962],{"className":48963,"style":3850},[1031],[86,48965,48967,48970],{"className":48966},[1003],[86,48968,5464],{"className":48969,"style":20401},[1003,20010],[86,48971,48973],{"className":48972},[1012],[86,48974,48976,48996],{"className":48975},[1016,3836],[86,48977,48979,48993],{"className":48978},[1020],[86,48980,48982],{"className":48981,"style":48909},[1024],[86,48983,48984,48987],{"style":21813},[86,48985],{"className":48986,"style":1032},[1031],[86,48988,48990],{"className":48989},[1036,1037,1038,1039],[86,48991,7285],{"className":48992},[1003,20010,1039],[86,48994,3963],{"className":48995},[3962],[86,48997,48999],{"className":48998},[1020],[86,49000,49002],{"className":49001,"style":7006},[1024],[86,49003],{},[86,49005,49006,49009],{"style":30684},[86,49007],{"className":49008,"style":3850},[1031],[86,49010,49012],{"className":49011,"style":3892},[3891],[86,49013,7242],{"className":49014},[1003],[86,49016,3963],{"className":49017},[3962],[86,49019,49021],{"className":49020},[1020],[86,49022,49024],{"className":49023,"style":30703},[1024],[86,49025],{},[12,49027,49028],{},"Que también se puede expresar como:",[86,49030,49032],{"className":49031},[3173],[86,49033,49035,49091],{"className":49034},[955],[86,49036,49038],{"className":49037},[959],[961,49039,49040],{"xmlns":963,"display":3182},[965,49041,49042,49088],{},[968,49043,49044,49052,49054,49060,49062,49064,49072,49074,49080,49086],{},[974,49045,49046],{},[6849,49047,49048,49050],{},[974,49049,47369],{"mathvariant":48468},[974,49051,7285],{"mathvariant":48468},[3191,49053,258],{},[6849,49055,49056,49058],{},[974,49057,5464],{"mathvariant":19893},[974,49059,7285],{"mathvariant":19893},[3191,49061,9864],{},[3191,49063,243],{"stretchy":3295},[974,49065,49066],{},[6849,49067,49068,49070],{},[974,49069,42473],{"mathvariant":48468},[978,49071,2553],{"mathvariant":19893},[3191,49073,6565],{},[6849,49075,49076,49078],{},[974,49077,42473],{},[978,49079,802],{},[6849,49081,49082,49084],{},[974,49083,3189],{},[974,49085,7285],{},[3191,49087,867],{"stretchy":3295},[982,49089,49090],{"encoding":984},"\\boldsymbol{\\epsilon _i} = \\mathbf{y_i} - (\\boldsymbol{\\beta_0} + \\beta_1 x_{i})",[86,49092,49094,49155,49210,49275],{"className":49093,"ariaHidden":990},[989],[86,49095,49097,49100,49146,49149,49152],{"className":49096},[994],[86,49098],{"className":49099,"style":21792},[998],[86,49101,49103],{"className":49102},[1003],[86,49104,49106],{"className":49105},[1003],[86,49107,49109,49112],{"className":49108},[1003],[86,49110,47369],{"className":49111},[1003,48490],[86,49113,49115],{"className":49114},[1012],[86,49116,49118,49138],{"className":49117},[1016,3836],[86,49119,49121,49135],{"className":49120},[1020],[86,49122,49124],{"className":49123,"style":48853},[1024],[86,49125,49126,49129],{"style":6987},[86,49127],{"className":49128,"style":1032},[1031],[86,49130,49132],{"className":49131},[1036,1037,1038,1039],[86,49133,7285],{"className":49134},[1003,48490,1039],[86,49136,3963],{"className":49137},[3962],[86,49139,49141],{"className":49140},[1020],[86,49142,49144],{"className":49143,"style":7006},[1024],[86,49145],{},[86,49147],{"className":49148,"style":3222},[3221],[86,49150,258],{"className":49151},[3226],[86,49153],{"className":49154,"style":3222},[3221],[86,49156,49158,49161,49201,49204,49207],{"className":49157},[994],[86,49159],{"className":49160,"style":20769},[998],[86,49162,49164,49167],{"className":49163},[1003],[86,49165,5464],{"className":49166,"style":20401},[1003,20010],[86,49168,49170],{"className":49169},[1012],[86,49171,49173,49193],{"className":49172},[1016,3836],[86,49174,49176,49190],{"className":49175},[1020],[86,49177,49179],{"className":49178,"style":48909},[1024],[86,49180,49181,49184],{"style":21813},[86,49182],{"className":49183,"style":1032},[1031],[86,49185,49187],{"className":49186},[1036,1037,1038,1039],[86,49188,7285],{"className":49189},[1003,20010,1039],[86,49191,3963],{"className":49192},[3962],[86,49194,49196],{"className":49195},[1020],[86,49197,49199],{"className":49198,"style":7006},[1024],[86,49200],{},[86,49202],{"className":49203,"style":5012},[3221],[86,49205,9864],{"className":49206},[5016],[86,49208],{"className":49209,"style":5012},[3221],[86,49211,49213,49216,49219,49266,49269,49272],{"className":49212},[994],[86,49214],{"className":49215,"style":3794},[998],[86,49217,243],{"className":49218},[3320],[86,49220,49222],{"className":49221},[1003],[86,49223,49225],{"className":49224},[1003],[86,49226,49228,49231],{"className":49227},[1003],[86,49229,42473],{"className":49230,"style":48491},[1003,48490],[86,49232,49234],{"className":49233},[1012],[86,49235,49237,49258],{"className":49236},[1016,3836],[86,49238,49240,49255],{"className":49239},[1020],[86,49241,49243],{"className":49242,"style":6984},[1024],[86,49244,49246,49249],{"style":49245},"top:-2.55em;margin-left:-0.034em;margin-right:0.05em;",[86,49247],{"className":49248,"style":1032},[1031],[86,49250,49252],{"className":49251},[1036,1037,1038,1039],[86,49253,2553],{"className":49254},[1003,20010,1039],[86,49256,3963],{"className":49257},[3962],[86,49259,49261],{"className":49260},[1020],[86,49262,49264],{"className":49263,"style":7006},[1024],[86,49265],{},[86,49267],{"className":49268,"style":5012},[3221],[86,49270,6565],{"className":49271},[5016],[86,49273],{"className":49274,"style":5012},[3221],[86,49276,49278,49281,49321,49364],{"className":49277},[994],[86,49279],{"className":49280,"style":3794},[998],[86,49282,49284,49287],{"className":49283},[1003],[86,49285,42473],{"className":49286,"style":42538},[1003,1007],[86,49288,49290],{"className":49289},[1012],[86,49291,49293,49313],{"className":49292},[1016,3836],[86,49294,49296,49310],{"className":49295},[1020],[86,49297,49299],{"className":49298,"style":6984},[1024],[86,49300,49301,49304],{"style":42553},[86,49302],{"className":49303,"style":1032},[1031],[86,49305,49307],{"className":49306},[1036,1037,1038,1039],[86,49308,802],{"className":49309},[1003,1039],[86,49311,3963],{"className":49312},[3962],[86,49314,49316],{"className":49315},[1020],[86,49317,49319],{"className":49318,"style":7006},[1024],[86,49320],{},[86,49322,49324,49327],{"className":49323},[1003],[86,49325,3189],{"className":49326},[1003,1007],[86,49328,49330],{"className":49329},[1012],[86,49331,49333,49356],{"className":49332},[1016,3836],[86,49334,49336,49353],{"className":49335},[1020],[86,49337,49339],{"className":49338,"style":7559},[1024],[86,49340,49341,49344],{"style":6987},[86,49342],{"className":49343,"style":1032},[1031],[86,49345,49347],{"className":49346},[1036,1037,1038,1039],[86,49348,49350],{"className":49349},[1003,1039],[86,49351,7285],{"className":49352},[1003,1007,1039],[86,49354,3963],{"className":49355},[3962],[86,49357,49359],{"className":49358},[1020],[86,49360,49362],{"className":49361,"style":7006},[1024],[86,49363],{},[86,49365,867],{"className":49366},[3356],[12,49368,49369],{},"Para medir el error podemos utilizar una función de pérdida. En el caso de la regresión lineal, una función de pérdida comúnmente utilizada es el error cuadrático medio (MSE, por sus siglas en inglés), que se define como:",[86,49371,49373],{"className":49372},[3173],[86,49374,49376,49444],{"className":49375},[955],[86,49377,49379],{"className":49378},[959],[961,49380,49381],{"xmlns":963,"display":3182},[965,49382,49383,49441],{},[968,49384,49385,49388,49390,49392,49394,49400,49415,49417,49423,49425,49435],{},[974,49386,49387],{},"M",[974,49389,4084],{},[974,49391,7871],{},[3191,49393,258],{},[3749,49395,49396,49398],{},[978,49397,802],{},[974,49399,6896],{},[7276,49401,49402,49405,49413],{},[3191,49403,49404],{},"∑",[968,49406,49407,49409,49411],{},[974,49408,7285],{},[3191,49410,258],{},[978,49412,802],{},[974,49414,6896],{},[3191,49416,243],{"stretchy":3295},[6849,49418,49419,49421],{},[974,49420,5464],{},[974,49422,7285],{},[3191,49424,9864],{},[3758,49426,49427,49433],{"accent":990},[6849,49428,49429,49431],{},[974,49430,5464],{},[974,49432,7285],{},[3191,49434,7242],{},[971,49436,49437,49439],{},[3191,49438,867],{"stretchy":3295},[978,49440,980],{},[982,49442,49443],{"encoding":984},"MSE = \\frac{1}{n} \\sum_{i=1}^{n} (y_i - \\hat{y_i})^2",[86,49445,49447,49471,49661],{"className":49446,"ariaHidden":990},[989],[86,49448,49450,49453,49456,49459,49462,49465,49468],{"className":49449},[994],[86,49451],{"className":49452,"style":3575},[998],[86,49454,49387],{"className":49455,"style":6055},[1003,1007],[86,49457,4084],{"className":49458,"style":4133},[1003,1007],[86,49460,7871],{"className":49461,"style":4133},[1003,1007],[86,49463],{"className":49464,"style":3222},[3221],[86,49466,258],{"className":49467},[3226],[86,49469],{"className":49470,"style":3222},[3221],[86,49472,49474,49477,49539,49542,49609,49612,49652,49655,49658],{"className":49473},[994],[86,49475],{"className":49476,"style":7369},[998],[86,49478,49480,49483,49536],{"className":49479},[1003],[86,49481],{"className":49482},[3320,3829],[86,49484,49486],{"className":49485},[3749],[86,49487,49489,49528],{"className":49488},[1016,3836],[86,49490,49492,49525],{"className":49491},[1020],[86,49493,49495,49506,49514],{"className":49494,"style":9568},[1024],[86,49496,49497,49500],{"style":3846},[86,49498],{"className":49499,"style":3850},[1031],[86,49501,49503],{"className":49502},[1003],[86,49504,6896],{"className":49505},[1003,1007],[86,49507,49508,49511],{"style":3901},[86,49509],{"className":49510,"style":3850},[1031],[86,49512],{"className":49513,"style":3909},[3908],[86,49515,49516,49519],{"style":3912},[86,49517],{"className":49518,"style":3850},[1031],[86,49520,49522],{"className":49521},[1003],[86,49523,802],{"className":49524},[1003],[86,49526,3963],{"className":49527},[3962],[86,49529,49531],{"className":49530},[1020],[86,49532,49534],{"className":49533,"style":9620},[1024],[86,49535],{},[86,49537],{"className":49538},[3356,3829],[86,49540],{"className":49541,"style":4162},[3221],[86,49543,49545],{"className":49544},[7373,7391],[86,49546,49548,49601],{"className":49547},[1016,3836],[86,49549,49551,49598],{"className":49550},[1020],[86,49552,49554,49574,49584],{"className":49553,"style":7469},[1024],[86,49555,49556,49559],{"style":7472},[86,49557],{"className":49558,"style":7476},[1031],[86,49560,49562],{"className":49561},[1036,1037,1038,1039],[86,49563,49565,49568,49571],{"className":49564},[1003,1039],[86,49566,7285],{"className":49567},[1003,1007,1039],[86,49569,258],{"className":49570},[3226,1039],[86,49572,802],{"className":49573},[1003,1039],[86,49575,49576,49579],{"style":7494},[86,49577],{"className":49578,"style":7476},[1031],[86,49580,49581],{},[86,49582,49404],{"className":49583},[7373,7503,7504],[86,49585,49586,49589],{"style":7507},[86,49587],{"className":49588,"style":7476},[1031],[86,49590,49592],{"className":49591},[1036,1037,1038,1039],[86,49593,49595],{"className":49594},[1003,1039],[86,49596,6896],{"className":49597},[1003,1007,1039],[86,49599,3963],{"className":49600},[3962],[86,49602,49604],{"className":49603},[1020],[86,49605,49607],{"className":49606,"style":7529},[1024],[86,49608],{},[86,49610,243],{"className":49611},[3320],[86,49613,49615,49618],{"className":49614},[1003],[86,49616,5464],{"className":49617,"style":8109},[1003,1007],[86,49619,49621],{"className":49620},[1012],[86,49622,49624,49644],{"className":49623},[1016,3836],[86,49625,49627,49641],{"className":49626},[1020],[86,49628,49630],{"className":49629,"style":7559},[1024],[86,49631,49632,49635],{"style":20440},[86,49633],{"className":49634,"style":1032},[1031],[86,49636,49638],{"className":49637},[1036,1037,1038,1039],[86,49639,7285],{"className":49640},[1003,1007,1039],[86,49642,3963],{"className":49643},[3962],[86,49645,49647],{"className":49646},[1020],[86,49648,49650],{"className":49649,"style":7006},[1024],[86,49651],{},[86,49653],{"className":49654,"style":5012},[3221],[86,49656,9864],{"className":49657},[5016],[86,49659],{"className":49660,"style":5012},[3221],[86,49662,49664,49668,49747],{"className":49663},[994],[86,49665],{"className":49666,"style":49667},[998],"height:1.1141em;vertical-align:-0.25em;",[86,49669,49671],{"className":49670},[1003,3863],[86,49672,49674,49739],{"className":49673},[1016,3836],[86,49675,49677,49736],{"className":49676},[1020],[86,49678,49680,49725],{"className":49679,"style":3873},[1024],[86,49681,49682,49685],{"style":3876},[86,49683],{"className":49684,"style":3850},[1031],[86,49686,49688,49691],{"className":49687},[1003],[86,49689,5464],{"className":49690,"style":8109},[1003,1007],[86,49692,49694],{"className":49693},[1012],[86,49695,49697,49717],{"className":49696},[1016,3836],[86,49698,49700,49714],{"className":49699},[1020],[86,49701,49703],{"className":49702,"style":7559},[1024],[86,49704,49705,49708],{"style":20440},[86,49706],{"className":49707,"style":1032},[1031],[86,49709,49711],{"className":49710},[1036,1037,1038,1039],[86,49712,7285],{"className":49713},[1003,1007,1039],[86,49715,3963],{"className":49716},[3962],[86,49718,49720],{"className":49719},[1020],[86,49721,49723],{"className":49722,"style":7006},[1024],[86,49724],{},[86,49726,49727,49730],{"style":3876},[86,49728],{"className":49729,"style":3850},[1031],[86,49731,49733],{"className":49732,"style":3892},[3891],[86,49734,7242],{"className":49735},[1003],[86,49737,3963],{"className":49738},[3962],[86,49740,49742],{"className":49741},[1020],[86,49743,49745],{"className":49744,"style":30703},[1024],[86,49746],{},[86,49748,49750,49753],{"className":49749},[3356],[86,49751,867],{"className":49752},[3356],[86,49754,49756],{"className":49755},[1012],[86,49757,49759],{"className":49758},[1016],[86,49760,49762],{"className":49761},[1020],[86,49763,49765],{"className":49764,"style":3236},[1024],[86,49766,49767,49770],{"style":3258},[86,49768],{"className":49769,"style":1032},[1031],[86,49771,49773],{"className":49772},[1036,1037,1038,1039],[86,49774,980],{"className":49775},[1003,1039],[12,49777,3273],{},[30,49779,49780,49811,49912],{},[33,49781,49782,49810],{},[86,49783,49785,49798],{"className":49784},[955],[86,49786,49788],{"className":49787},[959],[961,49789,49790],{"xmlns":963},[965,49791,49792,49796],{},[968,49793,49794],{},[974,49795,6896],{},[982,49797,6896],{"encoding":984},[86,49799,49801],{"className":49800,"ariaHidden":990},[989],[86,49802,49804,49807],{"className":49803},[994],[86,49805],{"className":49806,"style":7401},[998],[86,49808,6896],{"className":49809},[1003,1007]," es el número de ejemplos en el conjunto de datos.",[33,49812,49813,49882,49883,61],{},[86,49814,49816,49833],{"className":49815},[955],[86,49817,49819],{"className":49818},[959],[961,49820,49821],{"xmlns":963},[965,49822,49823,49831],{},[968,49824,49825],{},[6849,49826,49827,49829],{},[974,49828,5464],{},[974,49830,7285],{},[982,49832,46828],{"encoding":984},[86,49834,49836],{"className":49835,"ariaHidden":990},[989],[86,49837,49839,49842],{"className":49838},[994],[86,49840],{"className":49841,"style":16339},[998],[86,49843,49845,49848],{"className":49844},[1003],[86,49846,5464],{"className":49847,"style":8109},[1003,1007],[86,49849,49851],{"className":49850},[1012],[86,49852,49854,49874],{"className":49853},[1016,3836],[86,49855,49857,49871],{"className":49856},[1020],[86,49858,49860],{"className":49859,"style":7559},[1024],[86,49861,49862,49865],{"style":20440},[86,49863],{"className":49864,"style":1032},[1031],[86,49866,49868],{"className":49867},[1036,1037,1038,1039],[86,49869,7285],{"className":49870},[1003,1007,1039],[86,49872,3963],{"className":49873},[3962],[86,49875,49877],{"className":49876},[1020],[86,49878,49880],{"className":49879,"style":7006},[1024],[86,49881],{}," es el valor real de la variable dependiente para el ejemplo ",[86,49884,49886,49899],{"className":49885},[955],[86,49887,49889],{"className":49888},[959],[961,49890,49891],{"xmlns":963},[965,49892,49893,49897],{},[968,49894,49895],{},[974,49896,7285],{},[982,49898,7285],{"encoding":984},[86,49900,49902],{"className":49901,"ariaHidden":990},[989],[86,49903,49905,49909],{"className":49904},[994],[86,49906],{"className":49907,"style":49908},[998],"height:0.6595em;",[86,49910,7285],{"className":49911},[1003,1007],[33,49913,49914,50028,50029,61],{},[86,49915,49917,49939],{"className":49916},[955],[86,49918,49920],{"className":49919},[959],[961,49921,49922],{"xmlns":963},[965,49923,49924,49936],{},[968,49925,49926],{},[6849,49927,49928,49934],{},[3758,49929,49930,49932],{"accent":990},[974,49931,5464],{},[3191,49933,7242],{},[974,49935,7285],{},[982,49937,49938],{"encoding":984},"\\hat{y}_i",[86,49940,49942],{"className":49941,"ariaHidden":990},[989],[86,49943,49945,49948],{"className":49944},[994],[86,49946],{"className":49947,"style":4888},[998],[86,49949,49951,49994],{"className":49950},[1003],[86,49952,49954],{"className":49953},[1003,3863],[86,49955,49957,49986],{"className":49956},[1016,3836],[86,49958,49960,49983],{"className":49959},[1020],[86,49961,49963,49971],{"className":49962,"style":3873},[1024],[86,49964,49965,49968],{"style":3876},[86,49966],{"className":49967,"style":3850},[1031],[86,49969,5464],{"className":49970,"style":8109},[1003,1007],[86,49972,49973,49976],{"style":3876},[86,49974],{"className":49975,"style":3850},[1031],[86,49977,49980],{"className":49978,"style":49979},[3891],"left:-0.1944em;",[86,49981,7242],{"className":49982},[1003],[86,49984,3963],{"className":49985},[3962],[86,49987,49989],{"className":49988},[1020],[86,49990,49992],{"className":49991,"style":30703},[1024],[86,49993],{},[86,49995,49997],{"className":49996},[1012],[86,49998,50000,50020],{"className":49999},[1016,3836],[86,50001,50003,50017],{"className":50002},[1020],[86,50004,50006],{"className":50005,"style":7559},[1024],[86,50007,50008,50011],{"style":20440},[86,50009],{"className":50010,"style":1032},[1031],[86,50012,50014],{"className":50013},[1036,1037,1038,1039],[86,50015,7285],{"className":50016},[1003,1007,1039],[86,50018,3963],{"className":50019},[3962],[86,50021,50023],{"className":50022},[1020],[86,50024,50026],{"className":50025,"style":7006},[1024],[86,50027],{}," es la predicción del modelo para el ejemplo ",[86,50030,50032,50045],{"className":50031},[955],[86,50033,50035],{"className":50034},[959],[961,50036,50037],{"xmlns":963},[965,50038,50039,50043],{},[968,50040,50041],{},[974,50042,7285],{},[982,50044,7285],{"encoding":984},[86,50046,50048],{"className":50047,"ariaHidden":990},[989],[86,50049,50051,50054],{"className":50050},[994],[86,50052],{"className":50053,"style":49908},[998],[86,50055,7285],{"className":50056},[1003,1007],[12,50058,50059],{},"Minimizar el MSE es equivalente a minimizar la suma de errores cuadrados:",[86,50061,50063],{"className":50062},[3173],[86,50064,50066,50118],{"className":50065},[955],[86,50067,50069],{"className":50068},[959],[961,50070,50071],{"xmlns":963,"display":3182},[965,50072,50073,50115],{},[968,50074,50075,50089,50091,50097,50099,50109],{},[7276,50076,50077,50079,50087],{},[3191,50078,49404],{},[968,50080,50081,50083,50085],{},[974,50082,7285],{},[3191,50084,258],{},[978,50086,802],{},[974,50088,6896],{},[3191,50090,243],{"stretchy":3295},[6849,50092,50093,50095],{},[974,50094,5464],{},[974,50096,7285],{},[3191,50098,9864],{},[3758,50100,50101,50107],{"accent":990},[6849,50102,50103,50105],{},[974,50104,5464],{},[974,50106,7285],{},[3191,50108,7242],{},[971,50110,50111,50113],{},[3191,50112,867],{"stretchy":3295},[978,50114,980],{},[982,50116,50117],{"encoding":984},"\\sum_{i=1}^{n} (y_i - \\hat{y_i})^2",[86,50119,50121,50246],{"className":50120,"ariaHidden":990},[989],[86,50122,50124,50127,50194,50197,50237,50240,50243],{"className":50123},[994],[86,50125],{"className":50126,"style":7369},[998],[86,50128,50130],{"className":50129},[7373,7391],[86,50131,50133,50186],{"className":50132},[1016,3836],[86,50134,50136,50183],{"className":50135},[1020],[86,50137,50139,50159,50169],{"className":50138,"style":7469},[1024],[86,50140,50141,50144],{"style":7472},[86,50142],{"className":50143,"style":7476},[1031],[86,50145,50147],{"className":50146},[1036,1037,1038,1039],[86,50148,50150,50153,50156],{"className":50149},[1003,1039],[86,50151,7285],{"className":50152},[1003,1007,1039],[86,50154,258],{"className":50155},[3226,1039],[86,50157,802],{"className":50158},[1003,1039],[86,50160,50161,50164],{"style":7494},[86,50162],{"className":50163,"style":7476},[1031],[86,50165,50166],{},[86,50167,49404],{"className":50168},[7373,7503,7504],[86,50170,50171,50174],{"style":7507},[86,50172],{"className":50173,"style":7476},[1031],[86,50175,50177],{"className":50176},[1036,1037,1038,1039],[86,50178,50180],{"className":50179},[1003,1039],[86,50181,6896],{"className":50182},[1003,1007,1039],[86,50184,3963],{"className":50185},[3962],[86,50187,50189],{"className":50188},[1020],[86,50190,50192],{"className":50191,"style":7529},[1024],[86,50193],{},[86,50195,243],{"className":50196},[3320],[86,50198,50200,50203],{"className":50199},[1003],[86,50201,5464],{"className":50202,"style":8109},[1003,1007],[86,50204,50206],{"className":50205},[1012],[86,50207,50209,50229],{"className":50208},[1016,3836],[86,50210,50212,50226],{"className":50211},[1020],[86,50213,50215],{"className":50214,"style":7559},[1024],[86,50216,50217,50220],{"style":20440},[86,50218],{"className":50219,"style":1032},[1031],[86,50221,50223],{"className":50222},[1036,1037,1038,1039],[86,50224,7285],{"className":50225},[1003,1007,1039],[86,50227,3963],{"className":50228},[3962],[86,50230,50232],{"className":50231},[1020],[86,50233,50235],{"className":50234,"style":7006},[1024],[86,50236],{},[86,50238],{"className":50239,"style":5012},[3221],[86,50241,9864],{"className":50242},[5016],[86,50244],{"className":50245,"style":5012},[3221],[86,50247,50249,50252,50331],{"className":50248},[994],[86,50250],{"className":50251,"style":49667},[998],[86,50253,50255],{"className":50254},[1003,3863],[86,50256,50258,50323],{"className":50257},[1016,3836],[86,50259,50261,50320],{"className":50260},[1020],[86,50262,50264,50309],{"className":50263,"style":3873},[1024],[86,50265,50266,50269],{"style":3876},[86,50267],{"className":50268,"style":3850},[1031],[86,50270,50272,50275],{"className":50271},[1003],[86,50273,5464],{"className":50274,"style":8109},[1003,1007],[86,50276,50278],{"className":50277},[1012],[86,50279,50281,50301],{"className":50280},[1016,3836],[86,50282,50284,50298],{"className":50283},[1020],[86,50285,50287],{"className":50286,"style":7559},[1024],[86,50288,50289,50292],{"style":20440},[86,50290],{"className":50291,"style":1032},[1031],[86,50293,50295],{"className":50294},[1036,1037,1038,1039],[86,50296,7285],{"className":50297},[1003,1007,1039],[86,50299,3963],{"className":50300},[3962],[86,50302,50304],{"className":50303},[1020],[86,50305,50307],{"className":50306,"style":7006},[1024],[86,50308],{},[86,50310,50311,50314],{"style":3876},[86,50312],{"className":50313,"style":3850},[1031],[86,50315,50317],{"className":50316,"style":3892},[3891],[86,50318,7242],{"className":50319},[1003],[86,50321,3963],{"className":50322},[3962],[86,50324,50326],{"className":50325},[1020],[86,50327,50329],{"className":50328,"style":30703},[1024],[86,50330],{},[86,50332,50334,50337],{"className":50333},[3356],[86,50335,867],{"className":50336},[3356],[86,50338,50340],{"className":50339},[1012],[86,50341,50343],{"className":50342},[1016],[86,50344,50346],{"className":50345},[1020],[86,50347,50349],{"className":50348,"style":3236},[1024],[86,50350,50351,50354],{"style":3258},[86,50352],{"className":50353,"style":1032},[1031],[86,50355,50357],{"className":50356},[1036,1037,1038,1039],[86,50358,980],{"className":50359},[1003,1039],[12,50361,50362],{},"O también:",[86,50364,50366],{"className":50365},[3173],[86,50367,50369,50435],{"className":50368},[955],[86,50370,50372],{"className":50371},[959],[961,50373,50374],{"xmlns":963,"display":3182},[965,50375,50376,50432],{},[968,50377,50378,50392,50394,50400,50402,50404,50410,50412,50418,50424,50426],{},[7276,50379,50380,50382,50390],{},[3191,50381,49404],{},[968,50383,50384,50386,50388],{},[974,50385,7285],{},[3191,50387,258],{},[978,50389,802],{},[974,50391,6896],{},[3191,50393,243],{"stretchy":3295},[6849,50395,50396,50398],{},[974,50397,5464],{},[974,50399,7285],{},[3191,50401,9864],{},[3191,50403,243],{"stretchy":3295},[6849,50405,50406,50408],{},[974,50407,42473],{},[978,50409,2553],{},[3191,50411,6565],{},[6849,50413,50414,50416],{},[974,50415,42473],{},[978,50417,802],{},[6849,50419,50420,50422],{},[974,50421,3189],{},[974,50423,7285],{},[3191,50425,867],{"stretchy":3295},[971,50427,50428,50430],{},[3191,50429,867],{"stretchy":3295},[978,50431,980],{},[982,50433,50434],{"encoding":984},"\\sum_{i=1}^{n} (y_i - (\\beta_0 + \\beta_1 x_i))^2",[86,50436,50438,50563,50621],{"className":50437,"ariaHidden":990},[989],[86,50439,50441,50444,50511,50514,50554,50557,50560],{"className":50440},[994],[86,50442],{"className":50443,"style":7369},[998],[86,50445,50447],{"className":50446},[7373,7391],[86,50448,50450,50503],{"className":50449},[1016,3836],[86,50451,50453,50500],{"className":50452},[1020],[86,50454,50456,50476,50486],{"className":50455,"style":7469},[1024],[86,50457,50458,50461],{"style":7472},[86,50459],{"className":50460,"style":7476},[1031],[86,50462,50464],{"className":50463},[1036,1037,1038,1039],[86,50465,50467,50470,50473],{"className":50466},[1003,1039],[86,50468,7285],{"className":50469},[1003,1007,1039],[86,50471,258],{"className":50472},[3226,1039],[86,50474,802],{"className":50475},[1003,1039],[86,50477,50478,50481],{"style":7494},[86,50479],{"className":50480,"style":7476},[1031],[86,50482,50483],{},[86,50484,49404],{"className":50485},[7373,7503,7504],[86,50487,50488,50491],{"style":7507},[86,50489],{"className":50490,"style":7476},[1031],[86,50492,50494],{"className":50493},[1036,1037,1038,1039],[86,50495,50497],{"className":50496},[1003,1039],[86,50498,6896],{"className":50499},[1003,1007,1039],[86,50501,3963],{"className":50502},[3962],[86,50504,50506],{"className":50505},[1020],[86,50507,50509],{"className":50508,"style":7529},[1024],[86,50510],{},[86,50512,243],{"className":50513},[3320],[86,50515,50517,50520],{"className":50516},[1003],[86,50518,5464],{"className":50519,"style":8109},[1003,1007],[86,50521,50523],{"className":50522},[1012],[86,50524,50526,50546],{"className":50525},[1016,3836],[86,50527,50529,50543],{"className":50528},[1020],[86,50530,50532],{"className":50531,"style":7559},[1024],[86,50533,50534,50537],{"style":20440},[86,50535],{"className":50536,"style":1032},[1031],[86,50538,50540],{"className":50539},[1036,1037,1038,1039],[86,50541,7285],{"className":50542},[1003,1007,1039],[86,50544,3963],{"className":50545},[3962],[86,50547,50549],{"className":50548},[1020],[86,50550,50552],{"className":50551,"style":7006},[1024],[86,50553],{},[86,50555],{"className":50556,"style":5012},[3221],[86,50558,9864],{"className":50559},[5016],[86,50561],{"className":50562,"style":5012},[3221],[86,50564,50566,50569,50572,50612,50615,50618],{"className":50565},[994],[86,50567],{"className":50568,"style":3794},[998],[86,50570,243],{"className":50571},[3320],[86,50573,50575,50578],{"className":50574},[1003],[86,50576,42473],{"className":50577,"style":42538},[1003,1007],[86,50579,50581],{"className":50580},[1012],[86,50582,50584,50604],{"className":50583},[1016,3836],[86,50585,50587,50601],{"className":50586},[1020],[86,50588,50590],{"className":50589,"style":6984},[1024],[86,50591,50592,50595],{"style":42553},[86,50593],{"className":50594,"style":1032},[1031],[86,50596,50598],{"className":50597},[1036,1037,1038,1039],[86,50599,2553],{"className":50600},[1003,1039],[86,50602,3963],{"className":50603},[3962],[86,50605,50607],{"className":50606},[1020],[86,50608,50610],{"className":50609,"style":7006},[1024],[86,50611],{},[86,50613],{"className":50614,"style":5012},[3221],[86,50616,6565],{"className":50617},[5016],[86,50619],{"className":50620,"style":5012},[3221],[86,50622,50624,50627,50667,50707,50710],{"className":50623},[994],[86,50625],{"className":50626,"style":49667},[998],[86,50628,50630,50633],{"className":50629},[1003],[86,50631,42473],{"className":50632,"style":42538},[1003,1007],[86,50634,50636],{"className":50635},[1012],[86,50637,50639,50659],{"className":50638},[1016,3836],[86,50640,50642,50656],{"className":50641},[1020],[86,50643,50645],{"className":50644,"style":6984},[1024],[86,50646,50647,50650],{"style":42553},[86,50648],{"className":50649,"style":1032},[1031],[86,50651,50653],{"className":50652},[1036,1037,1038,1039],[86,50654,802],{"className":50655},[1003,1039],[86,50657,3963],{"className":50658},[3962],[86,50660,50662],{"className":50661},[1020],[86,50663,50665],{"className":50664,"style":7006},[1024],[86,50666],{},[86,50668,50670,50673],{"className":50669},[1003],[86,50671,3189],{"className":50672},[1003,1007],[86,50674,50676],{"className":50675},[1012],[86,50677,50679,50699],{"className":50678},[1016,3836],[86,50680,50682,50696],{"className":50681},[1020],[86,50683,50685],{"className":50684,"style":7559},[1024],[86,50686,50687,50690],{"style":6987},[86,50688],{"className":50689,"style":1032},[1031],[86,50691,50693],{"className":50692},[1036,1037,1038,1039],[86,50694,7285],{"className":50695},[1003,1007,1039],[86,50697,3963],{"className":50698},[3962],[86,50700,50702],{"className":50701},[1020],[86,50703,50705],{"className":50704,"style":7006},[1024],[86,50706],{},[86,50708,867],{"className":50709},[3356],[86,50711,50713,50716],{"className":50712},[3356],[86,50714,867],{"className":50715},[3356],[86,50717,50719],{"className":50718},[1012],[86,50720,50722],{"className":50721},[1016],[86,50723,50725],{"className":50724},[1020],[86,50726,50728],{"className":50727,"style":3236},[1024],[86,50729,50730,50733],{"style":3258},[86,50731],{"className":50732,"style":1032},[1031],[86,50734,50736],{"className":50735},[1036,1037,1038,1039],[86,50737,980],{"className":50738},[1003,1039],[12,50740,50741,50742,50745,50746,50780],{},"A esto se le conoce como el ",[122,50743,50744],{},"método de mínimos cuadrados",", y es una técnica comúnmente utilizada para encontrar los coeficientes ",[86,50747,50749,50762],{"className":50748},[955],[86,50750,50752],{"className":50751},[959],[961,50753,50754],{"xmlns":963},[965,50755,50756,50760],{},[968,50757,50758],{},[974,50759,42473],{"mathvariant":48468},[982,50761,48471],{"encoding":984},[86,50763,50765],{"className":50764,"ariaHidden":990},[989],[86,50766,50768,50771],{"className":50767},[994],[86,50769],{"className":50770,"style":4888},[998],[86,50772,50774],{"className":50773},[1003],[86,50775,50777],{"className":50776},[1003],[86,50778,42473],{"className":50779,"style":48491},[1003,48490]," que mejor se ajusten a los datos.",[16,50782,50783],{},[12,50784,50785],{},"¿Por qué se usan cuadrados? Porque al elevar al cuadrado las diferencias, se penalizan más los errores grandes, lo que ayuda a encontrar una mejor línea de ajuste para los datos.",[12,50787,50788,50789,50823,50824,392,50893,50963],{},"Veamos ahora como obtenemos esos coeficientes ",[86,50790,50792,50805],{"className":50791},[955],[86,50793,50795],{"className":50794},[959],[961,50796,50797],{"xmlns":963},[965,50798,50799,50803],{},[968,50800,50801],{},[974,50802,42473],{"mathvariant":48468},[982,50804,48471],{"encoding":984},[86,50806,50808],{"className":50807,"ariaHidden":990},[989],[86,50809,50811,50814],{"className":50810},[994],[86,50812],{"className":50813,"style":4888},[998],[86,50815,50817],{"className":50816},[1003],[86,50818,50820],{"className":50819},[1003],[86,50821,42473],{"className":50822,"style":48491},[1003,48490]," utilizando el método de mínimos cuadrados. Para encontrar los valores de ",[86,50825,50827,50844],{"className":50826},[955],[86,50828,50830],{"className":50829},[959],[961,50831,50832],{"xmlns":963},[965,50833,50834,50842],{},[968,50835,50836],{},[6849,50837,50838,50840],{},[974,50839,42473],{},[978,50841,2553],{},[982,50843,48018],{"encoding":984},[86,50845,50847],{"className":50846,"ariaHidden":990},[989],[86,50848,50850,50853],{"className":50849},[994],[86,50851],{"className":50852,"style":4888},[998],[86,50854,50856,50859],{"className":50855},[1003],[86,50857,42473],{"className":50858,"style":42538},[1003,1007],[86,50860,50862],{"className":50861},[1012],[86,50863,50865,50885],{"className":50864},[1016,3836],[86,50866,50868,50882],{"className":50867},[1020],[86,50869,50871],{"className":50870,"style":6984},[1024],[86,50872,50873,50876],{"style":42553},[86,50874],{"className":50875,"style":1032},[1031],[86,50877,50879],{"className":50878},[1036,1037,1038,1039],[86,50880,2553],{"className":50881},[1003,1039],[86,50883,3963],{"className":50884},[3962],[86,50886,50888],{"className":50887},[1020],[86,50889,50891],{"className":50890,"style":7006},[1024],[86,50892],{},[86,50894,50896,50914],{"className":50895},[955],[86,50897,50899],{"className":50898},[959],[961,50900,50901],{"xmlns":963},[965,50902,50903,50911],{},[968,50904,50905],{},[6849,50906,50907,50909],{},[974,50908,42473],{},[978,50910,802],{},[982,50912,50913],{"encoding":984},"\\beta_1",[86,50915,50917],{"className":50916,"ariaHidden":990},[989],[86,50918,50920,50923],{"className":50919},[994],[86,50921],{"className":50922,"style":4888},[998],[86,50924,50926,50929],{"className":50925},[1003],[86,50927,42473],{"className":50928,"style":42538},[1003,1007],[86,50930,50932],{"className":50931},[1012],[86,50933,50935,50955],{"className":50934},[1016,3836],[86,50936,50938,50952],{"className":50937},[1020],[86,50939,50941],{"className":50940,"style":6984},[1024],[86,50942,50943,50946],{"style":42553},[86,50944],{"className":50945,"style":1032},[1031],[86,50947,50949],{"className":50948},[1036,1037,1038,1039],[86,50950,802],{"className":50951},[1003,1039],[86,50953,3963],{"className":50954},[3962],[86,50956,50958],{"className":50957},[1020],[86,50959,50961],{"className":50960,"style":7006},[1024],[86,50962],{},", podemos usar las siguientes fórmulas, que se obtienen al derivar la función de pérdida MSE con respecto a los coeficientes y establecer las derivadas iguales a cero:",[86,50965,50967],{"className":50966},[3173],[86,50968,50970,51068],{"className":50969},[955],[86,50971,50973],{"className":50972},[959],[961,50974,50975],{"xmlns":963,"display":3182},[965,50976,50977,51065],{},[968,50978,50979,50985,50987],{},[6849,50980,50981,50983],{},[974,50982,42473],{},[978,50984,802],{},[3191,50986,258],{},[3749,50988,50989,51029],{},[968,50990,50991,50993,50995,50997,51003,51009,51011,51013,51015,51021,51023],{},[974,50992,6896],{},[3191,50994,49404],{},[3191,50996,243],{"stretchy":3295},[6849,50998,50999,51001],{},[974,51000,3189],{},[974,51002,7285],{},[6849,51004,51005,51007],{},[974,51006,5464],{},[974,51008,7285],{},[3191,51010,867],{"stretchy":3295},[3191,51012,9864],{},[3191,51014,49404],{},[6849,51016,51017,51019],{},[974,51018,3189],{},[974,51020,7285],{},[3191,51022,49404],{},[6849,51024,51025,51027],{},[974,51026,5464],{},[974,51028,7285],{},[968,51030,51031,51033,51035,51037,51045,51047,51049,51051,51053,51059],{},[974,51032,6896],{},[3191,51034,49404],{},[3191,51036,243],{"stretchy":3295},[9835,51038,51039,51041,51043],{},[974,51040,3189],{},[974,51042,7285],{},[978,51044,980],{},[3191,51046,867],{"stretchy":3295},[3191,51048,9864],{},[3191,51050,243],{"stretchy":3295},[3191,51052,49404],{},[6849,51054,51055,51057],{},[974,51056,3189],{},[974,51058,7285],{},[971,51060,51061,51063],{},[3191,51062,867],{"stretchy":3295},[978,51064,980],{},[982,51066,51067],{"encoding":984},"\\beta_1 = \\frac{n \\sum (x_i y_i) - \\sum x_i \\sum y_i}{n \\sum (x_i^2) - (\\sum x_i)^2}",[86,51069,51071,51126],{"className":51070,"ariaHidden":990},[989],[86,51072,51074,51077,51117,51120,51123],{"className":51073},[994],[86,51075],{"className":51076,"style":4888},[998],[86,51078,51080,51083],{"className":51079},[1003],[86,51081,42473],{"className":51082,"style":42538},[1003,1007],[86,51084,51086],{"className":51085},[1012],[86,51087,51089,51109],{"className":51088},[1016,3836],[86,51090,51092,51106],{"className":51091},[1020],[86,51093,51095],{"className":51094,"style":6984},[1024],[86,51096,51097,51100],{"style":42553},[86,51098],{"className":51099,"style":1032},[1031],[86,51101,51103],{"className":51102},[1036,1037,1038,1039],[86,51104,802],{"className":51105},[1003,1039],[86,51107,3963],{"className":51108},[3962],[86,51110,51112],{"className":51111},[1020],[86,51113,51115],{"className":51114,"style":7006},[1024],[86,51116],{},[86,51118],{"className":51119,"style":3222},[3221],[86,51121,258],{"className":51122},[3226],[86,51124],{"className":51125,"style":3222},[3221],[86,51127,51129,51133],{"className":51128},[994],[86,51130],{"className":51131,"style":51132},[998],"height:2.3899em;vertical-align:-0.9629em;",[86,51134,51136,51139,51545],{"className":51135},[1003],[86,51137],{"className":51138},[3320,3829],[86,51140,51142],{"className":51141},[3749],[86,51143,51145,51536],{"className":51144},[1016,3836],[86,51146,51148,51533],{"className":51147},[1020],[86,51149,51151,51318,51326],{"className":51150,"style":5706},[1024],[86,51152,51153,51156],{"style":3846},[86,51154],{"className":51155,"style":3850},[1031],[86,51157,51159,51162,51165,51170,51173,51226,51229,51232,51235,51238,51241,51244,51247,51287],{"className":51158},[1003],[86,51160,6896],{"className":51161},[1003,1007],[86,51163],{"className":51164,"style":4162},[3221],[86,51166,49404],{"className":51167,"style":51169},[7373,7503,51168],"small-op","position:relative;top:0em;",[86,51171,243],{"className":51172},[3320],[86,51174,51176,51179],{"className":51175},[1003],[86,51177,3189],{"className":51178},[1003,1007],[86,51180,51182],{"className":51181},[1012],[86,51183,51185,51217],{"className":51184},[1016,3836],[86,51186,51188,51214],{"className":51187},[1020],[86,51189,51191,51203],{"className":51190,"style":10092},[1024],[86,51192,51194,51197],{"style":51193},"top:-2.4231em;margin-left:0em;margin-right:0.05em;",[86,51195],{"className":51196,"style":1032},[1031],[86,51198,51200],{"className":51199},[1036,1037,1038,1039],[86,51201,7285],{"className":51202},[1003,1007,1039],[86,51204,51205,51208],{"style":10116},[86,51206],{"className":51207,"style":1032},[1031],[86,51209,51211],{"className":51210},[1036,1037,1038,1039],[86,51212,980],{"className":51213},[1003,1039],[86,51215,3963],{"className":51216},[3962],[86,51218,51220],{"className":51219},[1020],[86,51221,51224],{"className":51222,"style":51223},[1024],"height:0.2769em;",[86,51225],{},[86,51227,867],{"className":51228},[3356],[86,51230],{"className":51231,"style":5012},[3221],[86,51233,9864],{"className":51234},[5016],[86,51236],{"className":51237,"style":5012},[3221],[86,51239,243],{"className":51240},[3320],[86,51242,49404],{"className":51243,"style":51169},[7373,7503,51168],[86,51245],{"className":51246,"style":4162},[3221],[86,51248,51250,51253],{"className":51249},[1003],[86,51251,3189],{"className":51252},[1003,1007],[86,51254,51256],{"className":51255},[1012],[86,51257,51259,51279],{"className":51258},[1016,3836],[86,51260,51262,51276],{"className":51261},[1020],[86,51263,51265],{"className":51264,"style":7559},[1024],[86,51266,51267,51270],{"style":6987},[86,51268],{"className":51269,"style":1032},[1031],[86,51271,51273],{"className":51272},[1036,1037,1038,1039],[86,51274,7285],{"className":51275},[1003,1007,1039],[86,51277,3963],{"className":51278},[3962],[86,51280,51282],{"className":51281},[1020],[86,51283,51285],{"className":51284,"style":7006},[1024],[86,51286],{},[86,51288,51290,51293],{"className":51289},[3356],[86,51291,867],{"className":51292},[3356],[86,51294,51296],{"className":51295},[1012],[86,51297,51299],{"className":51298},[1016],[86,51300,51302],{"className":51301},[1020],[86,51303,51306],{"className":51304,"style":51305},[1024],"height:0.7401em;",[86,51307,51309,51312],{"style":51308},"top:-2.989em;margin-right:0.05em;",[86,51310],{"className":51311,"style":1032},[1031],[86,51313,51315],{"className":51314},[1036,1037,1038,1039],[86,51316,980],{"className":51317},[1003,1039],[86,51319,51320,51323],{"style":3901},[86,51321],{"className":51322,"style":3850},[1031],[86,51324],{"className":51325,"style":3909},[3908],[86,51327,51328,51331],{"style":3912},[86,51329],{"className":51330,"style":3850},[1031],[86,51332,51334,51337,51340,51343,51346,51386,51426,51429,51432,51435,51438,51441,51444,51484,51487,51490,51493],{"className":51333},[1003],[86,51335,6896],{"className":51336},[1003,1007],[86,51338],{"className":51339,"style":4162},[3221],[86,51341,49404],{"className":51342,"style":51169},[7373,7503,51168],[86,51344,243],{"className":51345},[3320],[86,51347,51349,51352],{"className":51348},[1003],[86,51350,3189],{"className":51351},[1003,1007],[86,51353,51355],{"className":51354},[1012],[86,51356,51358,51378],{"className":51357},[1016,3836],[86,51359,51361,51375],{"className":51360},[1020],[86,51362,51364],{"className":51363,"style":7559},[1024],[86,51365,51366,51369],{"style":6987},[86,51367],{"className":51368,"style":1032},[1031],[86,51370,51372],{"className":51371},[1036,1037,1038,1039],[86,51373,7285],{"className":51374},[1003,1007,1039],[86,51376,3963],{"className":51377},[3962],[86,51379,51381],{"className":51380},[1020],[86,51382,51384],{"className":51383,"style":7006},[1024],[86,51385],{},[86,51387,51389,51392],{"className":51388},[1003],[86,51390,5464],{"className":51391,"style":8109},[1003,1007],[86,51393,51395],{"className":51394},[1012],[86,51396,51398,51418],{"className":51397},[1016,3836],[86,51399,51401,51415],{"className":51400},[1020],[86,51402,51404],{"className":51403,"style":7559},[1024],[86,51405,51406,51409],{"style":20440},[86,51407],{"className":51408,"style":1032},[1031],[86,51410,51412],{"className":51411},[1036,1037,1038,1039],[86,51413,7285],{"className":51414},[1003,1007,1039],[86,51416,3963],{"className":51417},[3962],[86,51419,51421],{"className":51420},[1020],[86,51422,51424],{"className":51423,"style":7006},[1024],[86,51425],{},[86,51427,867],{"className":51428},[3356],[86,51430],{"className":51431,"style":5012},[3221],[86,51433,9864],{"className":51434},[5016],[86,51436],{"className":51437,"style":5012},[3221],[86,51439,49404],{"className":51440,"style":51169},[7373,7503,51168],[86,51442],{"className":51443,"style":4162},[3221],[86,51445,51447,51450],{"className":51446},[1003],[86,51448,3189],{"className":51449},[1003,1007],[86,51451,51453],{"className":51452},[1012],[86,51454,51456,51476],{"className":51455},[1016,3836],[86,51457,51459,51473],{"className":51458},[1020],[86,51460,51462],{"className":51461,"style":7559},[1024],[86,51463,51464,51467],{"style":6987},[86,51465],{"className":51466,"style":1032},[1031],[86,51468,51470],{"className":51469},[1036,1037,1038,1039],[86,51471,7285],{"className":51472},[1003,1007,1039],[86,51474,3963],{"className":51475},[3962],[86,51477,51479],{"className":51478},[1020],[86,51480,51482],{"className":51481,"style":7006},[1024],[86,51483],{},[86,51485],{"className":51486,"style":4162},[3221],[86,51488,49404],{"className":51489,"style":51169},[7373,7503,51168],[86,51491],{"className":51492,"style":4162},[3221],[86,51494,51496,51499],{"className":51495},[1003],[86,51497,5464],{"className":51498,"style":8109},[1003,1007],[86,51500,51502],{"className":51501},[1012],[86,51503,51505,51525],{"className":51504},[1016,3836],[86,51506,51508,51522],{"className":51507},[1020],[86,51509,51511],{"className":51510,"style":7559},[1024],[86,51512,51513,51516],{"style":20440},[86,51514],{"className":51515,"style":1032},[1031],[86,51517,51519],{"className":51518},[1036,1037,1038,1039],[86,51520,7285],{"className":51521},[1003,1007,1039],[86,51523,3963],{"className":51524},[3962],[86,51526,51528],{"className":51527},[1020],[86,51529,51531],{"className":51530,"style":7006},[1024],[86,51532],{},[86,51534,3963],{"className":51535},[3962],[86,51537,51539],{"className":51538},[1020],[86,51540,51543],{"className":51541,"style":51542},[1024],"height:0.9629em;",[86,51544],{},[86,51546],{"className":51547},[3356,3829],[86,51549,51551],{"className":51550},[3173],[86,51552,51554,51594],{"className":51553},[955],[86,51555,51557],{"className":51556},[959],[961,51558,51559],{"xmlns":963,"display":3182},[965,51560,51561,51591],{},[968,51562,51563,51569,51571,51577,51579,51585],{},[6849,51564,51565,51567],{},[974,51566,42473],{},[978,51568,2553],{},[3191,51570,258],{},[3758,51572,51573,51575],{"accent":990},[974,51574,5464],{},[3191,51576,14087],{},[3191,51578,9864],{},[6849,51580,51581,51583],{},[974,51582,42473],{},[978,51584,802],{},[3758,51586,51587,51589],{"accent":990},[974,51588,3189],{},[3191,51590,14087],{},[982,51592,51593],{"encoding":984},"\\beta_0 = \\bar{y} - \\beta_1 \\bar{x}",[86,51595,51597,51652,51709],{"className":51596,"ariaHidden":990},[989],[86,51598,51600,51603,51643,51646,51649],{"className":51599},[994],[86,51601],{"className":51602,"style":4888},[998],[86,51604,51606,51609],{"className":51605},[1003],[86,51607,42473],{"className":51608,"style":42538},[1003,1007],[86,51610,51612],{"className":51611},[1012],[86,51613,51615,51635],{"className":51614},[1016,3836],[86,51616,51618,51632],{"className":51617},[1020],[86,51619,51621],{"className":51620,"style":6984},[1024],[86,51622,51623,51626],{"style":42553},[86,51624],{"className":51625,"style":1032},[1031],[86,51627,51629],{"className":51628},[1036,1037,1038,1039],[86,51630,2553],{"className":51631},[1003,1039],[86,51633,3963],{"className":51634},[3962],[86,51636,51638],{"className":51637},[1020],[86,51639,51641],{"className":51640,"style":7006},[1024],[86,51642],{},[86,51644],{"className":51645,"style":3222},[3221],[86,51647,258],{"className":51648},[3226],[86,51650],{"className":51651,"style":3222},[3221],[86,51653,51655,51658,51700,51703,51706],{"className":51654},[994],[86,51656],{"className":51657,"style":20769},[998],[86,51659,51661],{"className":51660},[1003,3863],[86,51662,51664,51692],{"className":51663},[1016,3836],[86,51665,51667,51689],{"className":51666},[1020],[86,51668,51670,51678],{"className":51669,"style":14154},[1024],[86,51671,51672,51675],{"style":3876},[86,51673],{"className":51674,"style":3850},[1031],[86,51676,5464],{"className":51677,"style":8109},[1003,1007],[86,51679,51680,51683],{"style":3876},[86,51681],{"className":51682,"style":3850},[1031],[86,51684,51686],{"className":51685,"style":49979},[3891],[86,51687,14087],{"className":51688},[1003],[86,51690,3963],{"className":51691},[3962],[86,51693,51695],{"className":51694},[1020],[86,51696,51698],{"className":51697,"style":30703},[1024],[86,51699],{},[86,51701],{"className":51702,"style":5012},[3221],[86,51704,9864],{"className":51705},[5016],[86,51707],{"className":51708,"style":5012},[3221],[86,51710,51712,51715,51755],{"className":51711},[994],[86,51713],{"className":51714,"style":4888},[998],[86,51716,51718,51721],{"className":51717},[1003],[86,51719,42473],{"className":51720,"style":42538},[1003,1007],[86,51722,51724],{"className":51723},[1012],[86,51725,51727,51747],{"className":51726},[1016,3836],[86,51728,51730,51744],{"className":51729},[1020],[86,51731,51733],{"className":51732,"style":6984},[1024],[86,51734,51735,51738],{"style":42553},[86,51736],{"className":51737,"style":1032},[1031],[86,51739,51741],{"className":51740},[1036,1037,1038,1039],[86,51742,802],{"className":51743},[1003,1039],[86,51745,3963],{"className":51746},[3962],[86,51748,51750],{"className":51749},[1020],[86,51751,51753],{"className":51752,"style":7006},[1024],[86,51754],{},[86,51756,51758],{"className":51757},[1003,3863],[86,51759,51761],{"className":51760},[1016],[86,51762,51764],{"className":51763},[1020],[86,51765,51767,51775],{"className":51766,"style":14154},[1024],[86,51768,51769,51772],{"style":3876},[86,51770],{"className":51771,"style":3850},[1031],[86,51773,3189],{"className":51774},[1003,1007],[86,51776,51777,51780],{"style":3876},[86,51778],{"className":51779,"style":3850},[1031],[86,51781,51783],{"className":51782,"style":14171},[3891],[86,51784,14087],{"className":51785},[1003],[12,51787,3273],{},[30,51789,51790,51820,51961],{},[33,51791,51792,49810],{},[86,51793,51795,51808],{"className":51794},[955],[86,51796,51798],{"className":51797},[959],[961,51799,51800],{"xmlns":963},[965,51801,51802,51806],{},[968,51803,51804],{},[974,51805,6896],{},[982,51807,6896],{"encoding":984},[86,51809,51811],{"className":51810,"ariaHidden":990},[989],[86,51812,51814,51817],{"className":51813},[994],[86,51815],{"className":51816,"style":7401},[998],[86,51818,6896],{"className":51819},[1003,1007],[33,51821,51822,392,51891,51960],{},[86,51823,51825,51842],{"className":51824},[955],[86,51826,51828],{"className":51827},[959],[961,51829,51830],{"xmlns":963},[965,51831,51832,51840],{},[968,51833,51834],{},[6849,51835,51836,51838],{},[974,51837,3189],{},[974,51839,7285],{},[982,51841,46757],{"encoding":984},[86,51843,51845],{"className":51844,"ariaHidden":990},[989],[86,51846,51848,51851],{"className":51847},[994],[86,51849],{"className":51850,"style":21327},[998],[86,51852,51854,51857],{"className":51853},[1003],[86,51855,3189],{"className":51856},[1003,1007],[86,51858,51860],{"className":51859},[1012],[86,51861,51863,51883],{"className":51862},[1016,3836],[86,51864,51866,51880],{"className":51865},[1020],[86,51867,51869],{"className":51868,"style":7559},[1024],[86,51870,51871,51874],{"style":6987},[86,51872],{"className":51873,"style":1032},[1031],[86,51875,51877],{"className":51876},[1036,1037,1038,1039],[86,51878,7285],{"className":51879},[1003,1007,1039],[86,51881,3963],{"className":51882},[3962],[86,51884,51886],{"className":51885},[1020],[86,51887,51889],{"className":51888,"style":7006},[1024],[86,51890],{},[86,51892,51894,51911],{"className":51893},[955],[86,51895,51897],{"className":51896},[959],[961,51898,51899],{"xmlns":963},[965,51900,51901,51909],{},[968,51902,51903],{},[6849,51904,51905,51907],{},[974,51906,5464],{},[974,51908,7285],{},[982,51910,46828],{"encoding":984},[86,51912,51914],{"className":51913,"ariaHidden":990},[989],[86,51915,51917,51920],{"className":51916},[994],[86,51918],{"className":51919,"style":16339},[998],[86,51921,51923,51926],{"className":51922},[1003],[86,51924,5464],{"className":51925,"style":8109},[1003,1007],[86,51927,51929],{"className":51928},[1012],[86,51930,51932,51952],{"className":51931},[1016,3836],[86,51933,51935,51949],{"className":51934},[1020],[86,51936,51938],{"className":51937,"style":7559},[1024],[86,51939,51940,51943],{"style":20440},[86,51941],{"className":51942,"style":1032},[1031],[86,51944,51946],{"className":51945},[1036,1037,1038,1039],[86,51947,7285],{"className":51948},[1003,1007,1039],[86,51950,3963],{"className":51951},[3962],[86,51953,51955],{"className":51954},[1020],[86,51956,51958],{"className":51957,"style":7006},[1024],[86,51959],{}," son los valores de las variables independientes y dependientes para cada ejemplo.",[33,51962,51963,392,52023,52096],{},[86,51964,51966,51983],{"className":51965},[955],[86,51967,51969],{"className":51968},[959],[961,51970,51971],{"xmlns":963},[965,51972,51973,51981],{},[968,51974,51975],{},[3758,51976,51977,51979],{"accent":990},[974,51978,3189],{},[3191,51980,14087],{},[982,51982,14344],{"encoding":984},[86,51984,51986],{"className":51985,"ariaHidden":990},[989],[86,51987,51989,51992],{"className":51988},[994],[86,51990],{"className":51991,"style":14154},[998],[86,51993,51995],{"className":51994},[1003,3863],[86,51996,51998],{"className":51997},[1016],[86,51999,52001],{"className":52000},[1020],[86,52002,52004,52012],{"className":52003,"style":14154},[1024],[86,52005,52006,52009],{"style":3876},[86,52007],{"className":52008,"style":3850},[1031],[86,52010,3189],{"className":52011},[1003,1007],[86,52013,52014,52017],{"style":3876},[86,52015],{"className":52016,"style":3850},[1031],[86,52018,52020],{"className":52019,"style":14171},[3891],[86,52021,14087],{"className":52022},[1003],[86,52024,52026,52044],{"className":52025},[955],[86,52027,52029],{"className":52028},[959],[961,52030,52031],{"xmlns":963},[965,52032,52033,52041],{},[968,52034,52035],{},[3758,52036,52037,52039],{"accent":990},[974,52038,5464],{},[3191,52040,14087],{},[982,52042,52043],{"encoding":984},"\\bar{y}",[86,52045,52047],{"className":52046,"ariaHidden":990},[989],[86,52048,52050,52054],{"className":52049},[994],[86,52051],{"className":52052,"style":52053},[998],"height:0.7622em;vertical-align:-0.1944em;",[86,52055,52057],{"className":52056},[1003,3863],[86,52058,52060,52088],{"className":52059},[1016,3836],[86,52061,52063,52085],{"className":52062},[1020],[86,52064,52066,52074],{"className":52065,"style":14154},[1024],[86,52067,52068,52071],{"style":3876},[86,52069],{"className":52070,"style":3850},[1031],[86,52072,5464],{"className":52073,"style":8109},[1003,1007],[86,52075,52076,52079],{"style":3876},[86,52077],{"className":52078,"style":3850},[1031],[86,52080,52082],{"className":52081,"style":49979},[3891],[86,52083,14087],{"className":52084},[1003],[86,52086,3963],{"className":52087},[3962],[86,52089,52091],{"className":52090},[1020],[86,52092,52094],{"className":52093,"style":30703},[1024],[86,52095],{}," son las medias (o promedios) de las variables independientes y dependientes, respectivamente.",[12,52098,52099],{},"Hagámos un ejemplo para entender como aplicarlo. Supongamos que tenemos un conjunto de datos con las siguientes características:",[461,52101,52102,52112],{},[464,52103,52104],{},[467,52105,52106,52109],{},[470,52107,52108],{},"Tamaño (m²)",[470,52110,52111],{},"Precio (USD)",[480,52113,52114,52121,52128],{},[467,52115,52116,52118],{},[485,52117,15008],{},[485,52119,52120],{},"100,000",[467,52122,52123,52125],{},[485,52124,15026],{},[485,52126,52127],{},"200,000",[467,52129,52130,52133],{},[485,52131,52132],{},"150",[485,52134,52135],{},"300,000",[12,52137,52138,52139,52142],{},"Queremos construir un modelo de regresión lineal para ",[122,52140,52141],{},"predecir el precio"," de una casa basándonos en su tamaño. En este caso, la variable independiente es el tamaño (X) y la variable dependiente es el precio (Y). El modelo de regresión lineal se puede expresar como:",[86,52144,52146],{"className":52145},[3173],[86,52147,52149,52185],{"className":52148},[955],[86,52150,52152],{"className":52151},[959],[961,52153,52154],{"xmlns":963,"display":3182},[965,52155,52156,52182],{},[968,52157,52158,52160,52162,52168,52170,52176,52178,52180],{},[974,52159,5464],{},[3191,52161,258],{},[6849,52163,52164,52166],{},[974,52165,42473],{},[978,52167,2553],{},[3191,52169,6565],{},[6849,52171,52172,52174],{},[974,52173,42473],{},[978,52175,802],{},[974,52177,3189],{},[3191,52179,6565],{},[974,52181,47369],{},[982,52183,52184],{"encoding":984},"y = \\beta_0 + \\beta_1 x + \\epsilon",[86,52186,52188,52206,52261,52319],{"className":52187,"ariaHidden":990},[989],[86,52189,52191,52194,52197,52200,52203],{"className":52190},[994],[86,52192],{"className":52193,"style":16339},[998],[86,52195,5464],{"className":52196,"style":8109},[1003,1007],[86,52198],{"className":52199,"style":3222},[3221],[86,52201,258],{"className":52202},[3226],[86,52204],{"className":52205,"style":3222},[3221],[86,52207,52209,52212,52252,52255,52258],{"className":52208},[994],[86,52210],{"className":52211,"style":4888},[998],[86,52213,52215,52218],{"className":52214},[1003],[86,52216,42473],{"className":52217,"style":42538},[1003,1007],[86,52219,52221],{"className":52220},[1012],[86,52222,52224,52244],{"className":52223},[1016,3836],[86,52225,52227,52241],{"className":52226},[1020],[86,52228,52230],{"className":52229,"style":6984},[1024],[86,52231,52232,52235],{"style":42553},[86,52233],{"className":52234,"style":1032},[1031],[86,52236,52238],{"className":52237},[1036,1037,1038,1039],[86,52239,2553],{"className":52240},[1003,1039],[86,52242,3963],{"className":52243},[3962],[86,52245,52247],{"className":52246},[1020],[86,52248,52250],{"className":52249,"style":7006},[1024],[86,52251],{},[86,52253],{"className":52254,"style":5012},[3221],[86,52256,6565],{"className":52257},[5016],[86,52259],{"className":52260,"style":5012},[3221],[86,52262,52264,52267,52307,52310,52313,52316],{"className":52263},[994],[86,52265],{"className":52266,"style":4888},[998],[86,52268,52270,52273],{"className":52269},[1003],[86,52271,42473],{"className":52272,"style":42538},[1003,1007],[86,52274,52276],{"className":52275},[1012],[86,52277,52279,52299],{"className":52278},[1016,3836],[86,52280,52282,52296],{"className":52281},[1020],[86,52283,52285],{"className":52284,"style":6984},[1024],[86,52286,52287,52290],{"style":42553},[86,52288],{"className":52289,"style":1032},[1031],[86,52291,52293],{"className":52292},[1036,1037,1038,1039],[86,52294,802],{"className":52295},[1003,1039],[86,52297,3963],{"className":52298},[3962],[86,52300,52302],{"className":52301},[1020],[86,52303,52305],{"className":52304,"style":7006},[1024],[86,52306],{},[86,52308,3189],{"className":52309},[1003,1007],[86,52311],{"className":52312,"style":5012},[3221],[86,52314,6565],{"className":52315},[5016],[86,52317],{"className":52318,"style":5012},[3221],[86,52320,52322,52325],{"className":52321},[994],[86,52323],{"className":52324,"style":7401},[998],[86,52326,47369],{"className":52327},[1003,1007],[12,52329,3273],{},[30,52331,52332,52363,52394,52466,52538],{},[33,52333,52334,52362],{},[86,52335,52337,52350],{"className":52336},[955],[86,52338,52340],{"className":52339},[959],[961,52341,52342],{"xmlns":963},[965,52343,52344,52348],{},[968,52345,52346],{},[974,52347,5464],{},[982,52349,5464],{"encoding":984},[86,52351,52353],{"className":52352,"ariaHidden":990},[989],[86,52354,52356,52359],{"className":52355},[994],[86,52357],{"className":52358,"style":16339},[998],[86,52360,5464],{"className":52361,"style":8109},[1003,1007]," es el precio de la casa.",[33,52364,52365,52393],{},[86,52366,52368,52381],{"className":52367},[955],[86,52369,52371],{"className":52370},[959],[961,52372,52373],{"xmlns":963},[965,52374,52375,52379],{},[968,52376,52377],{},[974,52378,3189],{},[982,52380,3189],{"encoding":984},[86,52382,52384],{"className":52383,"ariaHidden":990},[989],[86,52385,52387,52390],{"className":52386},[994],[86,52388],{"className":52389,"style":7401},[998],[86,52391,3189],{"className":52392},[1003,1007]," es el tamaño de la casa.",[33,52395,52396,52465],{},[86,52397,52399,52416],{"className":52398},[955],[86,52400,52402],{"className":52401},[959],[961,52403,52404],{"xmlns":963},[965,52405,52406,52414],{},[968,52407,52408],{},[6849,52409,52410,52412],{},[974,52411,42473],{},[978,52413,2553],{},[982,52415,48018],{"encoding":984},[86,52417,52419],{"className":52418,"ariaHidden":990},[989],[86,52420,52422,52425],{"className":52421},[994],[86,52423],{"className":52424,"style":4888},[998],[86,52426,52428,52431],{"className":52427},[1003],[86,52429,42473],{"className":52430,"style":42538},[1003,1007],[86,52432,52434],{"className":52433},[1012],[86,52435,52437,52457],{"className":52436},[1016,3836],[86,52438,52440,52454],{"className":52439},[1020],[86,52441,52443],{"className":52442,"style":6984},[1024],[86,52444,52445,52448],{"style":42553},[86,52446],{"className":52447,"style":1032},[1031],[86,52449,52451],{"className":52450},[1036,1037,1038,1039],[86,52452,2553],{"className":52453},[1003,1039],[86,52455,3963],{"className":52456},[3962],[86,52458,52460],{"className":52459},[1020],[86,52461,52463],{"className":52462,"style":7006},[1024],[86,52464],{}," es el intercepto.",[33,52467,52468,52537],{},[86,52469,52471,52488],{"className":52470},[955],[86,52472,52474],{"className":52473},[959],[961,52475,52476],{"xmlns":963},[965,52477,52478,52486],{},[968,52479,52480],{},[6849,52481,52482,52484],{},[974,52483,42473],{},[978,52485,802],{},[982,52487,50913],{"encoding":984},[86,52489,52491],{"className":52490,"ariaHidden":990},[989],[86,52492,52494,52497],{"className":52493},[994],[86,52495],{"className":52496,"style":4888},[998],[86,52498,52500,52503],{"className":52499},[1003],[86,52501,42473],{"className":52502,"style":42538},[1003,1007],[86,52504,52506],{"className":52505},[1012],[86,52507,52509,52529],{"className":52508},[1016,3836],[86,52510,52512,52526],{"className":52511},[1020],[86,52513,52515],{"className":52514,"style":6984},[1024],[86,52516,52517,52520],{"style":42553},[86,52518],{"className":52519,"style":1032},[1031],[86,52521,52523],{"className":52522},[1036,1037,1038,1039],[86,52524,802],{"className":52525},[1003,1039],[86,52527,3963],{"className":52528},[3962],[86,52530,52532],{"className":52531},[1020],[86,52533,52535],{"className":52534,"style":7006},[1024],[86,52536],{}," es la pendiente.",[33,52539,52540,52568],{},[86,52541,52543,52556],{"className":52542},[955],[86,52544,52546],{"className":52545},[959],[961,52547,52548],{"xmlns":963},[965,52549,52550,52554],{},[968,52551,52552],{},[974,52553,47369],{},[982,52555,48343],{"encoding":984},[86,52557,52559],{"className":52558,"ariaHidden":990},[989],[86,52560,52562,52565],{"className":52561},[994],[86,52563],{"className":52564,"style":7401},[998],[86,52566,47369],{"className":52567},[1003,1007]," es el error o ruido, que para este ejemplo asumiremos que es cero para simplificar.",[12,52570,52571,52572,392,52641,52710],{},"Para encontrar los valores de ",[86,52573,52575,52592],{"className":52574},[955],[86,52576,52578],{"className":52577},[959],[961,52579,52580],{"xmlns":963},[965,52581,52582,52590],{},[968,52583,52584],{},[6849,52585,52586,52588],{},[974,52587,42473],{},[978,52589,2553],{},[982,52591,48018],{"encoding":984},[86,52593,52595],{"className":52594,"ariaHidden":990},[989],[86,52596,52598,52601],{"className":52597},[994],[86,52599],{"className":52600,"style":4888},[998],[86,52602,52604,52607],{"className":52603},[1003],[86,52605,42473],{"className":52606,"style":42538},[1003,1007],[86,52608,52610],{"className":52609},[1012],[86,52611,52613,52633],{"className":52612},[1016,3836],[86,52614,52616,52630],{"className":52615},[1020],[86,52617,52619],{"className":52618,"style":6984},[1024],[86,52620,52621,52624],{"style":42553},[86,52622],{"className":52623,"style":1032},[1031],[86,52625,52627],{"className":52626},[1036,1037,1038,1039],[86,52628,2553],{"className":52629},[1003,1039],[86,52631,3963],{"className":52632},[3962],[86,52634,52636],{"className":52635},[1020],[86,52637,52639],{"className":52638,"style":7006},[1024],[86,52640],{},[86,52642,52644,52661],{"className":52643},[955],[86,52645,52647],{"className":52646},[959],[961,52648,52649],{"xmlns":963},[965,52650,52651,52659],{},[968,52652,52653],{},[6849,52654,52655,52657],{},[974,52656,42473],{},[978,52658,802],{},[982,52660,50913],{"encoding":984},[86,52662,52664],{"className":52663,"ariaHidden":990},[989],[86,52665,52667,52670],{"className":52666},[994],[86,52668],{"className":52669,"style":4888},[998],[86,52671,52673,52676],{"className":52672},[1003],[86,52674,42473],{"className":52675,"style":42538},[1003,1007],[86,52677,52679],{"className":52678},[1012],[86,52680,52682,52702],{"className":52681},[1016,3836],[86,52683,52685,52699],{"className":52684},[1020],[86,52686,52688],{"className":52687,"style":6984},[1024],[86,52689,52690,52693],{"style":42553},[86,52691],{"className":52692,"style":1032},[1031],[86,52694,52696],{"className":52695},[1036,1037,1038,1039],[86,52697,802],{"className":52698},[1003,1039],[86,52700,3963],{"className":52701},[3962],[86,52703,52705],{"className":52704},[1020],[86,52706,52708],{"className":52707,"style":7006},[1024],[86,52709],{},", podemos usar el método de mínimos cuadrados con la fórmula que mencionamos anteriormente:",[86,52712,52714],{"className":52713},[3173],[86,52715,52717,52814],{"className":52716},[955],[86,52718,52720],{"className":52719},[959],[961,52721,52722],{"xmlns":963,"display":3182},[965,52723,52724,52812],{},[968,52725,52726,52732,52734],{},[6849,52727,52728,52730],{},[974,52729,42473],{},[978,52731,802],{},[3191,52733,258],{},[3749,52735,52736,52776],{},[968,52737,52738,52740,52742,52744,52750,52756,52758,52760,52762,52768,52770],{},[974,52739,6896],{},[3191,52741,49404],{},[3191,52743,243],{"stretchy":3295},[6849,52745,52746,52748],{},[974,52747,3189],{},[974,52749,7285],{},[6849,52751,52752,52754],{},[974,52753,5464],{},[974,52755,7285],{},[3191,52757,867],{"stretchy":3295},[3191,52759,9864],{},[3191,52761,49404],{},[6849,52763,52764,52766],{},[974,52765,3189],{},[974,52767,7285],{},[3191,52769,49404],{},[6849,52771,52772,52774],{},[974,52773,5464],{},[974,52775,7285],{},[968,52777,52778,52780,52782,52784,52792,52794,52796,52798,52800,52806],{},[974,52779,6896],{},[3191,52781,49404],{},[3191,52783,243],{"stretchy":3295},[9835,52785,52786,52788,52790],{},[974,52787,3189],{},[974,52789,7285],{},[978,52791,980],{},[3191,52793,867],{"stretchy":3295},[3191,52795,9864],{},[3191,52797,243],{"stretchy":3295},[3191,52799,49404],{},[6849,52801,52802,52804],{},[974,52803,3189],{},[974,52805,7285],{},[971,52807,52808,52810],{},[3191,52809,867],{"stretchy":3295},[978,52811,980],{},[982,52813,51067],{"encoding":984},[86,52815,52817,52872],{"className":52816,"ariaHidden":990},[989],[86,52818,52820,52823,52863,52866,52869],{"className":52819},[994],[86,52821],{"className":52822,"style":4888},[998],[86,52824,52826,52829],{"className":52825},[1003],[86,52827,42473],{"className":52828,"style":42538},[1003,1007],[86,52830,52832],{"className":52831},[1012],[86,52833,52835,52855],{"className":52834},[1016,3836],[86,52836,52838,52852],{"className":52837},[1020],[86,52839,52841],{"className":52840,"style":6984},[1024],[86,52842,52843,52846],{"style":42553},[86,52844],{"className":52845,"style":1032},[1031],[86,52847,52849],{"className":52848},[1036,1037,1038,1039],[86,52850,802],{"className":52851},[1003,1039],[86,52853,3963],{"className":52854},[3962],[86,52856,52858],{"className":52857},[1020],[86,52859,52861],{"className":52860,"style":7006},[1024],[86,52862],{},[86,52864],{"className":52865,"style":3222},[3221],[86,52867,258],{"className":52868},[3226],[86,52870],{"className":52871,"style":3222},[3221],[86,52873,52875,52878],{"className":52874},[994],[86,52876],{"className":52877,"style":51132},[998],[86,52879,52881,52884,53283],{"className":52880},[1003],[86,52882],{"className":52883},[3320,3829],[86,52885,52887],{"className":52886},[3749],[86,52888,52890,53275],{"className":52889},[1016,3836],[86,52891,52893,53272],{"className":52892},[1020],[86,52894,52896,53057,53065],{"className":52895,"style":5706},[1024],[86,52897,52898,52901],{"style":3846},[86,52899],{"className":52900,"style":3850},[1031],[86,52902,52904,52907,52910,52913,52916,52967,52970,52973,52976,52979,52982,52985,52988,53028],{"className":52903},[1003],[86,52905,6896],{"className":52906},[1003,1007],[86,52908],{"className":52909,"style":4162},[3221],[86,52911,49404],{"className":52912,"style":51169},[7373,7503,51168],[86,52914,243],{"className":52915},[3320],[86,52917,52919,52922],{"className":52918},[1003],[86,52920,3189],{"className":52921},[1003,1007],[86,52923,52925],{"className":52924},[1012],[86,52926,52928,52959],{"className":52927},[1016,3836],[86,52929,52931,52956],{"className":52930},[1020],[86,52932,52934,52945],{"className":52933,"style":10092},[1024],[86,52935,52936,52939],{"style":51193},[86,52937],{"className":52938,"style":1032},[1031],[86,52940,52942],{"className":52941},[1036,1037,1038,1039],[86,52943,7285],{"className":52944},[1003,1007,1039],[86,52946,52947,52950],{"style":10116},[86,52948],{"className":52949,"style":1032},[1031],[86,52951,52953],{"className":52952},[1036,1037,1038,1039],[86,52954,980],{"className":52955},[1003,1039],[86,52957,3963],{"className":52958},[3962],[86,52960,52962],{"className":52961},[1020],[86,52963,52965],{"className":52964,"style":51223},[1024],[86,52966],{},[86,52968,867],{"className":52969},[3356],[86,52971],{"className":52972,"style":5012},[3221],[86,52974,9864],{"className":52975},[5016],[86,52977],{"className":52978,"style":5012},[3221],[86,52980,243],{"className":52981},[3320],[86,52983,49404],{"className":52984,"style":51169},[7373,7503,51168],[86,52986],{"className":52987,"style":4162},[3221],[86,52989,52991,52994],{"className":52990},[1003],[86,52992,3189],{"className":52993},[1003,1007],[86,52995,52997],{"className":52996},[1012],[86,52998,53000,53020],{"className":52999},[1016,3836],[86,53001,53003,53017],{"className":53002},[1020],[86,53004,53006],{"className":53005,"style":7559},[1024],[86,53007,53008,53011],{"style":6987},[86,53009],{"className":53010,"style":1032},[1031],[86,53012,53014],{"className":53013},[1036,1037,1038,1039],[86,53015,7285],{"className":53016},[1003,1007,1039],[86,53018,3963],{"className":53019},[3962],[86,53021,53023],{"className":53022},[1020],[86,53024,53026],{"className":53025,"style":7006},[1024],[86,53027],{},[86,53029,53031,53034],{"className":53030},[3356],[86,53032,867],{"className":53033},[3356],[86,53035,53037],{"className":53036},[1012],[86,53038,53040],{"className":53039},[1016],[86,53041,53043],{"className":53042},[1020],[86,53044,53046],{"className":53045,"style":51305},[1024],[86,53047,53048,53051],{"style":51308},[86,53049],{"className":53050,"style":1032},[1031],[86,53052,53054],{"className":53053},[1036,1037,1038,1039],[86,53055,980],{"className":53056},[1003,1039],[86,53058,53059,53062],{"style":3901},[86,53060],{"className":53061,"style":3850},[1031],[86,53063],{"className":53064,"style":3909},[3908],[86,53066,53067,53070],{"style":3912},[86,53068],{"className":53069,"style":3850},[1031],[86,53071,53073,53076,53079,53082,53085,53125,53165,53168,53171,53174,53177,53180,53183,53223,53226,53229,53232],{"className":53072},[1003],[86,53074,6896],{"className":53075},[1003,1007],[86,53077],{"className":53078,"style":4162},[3221],[86,53080,49404],{"className":53081,"style":51169},[7373,7503,51168],[86,53083,243],{"className":53084},[3320],[86,53086,53088,53091],{"className":53087},[1003],[86,53089,3189],{"className":53090},[1003,1007],[86,53092,53094],{"className":53093},[1012],[86,53095,53097,53117],{"className":53096},[1016,3836],[86,53098,53100,53114],{"className":53099},[1020],[86,53101,53103],{"className":53102,"style":7559},[1024],[86,53104,53105,53108],{"style":6987},[86,53106],{"className":53107,"style":1032},[1031],[86,53109,53111],{"className":53110},[1036,1037,1038,1039],[86,53112,7285],{"className":53113},[1003,1007,1039],[86,53115,3963],{"className":53116},[3962],[86,53118,53120],{"className":53119},[1020],[86,53121,53123],{"className":53122,"style":7006},[1024],[86,53124],{},[86,53126,53128,53131],{"className":53127},[1003],[86,53129,5464],{"className":53130,"style":8109},[1003,1007],[86,53132,53134],{"className":53133},[1012],[86,53135,53137,53157],{"className":53136},[1016,3836],[86,53138,53140,53154],{"className":53139},[1020],[86,53141,53143],{"className":53142,"style":7559},[1024],[86,53144,53145,53148],{"style":20440},[86,53146],{"className":53147,"style":1032},[1031],[86,53149,53151],{"className":53150},[1036,1037,1038,1039],[86,53152,7285],{"className":53153},[1003,1007,1039],[86,53155,3963],{"className":53156},[3962],[86,53158,53160],{"className":53159},[1020],[86,53161,53163],{"className":53162,"style":7006},[1024],[86,53164],{},[86,53166,867],{"className":53167},[3356],[86,53169],{"className":53170,"style":5012},[3221],[86,53172,9864],{"className":53173},[5016],[86,53175],{"className":53176,"style":5012},[3221],[86,53178,49404],{"className":53179,"style":51169},[7373,7503,51168],[86,53181],{"className":53182,"style":4162},[3221],[86,53184,53186,53189],{"className":53185},[1003],[86,53187,3189],{"className":53188},[1003,1007],[86,53190,53192],{"className":53191},[1012],[86,53193,53195,53215],{"className":53194},[1016,3836],[86,53196,53198,53212],{"className":53197},[1020],[86,53199,53201],{"className":53200,"style":7559},[1024],[86,53202,53203,53206],{"style":6987},[86,53204],{"className":53205,"style":1032},[1031],[86,53207,53209],{"className":53208},[1036,1037,1038,1039],[86,53210,7285],{"className":53211},[1003,1007,1039],[86,53213,3963],{"className":53214},[3962],[86,53216,53218],{"className":53217},[1020],[86,53219,53221],{"className":53220,"style":7006},[1024],[86,53222],{},[86,53224],{"className":53225,"style":4162},[3221],[86,53227,49404],{"className":53228,"style":51169},[7373,7503,51168],[86,53230],{"className":53231,"style":4162},[3221],[86,53233,53235,53238],{"className":53234},[1003],[86,53236,5464],{"className":53237,"style":8109},[1003,1007],[86,53239,53241],{"className":53240},[1012],[86,53242,53244,53264],{"className":53243},[1016,3836],[86,53245,53247,53261],{"className":53246},[1020],[86,53248,53250],{"className":53249,"style":7559},[1024],[86,53251,53252,53255],{"style":20440},[86,53253],{"className":53254,"style":1032},[1031],[86,53256,53258],{"className":53257},[1036,1037,1038,1039],[86,53259,7285],{"className":53260},[1003,1007,1039],[86,53262,3963],{"className":53263},[3962],[86,53265,53267],{"className":53266},[1020],[86,53268,53270],{"className":53269,"style":7006},[1024],[86,53271],{},[86,53273,3963],{"className":53274},[3962],[86,53276,53278],{"className":53277},[1020],[86,53279,53281],{"className":53280,"style":51542},[1024],[86,53282],{},[86,53284],{"className":53285},[3356,3829],[86,53287,53289],{"className":53288},[3173],[86,53290,53292,53331],{"className":53291},[955],[86,53293,53295],{"className":53294},[959],[961,53296,53297],{"xmlns":963,"display":3182},[965,53298,53299,53329],{},[968,53300,53301,53307,53309,53315,53317,53323],{},[6849,53302,53303,53305],{},[974,53304,42473],{},[978,53306,2553],{},[3191,53308,258],{},[3758,53310,53311,53313],{"accent":990},[974,53312,5464],{},[3191,53314,14087],{},[3191,53316,9864],{},[6849,53318,53319,53321],{},[974,53320,42473],{},[978,53322,802],{},[3758,53324,53325,53327],{"accent":990},[974,53326,3189],{},[3191,53328,14087],{},[982,53330,51593],{"encoding":984},[86,53332,53334,53389,53446],{"className":53333,"ariaHidden":990},[989],[86,53335,53337,53340,53380,53383,53386],{"className":53336},[994],[86,53338],{"className":53339,"style":4888},[998],[86,53341,53343,53346],{"className":53342},[1003],[86,53344,42473],{"className":53345,"style":42538},[1003,1007],[86,53347,53349],{"className":53348},[1012],[86,53350,53352,53372],{"className":53351},[1016,3836],[86,53353,53355,53369],{"className":53354},[1020],[86,53356,53358],{"className":53357,"style":6984},[1024],[86,53359,53360,53363],{"style":42553},[86,53361],{"className":53362,"style":1032},[1031],[86,53364,53366],{"className":53365},[1036,1037,1038,1039],[86,53367,2553],{"className":53368},[1003,1039],[86,53370,3963],{"className":53371},[3962],[86,53373,53375],{"className":53374},[1020],[86,53376,53378],{"className":53377,"style":7006},[1024],[86,53379],{},[86,53381],{"className":53382,"style":3222},[3221],[86,53384,258],{"className":53385},[3226],[86,53387],{"className":53388,"style":3222},[3221],[86,53390,53392,53395,53437,53440,53443],{"className":53391},[994],[86,53393],{"className":53394,"style":20769},[998],[86,53396,53398],{"className":53397},[1003,3863],[86,53399,53401,53429],{"className":53400},[1016,3836],[86,53402,53404,53426],{"className":53403},[1020],[86,53405,53407,53415],{"className":53406,"style":14154},[1024],[86,53408,53409,53412],{"style":3876},[86,53410],{"className":53411,"style":3850},[1031],[86,53413,5464],{"className":53414,"style":8109},[1003,1007],[86,53416,53417,53420],{"style":3876},[86,53418],{"className":53419,"style":3850},[1031],[86,53421,53423],{"className":53422,"style":49979},[3891],[86,53424,14087],{"className":53425},[1003],[86,53427,3963],{"className":53428},[3962],[86,53430,53432],{"className":53431},[1020],[86,53433,53435],{"className":53434,"style":30703},[1024],[86,53436],{},[86,53438],{"className":53439,"style":5012},[3221],[86,53441,9864],{"className":53442},[5016],[86,53444],{"className":53445,"style":5012},[3221],[86,53447,53449,53452,53492],{"className":53448},[994],[86,53450],{"className":53451,"style":4888},[998],[86,53453,53455,53458],{"className":53454},[1003],[86,53456,42473],{"className":53457,"style":42538},[1003,1007],[86,53459,53461],{"className":53460},[1012],[86,53462,53464,53484],{"className":53463},[1016,3836],[86,53465,53467,53481],{"className":53466},[1020],[86,53468,53470],{"className":53469,"style":6984},[1024],[86,53471,53472,53475],{"style":42553},[86,53473],{"className":53474,"style":1032},[1031],[86,53476,53478],{"className":53477},[1036,1037,1038,1039],[86,53479,802],{"className":53480},[1003,1039],[86,53482,3963],{"className":53483},[3962],[86,53485,53487],{"className":53486},[1020],[86,53488,53490],{"className":53489,"style":7006},[1024],[86,53491],{},[86,53493,53495],{"className":53494},[1003,3863],[86,53496,53498],{"className":53497},[1016],[86,53499,53501],{"className":53500},[1020],[86,53502,53504,53512],{"className":53503,"style":14154},[1024],[86,53505,53506,53509],{"style":3876},[86,53507],{"className":53508,"style":3850},[1031],[86,53510,3189],{"className":53511},[1003,1007],[86,53513,53514,53517],{"style":3876},[86,53515],{"className":53516,"style":3850},[1031],[86,53518,53520],{"className":53519,"style":14171},[3891],[86,53521,14087],{"className":53522},[1003],[12,53524,3273],{},[30,53526,53527,53558,53699],{},[33,53528,53529,53557],{},[86,53530,53532,53545],{"className":53531},[955],[86,53533,53535],{"className":53534},[959],[961,53536,53537],{"xmlns":963},[965,53538,53539,53543],{},[968,53540,53541],{},[974,53542,6896],{},[982,53544,6896],{"encoding":984},[86,53546,53548],{"className":53547,"ariaHidden":990},[989],[86,53549,53551,53554],{"className":53550},[994],[86,53552],{"className":53553,"style":7401},[998],[86,53555,6896],{"className":53556},[1003,1007]," es el número de ejemplos (en este caso, 3).",[33,53559,53560,392,53629,53698],{},[86,53561,53563,53580],{"className":53562},[955],[86,53564,53566],{"className":53565},[959],[961,53567,53568],{"xmlns":963},[965,53569,53570,53578],{},[968,53571,53572],{},[6849,53573,53574,53576],{},[974,53575,3189],{},[974,53577,7285],{},[982,53579,46757],{"encoding":984},[86,53581,53583],{"className":53582,"ariaHidden":990},[989],[86,53584,53586,53589],{"className":53585},[994],[86,53587],{"className":53588,"style":21327},[998],[86,53590,53592,53595],{"className":53591},[1003],[86,53593,3189],{"className":53594},[1003,1007],[86,53596,53598],{"className":53597},[1012],[86,53599,53601,53621],{"className":53600},[1016,3836],[86,53602,53604,53618],{"className":53603},[1020],[86,53605,53607],{"className":53606,"style":7559},[1024],[86,53608,53609,53612],{"style":6987},[86,53610],{"className":53611,"style":1032},[1031],[86,53613,53615],{"className":53614},[1036,1037,1038,1039],[86,53616,7285],{"className":53617},[1003,1007,1039],[86,53619,3963],{"className":53620},[3962],[86,53622,53624],{"className":53623},[1020],[86,53625,53627],{"className":53626,"style":7006},[1024],[86,53628],{},[86,53630,53632,53649],{"className":53631},[955],[86,53633,53635],{"className":53634},[959],[961,53636,53637],{"xmlns":963},[965,53638,53639,53647],{},[968,53640,53641],{},[6849,53642,53643,53645],{},[974,53644,5464],{},[974,53646,7285],{},[982,53648,46828],{"encoding":984},[86,53650,53652],{"className":53651,"ariaHidden":990},[989],[86,53653,53655,53658],{"className":53654},[994],[86,53656],{"className":53657,"style":16339},[998],[86,53659,53661,53664],{"className":53660},[1003],[86,53662,5464],{"className":53663,"style":8109},[1003,1007],[86,53665,53667],{"className":53666},[1012],[86,53668,53670,53690],{"className":53669},[1016,3836],[86,53671,53673,53687],{"className":53672},[1020],[86,53674,53676],{"className":53675,"style":7559},[1024],[86,53677,53678,53681],{"style":20440},[86,53679],{"className":53680,"style":1032},[1031],[86,53682,53684],{"className":53683},[1036,1037,1038,1039],[86,53685,7285],{"className":53686},[1003,1007,1039],[86,53688,3963],{"className":53689},[3962],[86,53691,53693],{"className":53692},[1020],[86,53694,53696],{"className":53695,"style":7006},[1024],[86,53697],{}," son los valores de tamaño y precio para cada ejemplo.",[33,53700,53701,392,53761,53832],{},[86,53702,53704,53721],{"className":53703},[955],[86,53705,53707],{"className":53706},[959],[961,53708,53709],{"xmlns":963},[965,53710,53711,53719],{},[968,53712,53713],{},[3758,53714,53715,53717],{"accent":990},[974,53716,3189],{},[3191,53718,14087],{},[982,53720,14344],{"encoding":984},[86,53722,53724],{"className":53723,"ariaHidden":990},[989],[86,53725,53727,53730],{"className":53726},[994],[86,53728],{"className":53729,"style":14154},[998],[86,53731,53733],{"className":53732},[1003,3863],[86,53734,53736],{"className":53735},[1016],[86,53737,53739],{"className":53738},[1020],[86,53740,53742,53750],{"className":53741,"style":14154},[1024],[86,53743,53744,53747],{"style":3876},[86,53745],{"className":53746,"style":3850},[1031],[86,53748,3189],{"className":53749},[1003,1007],[86,53751,53752,53755],{"style":3876},[86,53753],{"className":53754,"style":3850},[1031],[86,53756,53758],{"className":53757,"style":14171},[3891],[86,53759,14087],{"className":53760},[1003],[86,53762,53764,53781],{"className":53763},[955],[86,53765,53767],{"className":53766},[959],[961,53768,53769],{"xmlns":963},[965,53770,53771,53779],{},[968,53772,53773],{},[3758,53774,53775,53777],{"accent":990},[974,53776,5464],{},[3191,53778,14087],{},[982,53780,52043],{"encoding":984},[86,53782,53784],{"className":53783,"ariaHidden":990},[989],[86,53785,53787,53790],{"className":53786},[994],[86,53788],{"className":53789,"style":52053},[998],[86,53791,53793],{"className":53792},[1003,3863],[86,53794,53796,53824],{"className":53795},[1016,3836],[86,53797,53799,53821],{"className":53798},[1020],[86,53800,53802,53810],{"className":53801,"style":14154},[1024],[86,53803,53804,53807],{"style":3876},[86,53805],{"className":53806,"style":3850},[1031],[86,53808,5464],{"className":53809,"style":8109},[1003,1007],[86,53811,53812,53815],{"style":3876},[86,53813],{"className":53814,"style":3850},[1031],[86,53816,53818],{"className":53817,"style":49979},[3891],[86,53819,14087],{"className":53820},[1003],[86,53822,3963],{"className":53823},[3962],[86,53825,53827],{"className":53826},[1020],[86,53828,53830],{"className":53829,"style":30703},[1024],[86,53831],{}," son las medias de las variables independientes y dependientes, respectivamente.",[12,53834,53835],{},"Tenemos entonces para este caso:",[86,53837,53839],{"className":53838},[3173],[86,53840,53842,53978],{"className":53841},[955],[86,53843,53845],{"className":53844},[959],[961,53846,53847],{"xmlns":963,"display":3182},[965,53848,53849,53975],{},[968,53850,53851,53857,53859],{},[6849,53852,53853,53855],{},[974,53854,42473],{},[978,53856,802],{},[3191,53858,258],{},[3749,53860,53861,53925],{},[968,53862,53863,53865,53867,53869,53872,53875,53877,53879,53881,53884,53886,53888,53890,53893,53895,53897,53899,53901,53903,53905,53907,53909,53911,53913,53915,53917,53919,53921,53923],{},[978,53864,4100],{},[3191,53866,243],{"stretchy":3295},[978,53868,15008],{},[3191,53870,53871],{},"∗",[978,53873,53874],{},"100000",[3191,53876,6565],{},[978,53878,15026],{},[3191,53880,53871],{},[978,53882,53883],{},"200000",[3191,53885,6565],{},[978,53887,52132],{},[3191,53889,53871],{},[978,53891,53892],{},"300000",[3191,53894,867],{"stretchy":3295},[3191,53896,9864],{},[3191,53898,243],{"stretchy":3295},[978,53900,15008],{},[3191,53902,6565],{},[978,53904,15026],{},[3191,53906,6565],{},[978,53908,52132],{},[3191,53910,867],{"stretchy":3295},[3191,53912,243],{"stretchy":3295},[978,53914,53874],{},[3191,53916,6565],{},[978,53918,53883],{},[3191,53920,6565],{},[978,53922,53892],{},[3191,53924,867],{"stretchy":3295},[968,53926,53927,53929,53931,53937,53939,53945,53947,53953,53955,53957,53959,53961,53963,53965,53967,53969],{},[978,53928,4100],{},[3191,53930,243],{"stretchy":3295},[971,53932,53933,53935],{},[978,53934,15008],{},[978,53936,980],{},[3191,53938,6565],{},[971,53940,53941,53943],{},[978,53942,15026],{},[978,53944,980],{},[3191,53946,6565],{},[971,53948,53949,53951],{},[978,53950,52132],{},[978,53952,980],{},[3191,53954,867],{"stretchy":3295},[3191,53956,9864],{},[3191,53958,243],{"stretchy":3295},[978,53960,15008],{},[3191,53962,6565],{},[978,53964,15026],{},[3191,53966,6565],{},[978,53968,52132],{},[971,53970,53971,53973],{},[3191,53972,867],{"stretchy":3295},[978,53974,980],{},[982,53976,53977],{"encoding":984},"\\beta_1 = \\frac{3(50*100000 + 100*200000 + 150*300000) - (50 + 100 + 150)(100000 + 200000 + 300000)}{3(50^2 + 100^2 + 150^2) - (50 + 100 + 150)^2}",[86,53979,53981,54036],{"className":53980,"ariaHidden":990},[989],[86,53982,53984,53987,54027,54030,54033],{"className":53983},[994],[86,53985],{"className":53986,"style":4888},[998],[86,53988,53990,53993],{"className":53989},[1003],[86,53991,42473],{"className":53992,"style":42538},[1003,1007],[86,53994,53996],{"className":53995},[1012],[86,53997,53999,54019],{"className":53998},[1016,3836],[86,54000,54002,54016],{"className":54001},[1020],[86,54003,54005],{"className":54004,"style":6984},[1024],[86,54006,54007,54010],{"style":42553},[86,54008],{"className":54009,"style":1032},[1031],[86,54011,54013],{"className":54012},[1036,1037,1038,1039],[86,54014,802],{"className":54015},[1003,1039],[86,54017,3963],{"className":54018},[3962],[86,54020,54022],{"className":54021},[1020],[86,54023,54025],{"className":54024,"style":7006},[1024],[86,54026],{},[86,54028],{"className":54029,"style":3222},[3221],[86,54031,258],{"className":54032},[3226],[86,54034],{"className":54035,"style":3222},[3221],[86,54037,54039,54042],{"className":54038},[994],[86,54040],{"className":54041,"style":5687},[998],[86,54043,54045,54048,54434],{"className":54044},[1003],[86,54046],{"className":54047},[3320,3829],[86,54049,54051],{"className":54050},[3749],[86,54052,54054,54426],{"className":54053},[1016,3836],[86,54055,54057,54423],{"className":54056},[1020],[86,54058,54060,54260,54268],{"className":54059,"style":5706},[1024],[86,54061,54062,54065],{"style":3846},[86,54063],{"className":54064,"style":3850},[1031],[86,54066,54068,54071,54074,54077,54106,54109,54112,54115,54118,54147,54150,54153,54156,54160,54189,54192,54195,54198,54201,54204,54207,54210,54213,54216,54219,54222,54225,54228,54231],{"className":54067},[1003],[86,54069,4100],{"className":54070},[1003],[86,54072,243],{"className":54073},[3320],[86,54075,1108],{"className":54076},[1003],[86,54078,54080,54083],{"className":54079},[1003],[86,54081,2553],{"className":54082},[1003],[86,54084,54086],{"className":54085},[1012],[86,54087,54089],{"className":54088},[1016],[86,54090,54092],{"className":54091},[1020],[86,54093,54095],{"className":54094,"style":51305},[1024],[86,54096,54097,54100],{"style":51308},[86,54098],{"className":54099,"style":1032},[1031],[86,54101,54103],{"className":54102},[1036,1037,1038,1039],[86,54104,980],{"className":54105},[1003,1039],[86,54107],{"className":54108,"style":5012},[3221],[86,54110,6565],{"className":54111},[5016],[86,54113],{"className":54114,"style":5012},[3221],[86,54116,15021],{"className":54117},[1003],[86,54119,54121,54124],{"className":54120},[1003],[86,54122,2553],{"className":54123},[1003],[86,54125,54127],{"className":54126},[1012],[86,54128,54130],{"className":54129},[1016],[86,54131,54133],{"className":54132},[1020],[86,54134,54136],{"className":54135,"style":51305},[1024],[86,54137,54138,54141],{"style":51308},[86,54139],{"className":54140,"style":1032},[1031],[86,54142,54144],{"className":54143},[1036,1037,1038,1039],[86,54145,980],{"className":54146},[1003,1039],[86,54148],{"className":54149,"style":5012},[3221],[86,54151,6565],{"className":54152},[5016],[86,54154],{"className":54155,"style":5012},[3221],[86,54157,54159],{"className":54158},[1003],"15",[86,54161,54163,54166],{"className":54162},[1003],[86,54164,2553],{"className":54165},[1003],[86,54167,54169],{"className":54168},[1012],[86,54170,54172],{"className":54171},[1016],[86,54173,54175],{"className":54174},[1020],[86,54176,54178],{"className":54177,"style":51305},[1024],[86,54179,54180,54183],{"style":51308},[86,54181],{"className":54182,"style":1032},[1031],[86,54184,54186],{"className":54185},[1036,1037,1038,1039],[86,54187,980],{"className":54188},[1003,1039],[86,54190,867],{"className":54191},[3356],[86,54193],{"className":54194,"style":5012},[3221],[86,54196,9864],{"className":54197},[5016],[86,54199],{"className":54200,"style":5012},[3221],[86,54202,243],{"className":54203},[3320],[86,54205,15008],{"className":54206},[1003],[86,54208],{"className":54209,"style":5012},[3221],[86,54211,6565],{"className":54212},[5016],[86,54214],{"className":54215,"style":5012},[3221],[86,54217,15026],{"className":54218},[1003],[86,54220],{"className":54221,"style":5012},[3221],[86,54223,6565],{"className":54224},[5016],[86,54226],{"className":54227,"style":5012},[3221],[86,54229,52132],{"className":54230},[1003],[86,54232,54234,54237],{"className":54233},[3356],[86,54235,867],{"className":54236},[3356],[86,54238,54240],{"className":54239},[1012],[86,54241,54243],{"className":54242},[1016],[86,54244,54246],{"className":54245},[1020],[86,54247,54249],{"className":54248,"style":51305},[1024],[86,54250,54251,54254],{"style":51308},[86,54252],{"className":54253,"style":1032},[1031],[86,54255,54257],{"className":54256},[1036,1037,1038,1039],[86,54258,980],{"className":54259},[1003,1039],[86,54261,54262,54265],{"style":3901},[86,54263],{"className":54264,"style":3850},[1031],[86,54266],{"className":54267,"style":3909},[3908],[86,54269,54270,54273],{"style":3912},[86,54271],{"className":54272,"style":3850},[1031],[86,54274,54276,54279,54282,54285,54288,54291,54294,54297,54300,54303,54306,54309,54312,54315,54318,54321,54324,54327,54330,54333,54336,54339,54342,54345,54348,54351,54354,54357,54360,54363,54366,54369,54372,54375,54378,54381,54384,54387,54390,54393,54396,54399,54402,54405,54408,54411,54414,54417,54420],{"className":54275},[1003],[86,54277,4100],{"className":54278},[1003],[86,54280,243],{"className":54281},[3320],[86,54283,15008],{"className":54284},[1003],[86,54286],{"className":54287,"style":5012},[3221],[86,54289,53871],{"className":54290},[5016],[86,54292],{"className":54293,"style":5012},[3221],[86,54295,53874],{"className":54296},[1003],[86,54298],{"className":54299,"style":5012},[3221],[86,54301,6565],{"className":54302},[5016],[86,54304],{"className":54305,"style":5012},[3221],[86,54307,15026],{"className":54308},[1003],[86,54310],{"className":54311,"style":5012},[3221],[86,54313,53871],{"className":54314},[5016],[86,54316],{"className":54317,"style":5012},[3221],[86,54319,53883],{"className":54320},[1003],[86,54322],{"className":54323,"style":5012},[3221],[86,54325,6565],{"className":54326},[5016],[86,54328],{"className":54329,"style":5012},[3221],[86,54331,52132],{"className":54332},[1003],[86,54334],{"className":54335,"style":5012},[3221],[86,54337,53871],{"className":54338},[5016],[86,54340],{"className":54341,"style":5012},[3221],[86,54343,53892],{"className":54344},[1003],[86,54346,867],{"className":54347},[3356],[86,54349],{"className":54350,"style":5012},[3221],[86,54352,9864],{"className":54353},[5016],[86,54355],{"className":54356,"style":5012},[3221],[86,54358,243],{"className":54359},[3320],[86,54361,15008],{"className":54362},[1003],[86,54364],{"className":54365,"style":5012},[3221],[86,54367,6565],{"className":54368},[5016],[86,54370],{"className":54371,"style":5012},[3221],[86,54373,15026],{"className":54374},[1003],[86,54376],{"className":54377,"style":5012},[3221],[86,54379,6565],{"className":54380},[5016],[86,54382],{"className":54383,"style":5012},[3221],[86,54385,52132],{"className":54386},[1003],[86,54388,867],{"className":54389},[3356],[86,54391,243],{"className":54392},[3320],[86,54394,53874],{"className":54395},[1003],[86,54397],{"className":54398,"style":5012},[3221],[86,54400,6565],{"className":54401},[5016],[86,54403],{"className":54404,"style":5012},[3221],[86,54406,53883],{"className":54407},[1003],[86,54409],{"className":54410,"style":5012},[3221],[86,54412,6565],{"className":54413},[5016],[86,54415],{"className":54416,"style":5012},[3221],[86,54418,53892],{"className":54419},[1003],[86,54421,867],{"className":54422},[3356],[86,54424,3963],{"className":54425},[3962],[86,54427,54429],{"className":54428},[1020],[86,54430,54432],{"className":54431,"style":5797},[1024],[86,54433],{},[86,54435],{"className":54436},[3356,3829],[86,54438,54440],{"className":54439},[3173],[86,54441,54443,54503],{"className":54442},[955],[86,54444,54446],{"className":54445},[959],[961,54447,54448],{"xmlns":963,"display":3182},[965,54449,54450,54500],{},[968,54451,54452,54458,54460,54476,54478,54484],{},[6849,54453,54454,54456],{},[974,54455,42473],{},[978,54457,2553],{},[3191,54459,258],{},[3749,54461,54462,54474],{},[968,54463,54464,54466,54468,54470,54472],{},[978,54465,53874],{},[3191,54467,6565],{},[978,54469,53883],{},[3191,54471,6565],{},[978,54473,53892],{},[978,54475,4100],{},[3191,54477,9864],{},[6849,54479,54480,54482],{},[974,54481,42473],{},[978,54483,802],{},[3749,54485,54486,54498],{},[968,54487,54488,54490,54492,54494,54496],{},[978,54489,15008],{},[3191,54491,6565],{},[978,54493,15026],{},[3191,54495,6565],{},[978,54497,52132],{},[978,54499,4100],{},[982,54501,54502],{"encoding":984},"\\beta_0 = \\frac{100000 + 200000 + 300000}{3} - \\beta_1 \\frac{50 + 100 + 150}{3}",[86,54504,54506,54561,54662],{"className":54505,"ariaHidden":990},[989],[86,54507,54509,54512,54552,54555,54558],{"className":54508},[994],[86,54510],{"className":54511,"style":4888},[998],[86,54513,54515,54518],{"className":54514},[1003],[86,54516,42473],{"className":54517,"style":42538},[1003,1007],[86,54519,54521],{"className":54520},[1012],[86,54522,54524,54544],{"className":54523},[1016,3836],[86,54525,54527,54541],{"className":54526},[1020],[86,54528,54530],{"className":54529,"style":6984},[1024],[86,54531,54532,54535],{"style":42553},[86,54533],{"className":54534,"style":1032},[1031],[86,54536,54538],{"className":54537},[1036,1037,1038,1039],[86,54539,2553],{"className":54540},[1003,1039],[86,54542,3963],{"className":54543},[3962],[86,54545,54547],{"className":54546},[1020],[86,54548,54550],{"className":54549,"style":7006},[1024],[86,54551],{},[86,54553],{"className":54554,"style":3222},[3221],[86,54556,258],{"className":54557},[3226],[86,54559],{"className":54560,"style":3222},[3221],[86,54562,54564,54567,54653,54656,54659],{"className":54563},[994],[86,54565],{"className":54566,"style":9549},[998],[86,54568,54570,54573,54650],{"className":54569},[1003],[86,54571],{"className":54572},[3320,3829],[86,54574,54576],{"className":54575},[3749],[86,54577,54579,54642],{"className":54578},[1016,3836],[86,54580,54582,54639],{"className":54581},[1020],[86,54583,54585,54596,54604],{"className":54584,"style":9568},[1024],[86,54586,54587,54590],{"style":3846},[86,54588],{"className":54589,"style":3850},[1031],[86,54591,54593],{"className":54592},[1003],[86,54594,4100],{"className":54595},[1003],[86,54597,54598,54601],{"style":3901},[86,54599],{"className":54600,"style":3850},[1031],[86,54602],{"className":54603,"style":3909},[3908],[86,54605,54606,54609],{"style":3912},[86,54607],{"className":54608,"style":3850},[1031],[86,54610,54612,54615,54618,54621,54624,54627,54630,54633,54636],{"className":54611},[1003],[86,54613,53874],{"className":54614},[1003],[86,54616],{"className":54617,"style":5012},[3221],[86,54619,6565],{"className":54620},[5016],[86,54622],{"className":54623,"style":5012},[3221],[86,54625,53883],{"className":54626},[1003],[86,54628],{"className":54629,"style":5012},[3221],[86,54631,6565],{"className":54632},[5016],[86,54634],{"className":54635,"style":5012},[3221],[86,54637,53892],{"className":54638},[1003],[86,54640,3963],{"className":54641},[3962],[86,54643,54645],{"className":54644},[1020],[86,54646,54648],{"className":54647,"style":9620},[1024],[86,54649],{},[86,54651],{"className":54652},[3356,3829],[86,54654],{"className":54655,"style":5012},[3221],[86,54657,9864],{"className":54658},[5016],[86,54660],{"className":54661,"style":5012},[3221],[86,54663,54665,54668,54708],{"className":54664},[994],[86,54666],{"className":54667,"style":9549},[998],[86,54669,54671,54674],{"className":54670},[1003],[86,54672,42473],{"className":54673,"style":42538},[1003,1007],[86,54675,54677],{"className":54676},[1012],[86,54678,54680,54700],{"className":54679},[1016,3836],[86,54681,54683,54697],{"className":54682},[1020],[86,54684,54686],{"className":54685,"style":6984},[1024],[86,54687,54688,54691],{"style":42553},[86,54689],{"className":54690,"style":1032},[1031],[86,54692,54694],{"className":54693},[1036,1037,1038,1039],[86,54695,802],{"className":54696},[1003,1039],[86,54698,3963],{"className":54699},[3962],[86,54701,54703],{"className":54702},[1020],[86,54704,54706],{"className":54705,"style":7006},[1024],[86,54707],{},[86,54709,54711,54714,54791],{"className":54710},[1003],[86,54712],{"className":54713},[3320,3829],[86,54715,54717],{"className":54716},[3749],[86,54718,54720,54783],{"className":54719},[1016,3836],[86,54721,54723,54780],{"className":54722},[1020],[86,54724,54726,54737,54745],{"className":54725,"style":9568},[1024],[86,54727,54728,54731],{"style":3846},[86,54729],{"className":54730,"style":3850},[1031],[86,54732,54734],{"className":54733},[1003],[86,54735,4100],{"className":54736},[1003],[86,54738,54739,54742],{"style":3901},[86,54740],{"className":54741,"style":3850},[1031],[86,54743],{"className":54744,"style":3909},[3908],[86,54746,54747,54750],{"style":3912},[86,54748],{"className":54749,"style":3850},[1031],[86,54751,54753,54756,54759,54762,54765,54768,54771,54774,54777],{"className":54752},[1003],[86,54754,15008],{"className":54755},[1003],[86,54757],{"className":54758,"style":5012},[3221],[86,54760,6565],{"className":54761},[5016],[86,54763],{"className":54764,"style":5012},[3221],[86,54766,15026],{"className":54767},[1003],[86,54769],{"className":54770,"style":5012},[3221],[86,54772,6565],{"className":54773},[5016],[86,54775],{"className":54776,"style":5012},[3221],[86,54778,52132],{"className":54779},[1003],[86,54781,3963],{"className":54782},[3962],[86,54784,54786],{"className":54785},[1020],[86,54787,54789],{"className":54788,"style":9620},[1024],[86,54790],{},[86,54792],{"className":54793},[3356,3829],[12,54795,54796,54797,392,54889,54981],{},"Resolviendo estas fórmulas, obtenemos los valores de ",[86,54798,54800,54822],{"className":54799},[955],[86,54801,54803],{"className":54802},[959],[961,54804,54805],{"xmlns":963},[965,54806,54807,54819],{},[968,54808,54809,54815,54817],{},[6849,54810,54811,54813],{},[974,54812,42473],{},[978,54814,2553],{},[3191,54816,258],{},[978,54818,2553],{},[982,54820,54821],{"encoding":984},"\\beta_0 = 0",[86,54823,54825,54880],{"className":54824,"ariaHidden":990},[989],[86,54826,54828,54831,54871,54874,54877],{"className":54827},[994],[86,54829],{"className":54830,"style":4888},[998],[86,54832,54834,54837],{"className":54833},[1003],[86,54835,42473],{"className":54836,"style":42538},[1003,1007],[86,54838,54840],{"className":54839},[1012],[86,54841,54843,54863],{"className":54842},[1016,3836],[86,54844,54846,54860],{"className":54845},[1020],[86,54847,54849],{"className":54848,"style":6984},[1024],[86,54850,54851,54854],{"style":42553},[86,54852],{"className":54853,"style":1032},[1031],[86,54855,54857],{"className":54856},[1036,1037,1038,1039],[86,54858,2553],{"className":54859},[1003,1039],[86,54861,3963],{"className":54862},[3962],[86,54864,54866],{"className":54865},[1020],[86,54867,54869],{"className":54868,"style":7006},[1024],[86,54870],{},[86,54872],{"className":54873,"style":3222},[3221],[86,54875,258],{"className":54876},[3226],[86,54878],{"className":54879,"style":3222},[3221],[86,54881,54883,54886],{"className":54882},[994],[86,54884],{"className":54885,"style":5994},[998],[86,54887,2553],{"className":54888},[1003],[86,54890,54892,54914],{"className":54891},[955],[86,54893,54895],{"className":54894},[959],[961,54896,54897],{"xmlns":963},[965,54898,54899,54911],{},[968,54900,54901,54907,54909],{},[6849,54902,54903,54905],{},[974,54904,42473],{},[978,54906,802],{},[3191,54908,258],{},[978,54910,13127],{},[982,54912,54913],{"encoding":984},"\\beta_1 = 2000",[86,54915,54917,54972],{"className":54916,"ariaHidden":990},[989],[86,54918,54920,54923,54963,54966,54969],{"className":54919},[994],[86,54921],{"className":54922,"style":4888},[998],[86,54924,54926,54929],{"className":54925},[1003],[86,54927,42473],{"className":54928,"style":42538},[1003,1007],[86,54930,54932],{"className":54931},[1012],[86,54933,54935,54955],{"className":54934},[1016,3836],[86,54936,54938,54952],{"className":54937},[1020],[86,54939,54941],{"className":54940,"style":6984},[1024],[86,54942,54943,54946],{"style":42553},[86,54944],{"className":54945,"style":1032},[1031],[86,54947,54949],{"className":54948},[1036,1037,1038,1039],[86,54950,802],{"className":54951},[1003,1039],[86,54953,3963],{"className":54954},[3962],[86,54956,54958],{"className":54957},[1020],[86,54959,54961],{"className":54960,"style":7006},[1024],[86,54962],{},[86,54964],{"className":54965,"style":3222},[3221],[86,54967,258],{"className":54968},[3226],[86,54970],{"className":54971,"style":3222},[3221],[86,54973,54975,54978],{"className":54974},[994],[86,54976],{"className":54977,"style":5994},[998],[86,54979,13127],{"className":54980},[1003],", que nos permiten construir el siguiente modelo:",[86,54983,54985],{"className":54984},[3173],[86,54986,54988,55016],{"className":54987},[955],[86,54989,54991],{"className":54990},[959],[961,54992,54993],{"xmlns":963,"display":3182},[965,54994,54995,55013],{},[968,54996,54997,55003,55005,55007,55009,55011],{},[3758,54998,54999,55001],{"accent":990},[974,55000,5464],{},[3191,55002,7242],{},[3191,55004,258],{},[978,55006,2553],{},[3191,55008,6565],{},[978,55010,13127],{},[974,55012,3189],{},[982,55014,55015],{"encoding":984},"\\hat{y} = 0 + 2000x",[86,55017,55019,55076,55094],{"className":55018,"ariaHidden":990},[989],[86,55020,55022,55025,55067,55070,55073],{"className":55021},[994],[86,55023],{"className":55024,"style":4888},[998],[86,55026,55028],{"className":55027},[1003,3863],[86,55029,55031,55059],{"className":55030},[1016,3836],[86,55032,55034,55056],{"className":55033},[1020],[86,55035,55037,55045],{"className":55036,"style":3873},[1024],[86,55038,55039,55042],{"style":3876},[86,55040],{"className":55041,"style":3850},[1031],[86,55043,5464],{"className":55044,"style":8109},[1003,1007],[86,55046,55047,55050],{"style":3876},[86,55048],{"className":55049,"style":3850},[1031],[86,55051,55053],{"className":55052,"style":49979},[3891],[86,55054,7242],{"className":55055},[1003],[86,55057,3963],{"className":55058},[3962],[86,55060,55062],{"className":55061},[1020],[86,55063,55065],{"className":55064,"style":30703},[1024],[86,55066],{},[86,55068],{"className":55069,"style":3222},[3221],[86,55071,258],{"className":55072},[3226],[86,55074],{"className":55075,"style":3222},[3221],[86,55077,55079,55082,55085,55088,55091],{"className":55078},[994],[86,55080],{"className":55081,"style":9303},[998],[86,55083,2553],{"className":55084},[1003],[86,55086],{"className":55087,"style":5012},[3221],[86,55089,6565],{"className":55090},[5016],[86,55092],{"className":55093,"style":5012},[3221],[86,55095,55097,55100,55103],{"className":55096},[994],[86,55098],{"className":55099,"style":5994},[998],[86,55101,13127],{"className":55102},[1003],[86,55104,3189],{"className":55105},[1003,1007],[86,55107,55109],{"className":55108},[3173],[86,55110,55112,55136],{"className":55111},[955],[86,55113,55115],{"className":55114},[959],[961,55116,55117],{"xmlns":963,"display":3182},[965,55118,55119,55133],{},[968,55120,55121,55127,55129,55131],{},[3758,55122,55123,55125],{"accent":990},[974,55124,5464],{},[3191,55126,7242],{},[3191,55128,258],{},[978,55130,13127],{},[974,55132,3189],{},[982,55134,55135],{"encoding":984},"\\hat{y} = 2000x",[86,55137,55139,55196],{"className":55138,"ariaHidden":990},[989],[86,55140,55142,55145,55187,55190,55193],{"className":55141},[994],[86,55143],{"className":55144,"style":4888},[998],[86,55146,55148],{"className":55147},[1003,3863],[86,55149,55151,55179],{"className":55150},[1016,3836],[86,55152,55154,55176],{"className":55153},[1020],[86,55155,55157,55165],{"className":55156,"style":3873},[1024],[86,55158,55159,55162],{"style":3876},[86,55160],{"className":55161,"style":3850},[1031],[86,55163,5464],{"className":55164,"style":8109},[1003,1007],[86,55166,55167,55170],{"style":3876},[86,55168],{"className":55169,"style":3850},[1031],[86,55171,55173],{"className":55172,"style":49979},[3891],[86,55174,7242],{"className":55175},[1003],[86,55177,3963],{"className":55178},[3962],[86,55180,55182],{"className":55181},[1020],[86,55183,55185],{"className":55184,"style":30703},[1024],[86,55186],{},[86,55188],{"className":55189,"style":3222},[3221],[86,55191,258],{"className":55192},[3226],[86,55194],{"className":55195,"style":3222},[3221],[86,55197,55199,55202,55205],{"className":55198},[994],[86,55200],{"className":55201,"style":5994},[998],[86,55203,13127],{"className":55204},[1003],[86,55206,3189],{"className":55207},[1003,1007],[12,55209,55210],{},"Ahora podemos hacer predicciones para nuevos valores de tamaño. Por ejemplo, para una casa de 120 m², el modelo predice un precio de:",[86,55212,55214],{"className":55213},[3173],[86,55215,55217,55254],{"className":55216},[955],[86,55218,55220],{"className":55219},[959],[961,55221,55222],{"xmlns":963,"display":3182},[965,55223,55224,55251],{},[968,55225,55226,55232,55234,55236,55238,55241,55243,55246,55248],{},[3758,55227,55228,55230],{"accent":990},[974,55229,5464],{},[3191,55231,7242],{},[3191,55233,258],{},[978,55235,13127],{},[3191,55237,53871],{},[978,55239,55240],{},"120",[3191,55242,258],{},[978,55244,55245],{},"240",[3191,55247,291],{"separator":990},[978,55249,55250],{},"000",[982,55252,55253],{"encoding":984},"\\hat{y} = 2000 * 120 = 240,000",[86,55255,55257,55314,55332,55350],{"className":55256,"ariaHidden":990},[989],[86,55258,55260,55263,55305,55308,55311],{"className":55259},[994],[86,55261],{"className":55262,"style":4888},[998],[86,55264,55266],{"className":55265},[1003,3863],[86,55267,55269,55297],{"className":55268},[1016,3836],[86,55270,55272,55294],{"className":55271},[1020],[86,55273,55275,55283],{"className":55274,"style":3873},[1024],[86,55276,55277,55280],{"style":3876},[86,55278],{"className":55279,"style":3850},[1031],[86,55281,5464],{"className":55282,"style":8109},[1003,1007],[86,55284,55285,55288],{"style":3876},[86,55286],{"className":55287,"style":3850},[1031],[86,55289,55291],{"className":55290,"style":49979},[3891],[86,55292,7242],{"className":55293},[1003],[86,55295,3963],{"className":55296},[3962],[86,55298,55300],{"className":55299},[1020],[86,55301,55303],{"className":55302,"style":30703},[1024],[86,55304],{},[86,55306],{"className":55307,"style":3222},[3221],[86,55309,258],{"className":55310},[3226],[86,55312],{"className":55313,"style":3222},[3221],[86,55315,55317,55320,55323,55326,55329],{"className":55316},[994],[86,55318],{"className":55319,"style":5994},[998],[86,55321,13127],{"className":55322},[1003],[86,55324],{"className":55325,"style":5012},[3221],[86,55327,53871],{"className":55328},[5016],[86,55330],{"className":55331,"style":5012},[3221],[86,55333,55335,55338,55341,55344,55347],{"className":55334},[994],[86,55336],{"className":55337,"style":5994},[998],[86,55339,55240],{"className":55340},[1003],[86,55342],{"className":55343,"style":3222},[3221],[86,55345,258],{"className":55346},[3226],[86,55348],{"className":55349,"style":3222},[3221],[86,55351,55353,55357,55360,55363,55366],{"className":55352},[994],[86,55354],{"className":55355,"style":55356},[998],"height:0.8389em;vertical-align:-0.1944em;",[86,55358,55245],{"className":55359},[1003],[86,55361,291],{"className":55362},[4158],[86,55364],{"className":55365,"style":4162},[3221],[86,55367,55250],{"className":55368},[1003],[12,55370,55371,55372,55375],{},"Los cálculos nos han dado los mejores coeficientes que ",[122,55373,55374],{},"minimizan"," el error cuadrático medio (pero no que lo eliminan completamente). Para medir el error de nuestro modelo, podemos calcular el MSE utilizando la fórmula que mencionamos antes:",[86,55377,55379],{"className":55378},[3173],[86,55380,55382,55447],{"className":55381},[955],[86,55383,55385],{"className":55384},[959],[961,55386,55387],{"xmlns":963,"display":3182},[965,55388,55389,55445],{},[968,55390,55391,55393,55395,55397,55399,55405,55419,55421,55427,55429,55439],{},[974,55392,49387],{},[974,55394,4084],{},[974,55396,7871],{},[3191,55398,258],{},[3749,55400,55401,55403],{},[978,55402,802],{},[974,55404,6896],{},[7276,55406,55407,55409,55417],{},[3191,55408,49404],{},[968,55410,55411,55413,55415],{},[974,55412,7285],{},[3191,55414,258],{},[978,55416,802],{},[974,55418,6896],{},[3191,55420,243],{"stretchy":3295},[6849,55422,55423,55425],{},[974,55424,5464],{},[974,55426,7285],{},[3191,55428,9864],{},[3758,55430,55431,55437],{"accent":990},[6849,55432,55433,55435],{},[974,55434,5464],{},[974,55436,7285],{},[3191,55438,7242],{},[971,55440,55441,55443],{},[3191,55442,867],{"stretchy":3295},[978,55444,980],{},[982,55446,49443],{"encoding":984},[86,55448,55450,55474,55664],{"className":55449,"ariaHidden":990},[989],[86,55451,55453,55456,55459,55462,55465,55468,55471],{"className":55452},[994],[86,55454],{"className":55455,"style":3575},[998],[86,55457,49387],{"className":55458,"style":6055},[1003,1007],[86,55460,4084],{"className":55461,"style":4133},[1003,1007],[86,55463,7871],{"className":55464,"style":4133},[1003,1007],[86,55466],{"className":55467,"style":3222},[3221],[86,55469,258],{"className":55470},[3226],[86,55472],{"className":55473,"style":3222},[3221],[86,55475,55477,55480,55542,55545,55612,55615,55655,55658,55661],{"className":55476},[994],[86,55478],{"className":55479,"style":7369},[998],[86,55481,55483,55486,55539],{"className":55482},[1003],[86,55484],{"className":55485},[3320,3829],[86,55487,55489],{"className":55488},[3749],[86,55490,55492,55531],{"className":55491},[1016,3836],[86,55493,55495,55528],{"className":55494},[1020],[86,55496,55498,55509,55517],{"className":55497,"style":9568},[1024],[86,55499,55500,55503],{"style":3846},[86,55501],{"className":55502,"style":3850},[1031],[86,55504,55506],{"className":55505},[1003],[86,55507,6896],{"className":55508},[1003,1007],[86,55510,55511,55514],{"style":3901},[86,55512],{"className":55513,"style":3850},[1031],[86,55515],{"className":55516,"style":3909},[3908],[86,55518,55519,55522],{"style":3912},[86,55520],{"className":55521,"style":3850},[1031],[86,55523,55525],{"className":55524},[1003],[86,55526,802],{"className":55527},[1003],[86,55529,3963],{"className":55530},[3962],[86,55532,55534],{"className":55533},[1020],[86,55535,55537],{"className":55536,"style":9620},[1024],[86,55538],{},[86,55540],{"className":55541},[3356,3829],[86,55543],{"className":55544,"style":4162},[3221],[86,55546,55548],{"className":55547},[7373,7391],[86,55549,55551,55604],{"className":55550},[1016,3836],[86,55552,55554,55601],{"className":55553},[1020],[86,55555,55557,55577,55587],{"className":55556,"style":7469},[1024],[86,55558,55559,55562],{"style":7472},[86,55560],{"className":55561,"style":7476},[1031],[86,55563,55565],{"className":55564},[1036,1037,1038,1039],[86,55566,55568,55571,55574],{"className":55567},[1003,1039],[86,55569,7285],{"className":55570},[1003,1007,1039],[86,55572,258],{"className":55573},[3226,1039],[86,55575,802],{"className":55576},[1003,1039],[86,55578,55579,55582],{"style":7494},[86,55580],{"className":55581,"style":7476},[1031],[86,55583,55584],{},[86,55585,49404],{"className":55586},[7373,7503,7504],[86,55588,55589,55592],{"style":7507},[86,55590],{"className":55591,"style":7476},[1031],[86,55593,55595],{"className":55594},[1036,1037,1038,1039],[86,55596,55598],{"className":55597},[1003,1039],[86,55599,6896],{"className":55600},[1003,1007,1039],[86,55602,3963],{"className":55603},[3962],[86,55605,55607],{"className":55606},[1020],[86,55608,55610],{"className":55609,"style":7529},[1024],[86,55611],{},[86,55613,243],{"className":55614},[3320],[86,55616,55618,55621],{"className":55617},[1003],[86,55619,5464],{"className":55620,"style":8109},[1003,1007],[86,55622,55624],{"className":55623},[1012],[86,55625,55627,55647],{"className":55626},[1016,3836],[86,55628,55630,55644],{"className":55629},[1020],[86,55631,55633],{"className":55632,"style":7559},[1024],[86,55634,55635,55638],{"style":20440},[86,55636],{"className":55637,"style":1032},[1031],[86,55639,55641],{"className":55640},[1036,1037,1038,1039],[86,55642,7285],{"className":55643},[1003,1007,1039],[86,55645,3963],{"className":55646},[3962],[86,55648,55650],{"className":55649},[1020],[86,55651,55653],{"className":55652,"style":7006},[1024],[86,55654],{},[86,55656],{"className":55657,"style":5012},[3221],[86,55659,9864],{"className":55660},[5016],[86,55662],{"className":55663,"style":5012},[3221],[86,55665,55667,55670,55749],{"className":55666},[994],[86,55668],{"className":55669,"style":49667},[998],[86,55671,55673],{"className":55672},[1003,3863],[86,55674,55676,55741],{"className":55675},[1016,3836],[86,55677,55679,55738],{"className":55678},[1020],[86,55680,55682,55727],{"className":55681,"style":3873},[1024],[86,55683,55684,55687],{"style":3876},[86,55685],{"className":55686,"style":3850},[1031],[86,55688,55690,55693],{"className":55689},[1003],[86,55691,5464],{"className":55692,"style":8109},[1003,1007],[86,55694,55696],{"className":55695},[1012],[86,55697,55699,55719],{"className":55698},[1016,3836],[86,55700,55702,55716],{"className":55701},[1020],[86,55703,55705],{"className":55704,"style":7559},[1024],[86,55706,55707,55710],{"style":20440},[86,55708],{"className":55709,"style":1032},[1031],[86,55711,55713],{"className":55712},[1036,1037,1038,1039],[86,55714,7285],{"className":55715},[1003,1007,1039],[86,55717,3963],{"className":55718},[3962],[86,55720,55722],{"className":55721},[1020],[86,55723,55725],{"className":55724,"style":7006},[1024],[86,55726],{},[86,55728,55729,55732],{"style":3876},[86,55730],{"className":55731,"style":3850},[1031],[86,55733,55735],{"className":55734,"style":3892},[3891],[86,55736,7242],{"className":55737},[1003],[86,55739,3963],{"className":55740},[3962],[86,55742,55744],{"className":55743},[1020],[86,55745,55747],{"className":55746,"style":30703},[1024],[86,55748],{},[86,55750,55752,55755],{"className":55751},[3356],[86,55753,867],{"className":55754},[3356],[86,55756,55758],{"className":55757},[1012],[86,55759,55761],{"className":55760},[1016],[86,55762,55764],{"className":55763},[1020],[86,55765,55767],{"className":55766,"style":3236},[1024],[86,55768,55769,55772],{"style":3258},[86,55770],{"className":55771,"style":1032},[1031],[86,55773,55775],{"className":55774},[1036,1037,1038,1039],[86,55776,980],{"className":55777},[1003,1039],[12,55779,3273],{},[30,55781,55782,55812,55884],{},[33,55783,55784,53557],{},[86,55785,55787,55800],{"className":55786},[955],[86,55788,55790],{"className":55789},[959],[961,55791,55792],{"xmlns":963},[965,55793,55794,55798],{},[968,55795,55796],{},[974,55797,6896],{},[982,55799,6896],{"encoding":984},[86,55801,55803],{"className":55802,"ariaHidden":990},[989],[86,55804,55806,55809],{"className":55805},[994],[86,55807],{"className":55808,"style":7401},[998],[86,55810,6896],{"className":55811},[1003,1007],[33,55813,55814,55883],{},[86,55815,55817,55834],{"className":55816},[955],[86,55818,55820],{"className":55819},[959],[961,55821,55822],{"xmlns":963},[965,55823,55824,55832],{},[968,55825,55826],{},[6849,55827,55828,55830],{},[974,55829,5464],{},[974,55831,7285],{},[982,55833,46828],{"encoding":984},[86,55835,55837],{"className":55836,"ariaHidden":990},[989],[86,55838,55840,55843],{"className":55839},[994],[86,55841],{"className":55842,"style":16339},[998],[86,55844,55846,55849],{"className":55845},[1003],[86,55847,5464],{"className":55848,"style":8109},[1003,1007],[86,55850,55852],{"className":55851},[1012],[86,55853,55855,55875],{"className":55854},[1016,3836],[86,55856,55858,55872],{"className":55857},[1020],[86,55859,55861],{"className":55860,"style":7559},[1024],[86,55862,55863,55866],{"style":20440},[86,55864],{"className":55865,"style":1032},[1031],[86,55867,55869],{"className":55868},[1036,1037,1038,1039],[86,55870,7285],{"className":55871},[1003,1007,1039],[86,55873,3963],{"className":55874},[3962],[86,55876,55878],{"className":55877},[1020],[86,55879,55881],{"className":55880,"style":7006},[1024],[86,55882],{}," son los valores reales de precio para cada ejemplo.",[33,55885,55886,55998],{},[86,55887,55889,55910],{"className":55888},[955],[86,55890,55892],{"className":55891},[959],[961,55893,55894],{"xmlns":963},[965,55895,55896,55908],{},[968,55897,55898],{},[6849,55899,55900,55906],{},[3758,55901,55902,55904],{"accent":990},[974,55903,5464],{},[3191,55905,7242],{},[974,55907,7285],{},[982,55909,49938],{"encoding":984},[86,55911,55913],{"className":55912,"ariaHidden":990},[989],[86,55914,55916,55919],{"className":55915},[994],[86,55917],{"className":55918,"style":4888},[998],[86,55920,55922,55964],{"className":55921},[1003],[86,55923,55925],{"className":55924},[1003,3863],[86,55926,55928,55956],{"className":55927},[1016,3836],[86,55929,55931,55953],{"className":55930},[1020],[86,55932,55934,55942],{"className":55933,"style":3873},[1024],[86,55935,55936,55939],{"style":3876},[86,55937],{"className":55938,"style":3850},[1031],[86,55940,5464],{"className":55941,"style":8109},[1003,1007],[86,55943,55944,55947],{"style":3876},[86,55945],{"className":55946,"style":3850},[1031],[86,55948,55950],{"className":55949,"style":49979},[3891],[86,55951,7242],{"className":55952},[1003],[86,55954,3963],{"className":55955},[3962],[86,55957,55959],{"className":55958},[1020],[86,55960,55962],{"className":55961,"style":30703},[1024],[86,55963],{},[86,55965,55967],{"className":55966},[1012],[86,55968,55970,55990],{"className":55969},[1016,3836],[86,55971,55973,55987],{"className":55972},[1020],[86,55974,55976],{"className":55975,"style":7559},[1024],[86,55977,55978,55981],{"style":20440},[86,55979],{"className":55980,"style":1032},[1031],[86,55982,55984],{"className":55983},[1036,1037,1038,1039],[86,55985,7285],{"className":55986},[1003,1007,1039],[86,55988,3963],{"className":55989},[3962],[86,55991,55993],{"className":55992},[1020],[86,55994,55996],{"className":55995,"style":7006},[1024],[86,55997],{}," son las predicciones del modelo para cada ejemplo, que se calculan usando el modelo de regresión lineal.",[117,56000,56001],{},[33,56002,56003],{},"Calculamos las predicciones para cada ejemplo:",[30,56005,56006,56201,56397],{},[33,56007,56008,56009],{},"Para 50 m²: ",[86,56010,56012,56050],{"className":56011},[955],[86,56013,56015],{"className":56014},[959],[961,56016,56017],{"xmlns":963},[965,56018,56019,56047],{},[968,56020,56021,56031,56033,56035,56037,56039,56041,56043,56045],{},[3758,56022,56023,56029],{"accent":990},[6849,56024,56025,56027],{},[974,56026,5464],{},[978,56028,802],{},[3191,56030,7242],{},[3191,56032,258],{},[978,56034,13127],{},[3191,56036,53871],{},[978,56038,15008],{},[3191,56040,258],{},[978,56042,15026],{},[3191,56044,291],{"separator":990},[978,56046,55250],{},[982,56048,56049],{"encoding":984},"\\hat{y_1} = 2000 * 50 = 100,000",[86,56051,56053,56147,56165,56183],{"className":56052,"ariaHidden":990},[989],[86,56054,56056,56059,56138,56141,56144],{"className":56055},[994],[86,56057],{"className":56058,"style":4888},[998],[86,56060,56062],{"className":56061},[1003,3863],[86,56063,56065,56130],{"className":56064},[1016,3836],[86,56066,56068,56127],{"className":56067},[1020],[86,56069,56071,56116],{"className":56070,"style":3873},[1024],[86,56072,56073,56076],{"style":3876},[86,56074],{"className":56075,"style":3850},[1031],[86,56077,56079,56082],{"className":56078},[1003],[86,56080,5464],{"className":56081,"style":8109},[1003,1007],[86,56083,56085],{"className":56084},[1012],[86,56086,56088,56108],{"className":56087},[1016,3836],[86,56089,56091,56105],{"className":56090},[1020],[86,56092,56094],{"className":56093,"style":6984},[1024],[86,56095,56096,56099],{"style":20440},[86,56097],{"className":56098,"style":1032},[1031],[86,56100,56102],{"className":56101},[1036,1037,1038,1039],[86,56103,802],{"className":56104},[1003,1039],[86,56106,3963],{"className":56107},[3962],[86,56109,56111],{"className":56110},[1020],[86,56112,56114],{"className":56113,"style":7006},[1024],[86,56115],{},[86,56117,56118,56121],{"style":3876},[86,56119],{"className":56120,"style":3850},[1031],[86,56122,56124],{"className":56123,"style":3892},[3891],[86,56125,7242],{"className":56126},[1003],[86,56128,3963],{"className":56129},[3962],[86,56131,56133],{"className":56132},[1020],[86,56134,56136],{"className":56135,"style":30703},[1024],[86,56137],{},[86,56139],{"className":56140,"style":3222},[3221],[86,56142,258],{"className":56143},[3226],[86,56145],{"className":56146,"style":3222},[3221],[86,56148,56150,56153,56156,56159,56162],{"className":56149},[994],[86,56151],{"className":56152,"style":5994},[998],[86,56154,13127],{"className":56155},[1003],[86,56157],{"className":56158,"style":5012},[3221],[86,56160,53871],{"className":56161},[5016],[86,56163],{"className":56164,"style":5012},[3221],[86,56166,56168,56171,56174,56177,56180],{"className":56167},[994],[86,56169],{"className":56170,"style":5994},[998],[86,56172,15008],{"className":56173},[1003],[86,56175],{"className":56176,"style":3222},[3221],[86,56178,258],{"className":56179},[3226],[86,56181],{"className":56182,"style":3222},[3221],[86,56184,56186,56189,56192,56195,56198],{"className":56185},[994],[86,56187],{"className":56188,"style":55356},[998],[86,56190,15026],{"className":56191},[1003],[86,56193,291],{"className":56194},[4158],[86,56196],{"className":56197,"style":4162},[3221],[86,56199,55250],{"className":56200},[1003],[33,56202,56203,56204],{},"Para 100 m²: ",[86,56205,56207,56246],{"className":56206},[955],[86,56208,56210],{"className":56209},[959],[961,56211,56212],{"xmlns":963},[965,56213,56214,56243],{},[968,56215,56216,56226,56228,56230,56232,56234,56236,56239,56241],{},[3758,56217,56218,56224],{"accent":990},[6849,56219,56220,56222],{},[974,56221,5464],{},[978,56223,980],{},[3191,56225,7242],{},[3191,56227,258],{},[978,56229,13127],{},[3191,56231,53871],{},[978,56233,15026],{},[3191,56235,258],{},[978,56237,56238],{},"200",[3191,56240,291],{"separator":990},[978,56242,55250],{},[982,56244,56245],{"encoding":984},"\\hat{y_2} = 2000 * 100 = 200,000",[86,56247,56249,56343,56361,56379],{"className":56248,"ariaHidden":990},[989],[86,56250,56252,56255,56334,56337,56340],{"className":56251},[994],[86,56253],{"className":56254,"style":4888},[998],[86,56256,56258],{"className":56257},[1003,3863],[86,56259,56261,56326],{"className":56260},[1016,3836],[86,56262,56264,56323],{"className":56263},[1020],[86,56265,56267,56312],{"className":56266,"style":3873},[1024],[86,56268,56269,56272],{"style":3876},[86,56270],{"className":56271,"style":3850},[1031],[86,56273,56275,56278],{"className":56274},[1003],[86,56276,5464],{"className":56277,"style":8109},[1003,1007],[86,56279,56281],{"className":56280},[1012],[86,56282,56284,56304],{"className":56283},[1016,3836],[86,56285,56287,56301],{"className":56286},[1020],[86,56288,56290],{"className":56289,"style":6984},[1024],[86,56291,56292,56295],{"style":20440},[86,56293],{"className":56294,"style":1032},[1031],[86,56296,56298],{"className":56297},[1036,1037,1038,1039],[86,56299,980],{"className":56300},[1003,1039],[86,56302,3963],{"className":56303},[3962],[86,56305,56307],{"className":56306},[1020],[86,56308,56310],{"className":56309,"style":7006},[1024],[86,56311],{},[86,56313,56314,56317],{"style":3876},[86,56315],{"className":56316,"style":3850},[1031],[86,56318,56320],{"className":56319,"style":3892},[3891],[86,56321,7242],{"className":56322},[1003],[86,56324,3963],{"className":56325},[3962],[86,56327,56329],{"className":56328},[1020],[86,56330,56332],{"className":56331,"style":30703},[1024],[86,56333],{},[86,56335],{"className":56336,"style":3222},[3221],[86,56338,258],{"className":56339},[3226],[86,56341],{"className":56342,"style":3222},[3221],[86,56344,56346,56349,56352,56355,56358],{"className":56345},[994],[86,56347],{"className":56348,"style":5994},[998],[86,56350,13127],{"className":56351},[1003],[86,56353],{"className":56354,"style":5012},[3221],[86,56356,53871],{"className":56357},[5016],[86,56359],{"className":56360,"style":5012},[3221],[86,56362,56364,56367,56370,56373,56376],{"className":56363},[994],[86,56365],{"className":56366,"style":5994},[998],[86,56368,15026],{"className":56369},[1003],[86,56371],{"className":56372,"style":3222},[3221],[86,56374,258],{"className":56375},[3226],[86,56377],{"className":56378,"style":3222},[3221],[86,56380,56382,56385,56388,56391,56394],{"className":56381},[994],[86,56383],{"className":56384,"style":55356},[998],[86,56386,56238],{"className":56387},[1003],[86,56389,291],{"className":56390},[4158],[86,56392],{"className":56393,"style":4162},[3221],[86,56395,55250],{"className":56396},[1003],[33,56398,56399,56400],{},"Para 150 m²: ",[86,56401,56403,56442],{"className":56402},[955],[86,56404,56406],{"className":56405},[959],[961,56407,56408],{"xmlns":963},[965,56409,56410,56439],{},[968,56411,56412,56422,56424,56426,56428,56430,56432,56435,56437],{},[3758,56413,56414,56420],{"accent":990},[6849,56415,56416,56418],{},[974,56417,5464],{},[978,56419,4100],{},[3191,56421,7242],{},[3191,56423,258],{},[978,56425,13127],{},[3191,56427,53871],{},[978,56429,52132],{},[3191,56431,258],{},[978,56433,56434],{},"300",[3191,56436,291],{"separator":990},[978,56438,55250],{},[982,56440,56441],{"encoding":984},"\\hat{y_3} = 2000 * 150 = 300,000",[86,56443,56445,56539,56557,56575],{"className":56444,"ariaHidden":990},[989],[86,56446,56448,56451,56530,56533,56536],{"className":56447},[994],[86,56449],{"className":56450,"style":4888},[998],[86,56452,56454],{"className":56453},[1003,3863],[86,56455,56457,56522],{"className":56456},[1016,3836],[86,56458,56460,56519],{"className":56459},[1020],[86,56461,56463,56508],{"className":56462,"style":3873},[1024],[86,56464,56465,56468],{"style":3876},[86,56466],{"className":56467,"style":3850},[1031],[86,56469,56471,56474],{"className":56470},[1003],[86,56472,5464],{"className":56473,"style":8109},[1003,1007],[86,56475,56477],{"className":56476},[1012],[86,56478,56480,56500],{"className":56479},[1016,3836],[86,56481,56483,56497],{"className":56482},[1020],[86,56484,56486],{"className":56485,"style":6984},[1024],[86,56487,56488,56491],{"style":20440},[86,56489],{"className":56490,"style":1032},[1031],[86,56492,56494],{"className":56493},[1036,1037,1038,1039],[86,56495,4100],{"className":56496},[1003,1039],[86,56498,3963],{"className":56499},[3962],[86,56501,56503],{"className":56502},[1020],[86,56504,56506],{"className":56505,"style":7006},[1024],[86,56507],{},[86,56509,56510,56513],{"style":3876},[86,56511],{"className":56512,"style":3850},[1031],[86,56514,56516],{"className":56515,"style":3892},[3891],[86,56517,7242],{"className":56518},[1003],[86,56520,3963],{"className":56521},[3962],[86,56523,56525],{"className":56524},[1020],[86,56526,56528],{"className":56527,"style":30703},[1024],[86,56529],{},[86,56531],{"className":56532,"style":3222},[3221],[86,56534,258],{"className":56535},[3226],[86,56537],{"className":56538,"style":3222},[3221],[86,56540,56542,56545,56548,56551,56554],{"className":56541},[994],[86,56543],{"className":56544,"style":5994},[998],[86,56546,13127],{"className":56547},[1003],[86,56549],{"className":56550,"style":5012},[3221],[86,56552,53871],{"className":56553},[5016],[86,56555],{"className":56556,"style":5012},[3221],[86,56558,56560,56563,56566,56569,56572],{"className":56559},[994],[86,56561],{"className":56562,"style":5994},[998],[86,56564,52132],{"className":56565},[1003],[86,56567],{"className":56568,"style":3222},[3221],[86,56570,258],{"className":56571},[3226],[86,56573],{"className":56574,"style":3222},[3221],[86,56576,56578,56581,56584,56587,56590],{"className":56577},[994],[86,56579],{"className":56580,"style":55356},[998],[86,56582,56434],{"className":56583},[1003],[86,56585,291],{"className":56586},[4158],[86,56588],{"className":56589,"style":4162},[3221],[86,56591,55250],{"className":56592},[1003],[117,56594,56595],{"start":192},[33,56596,56597],{},"Calculamos los errores para cada ejemplo:",[86,56599,56601],{"className":56600},[3173],[86,56602,56604,56642],{"className":56603},[955],[86,56605,56607],{"className":56606},[959],[961,56608,56609],{"xmlns":963,"display":3182},[965,56610,56611,56639],{},[968,56612,56613,56619,56621,56627,56629],{},[6849,56614,56615,56617],{},[974,56616,6181],{},[974,56618,7285],{},[3191,56620,258],{},[6849,56622,56623,56625],{},[974,56624,5464],{},[974,56626,7285],{},[3191,56628,9864],{},[3758,56630,56631,56637],{"accent":990},[6849,56632,56633,56635],{},[974,56634,5464],{},[974,56636,7285],{},[3191,56638,7242],{},[982,56640,56641],{"encoding":984},"e_i = y_i - \\hat{y_i}",[86,56643,56645,56700,56755],{"className":56644,"ariaHidden":990},[989],[86,56646,56648,56651,56691,56694,56697],{"className":56647},[994],[86,56649],{"className":56650,"style":21327},[998],[86,56652,56654,56657],{"className":56653},[1003],[86,56655,6181],{"className":56656},[1003,1007],[86,56658,56660],{"className":56659},[1012],[86,56661,56663,56683],{"className":56662},[1016,3836],[86,56664,56666,56680],{"className":56665},[1020],[86,56667,56669],{"className":56668,"style":7559},[1024],[86,56670,56671,56674],{"style":6987},[86,56672],{"className":56673,"style":1032},[1031],[86,56675,56677],{"className":56676},[1036,1037,1038,1039],[86,56678,7285],{"className":56679},[1003,1007,1039],[86,56681,3963],{"className":56682},[3962],[86,56684,56686],{"className":56685},[1020],[86,56687,56689],{"className":56688,"style":7006},[1024],[86,56690],{},[86,56692],{"className":56693,"style":3222},[3221],[86,56695,258],{"className":56696},[3226],[86,56698],{"className":56699,"style":3222},[3221],[86,56701,56703,56706,56746,56749,56752],{"className":56702},[994],[86,56704],{"className":56705,"style":20769},[998],[86,56707,56709,56712],{"className":56708},[1003],[86,56710,5464],{"className":56711,"style":8109},[1003,1007],[86,56713,56715],{"className":56714},[1012],[86,56716,56718,56738],{"className":56717},[1016,3836],[86,56719,56721,56735],{"className":56720},[1020],[86,56722,56724],{"className":56723,"style":7559},[1024],[86,56725,56726,56729],{"style":20440},[86,56727],{"className":56728,"style":1032},[1031],[86,56730,56732],{"className":56731},[1036,1037,1038,1039],[86,56733,7285],{"className":56734},[1003,1007,1039],[86,56736,3963],{"className":56737},[3962],[86,56739,56741],{"className":56740},[1020],[86,56742,56744],{"className":56743,"style":7006},[1024],[86,56745],{},[86,56747],{"className":56748,"style":5012},[3221],[86,56750,9864],{"className":56751},[5016],[86,56753],{"className":56754,"style":5012},[3221],[86,56756,56758,56761],{"className":56757},[994],[86,56759],{"className":56760,"style":4888},[998],[86,56762,56764],{"className":56763},[1003,3863],[86,56765,56767,56832],{"className":56766},[1016,3836],[86,56768,56770,56829],{"className":56769},[1020],[86,56771,56773,56818],{"className":56772,"style":3873},[1024],[86,56774,56775,56778],{"style":3876},[86,56776],{"className":56777,"style":3850},[1031],[86,56779,56781,56784],{"className":56780},[1003],[86,56782,5464],{"className":56783,"style":8109},[1003,1007],[86,56785,56787],{"className":56786},[1012],[86,56788,56790,56810],{"className":56789},[1016,3836],[86,56791,56793,56807],{"className":56792},[1020],[86,56794,56796],{"className":56795,"style":7559},[1024],[86,56797,56798,56801],{"style":20440},[86,56799],{"className":56800,"style":1032},[1031],[86,56802,56804],{"className":56803},[1036,1037,1038,1039],[86,56805,7285],{"className":56806},[1003,1007,1039],[86,56808,3963],{"className":56809},[3962],[86,56811,56813],{"className":56812},[1020],[86,56814,56816],{"className":56815,"style":7006},[1024],[86,56817],{},[86,56819,56820,56823],{"style":3876},[86,56821],{"className":56822,"style":3850},[1031],[86,56824,56826],{"className":56825,"style":3892},[3891],[86,56827,7242],{"className":56828},[1003],[86,56830,3963],{"className":56831},[3962],[86,56833,56835],{"className":56834},[1020],[86,56836,56838],{"className":56837,"style":30703},[1024],[86,56839],{},[30,56841,56842,56981,57120],{},[33,56843,56844,56845],{},"Error para 50 m²: ",[86,56846,56848,56878],{"className":56847},[955],[86,56849,56851],{"className":56850},[959],[961,56852,56853],{"xmlns":963},[965,56854,56855,56875],{},[968,56856,56857,56863,56865,56867,56869,56871,56873],{},[6849,56858,56859,56861],{},[974,56860,6181],{},[978,56862,802],{},[3191,56864,258],{},[978,56866,53874],{},[3191,56868,9864],{},[978,56870,53874],{},[3191,56872,258],{},[978,56874,2553],{},[982,56876,56877],{"encoding":984},"e_1 = 100000 - 100000 = 0",[86,56879,56881,56936,56954,56972],{"className":56880,"ariaHidden":990},[989],[86,56882,56884,56887,56927,56930,56933],{"className":56883},[994],[86,56885],{"className":56886,"style":21327},[998],[86,56888,56890,56893],{"className":56889},[1003],[86,56891,6181],{"className":56892},[1003,1007],[86,56894,56896],{"className":56895},[1012],[86,56897,56899,56919],{"className":56898},[1016,3836],[86,56900,56902,56916],{"className":56901},[1020],[86,56903,56905],{"className":56904,"style":6984},[1024],[86,56906,56907,56910],{"style":6987},[86,56908],{"className":56909,"style":1032},[1031],[86,56911,56913],{"className":56912},[1036,1037,1038,1039],[86,56914,802],{"className":56915},[1003,1039],[86,56917,3963],{"className":56918},[3962],[86,56920,56922],{"className":56921},[1020],[86,56923,56925],{"className":56924,"style":7006},[1024],[86,56926],{},[86,56928],{"className":56929,"style":3222},[3221],[86,56931,258],{"className":56932},[3226],[86,56934],{"className":56935,"style":3222},[3221],[86,56937,56939,56942,56945,56948,56951],{"className":56938},[994],[86,56940],{"className":56941,"style":9303},[998],[86,56943,53874],{"className":56944},[1003],[86,56946],{"className":56947,"style":5012},[3221],[86,56949,9864],{"className":56950},[5016],[86,56952],{"className":56953,"style":5012},[3221],[86,56955,56957,56960,56963,56966,56969],{"className":56956},[994],[86,56958],{"className":56959,"style":5994},[998],[86,56961,53874],{"className":56962},[1003],[86,56964],{"className":56965,"style":3222},[3221],[86,56967,258],{"className":56968},[3226],[86,56970],{"className":56971,"style":3222},[3221],[86,56973,56975,56978],{"className":56974},[994],[86,56976],{"className":56977,"style":5994},[998],[86,56979,2553],{"className":56980},[1003],[33,56982,56983,56984],{},"Error para 100 m²: ",[86,56985,56987,57017],{"className":56986},[955],[86,56988,56990],{"className":56989},[959],[961,56991,56992],{"xmlns":963},[965,56993,56994,57014],{},[968,56995,56996,57002,57004,57006,57008,57010,57012],{},[6849,56997,56998,57000],{},[974,56999,6181],{},[978,57001,980],{},[3191,57003,258],{},[978,57005,53883],{},[3191,57007,9864],{},[978,57009,53883],{},[3191,57011,258],{},[978,57013,2553],{},[982,57015,57016],{"encoding":984},"e_2 = 200000 - 200000 = 0",[86,57018,57020,57075,57093,57111],{"className":57019,"ariaHidden":990},[989],[86,57021,57023,57026,57066,57069,57072],{"className":57022},[994],[86,57024],{"className":57025,"style":21327},[998],[86,57027,57029,57032],{"className":57028},[1003],[86,57030,6181],{"className":57031},[1003,1007],[86,57033,57035],{"className":57034},[1012],[86,57036,57038,57058],{"className":57037},[1016,3836],[86,57039,57041,57055],{"className":57040},[1020],[86,57042,57044],{"className":57043,"style":6984},[1024],[86,57045,57046,57049],{"style":6987},[86,57047],{"className":57048,"style":1032},[1031],[86,57050,57052],{"className":57051},[1036,1037,1038,1039],[86,57053,980],{"className":57054},[1003,1039],[86,57056,3963],{"className":57057},[3962],[86,57059,57061],{"className":57060},[1020],[86,57062,57064],{"className":57063,"style":7006},[1024],[86,57065],{},[86,57067],{"className":57068,"style":3222},[3221],[86,57070,258],{"className":57071},[3226],[86,57073],{"className":57074,"style":3222},[3221],[86,57076,57078,57081,57084,57087,57090],{"className":57077},[994],[86,57079],{"className":57080,"style":9303},[998],[86,57082,53883],{"className":57083},[1003],[86,57085],{"className":57086,"style":5012},[3221],[86,57088,9864],{"className":57089},[5016],[86,57091],{"className":57092,"style":5012},[3221],[86,57094,57096,57099,57102,57105,57108],{"className":57095},[994],[86,57097],{"className":57098,"style":5994},[998],[86,57100,53883],{"className":57101},[1003],[86,57103],{"className":57104,"style":3222},[3221],[86,57106,258],{"className":57107},[3226],[86,57109],{"className":57110,"style":3222},[3221],[86,57112,57114,57117],{"className":57113},[994],[86,57115],{"className":57116,"style":5994},[998],[86,57118,2553],{"className":57119},[1003],[33,57121,57122,57123],{},"Error para 150 m²: ",[86,57124,57126,57156],{"className":57125},[955],[86,57127,57129],{"className":57128},[959],[961,57130,57131],{"xmlns":963},[965,57132,57133,57153],{},[968,57134,57135,57141,57143,57145,57147,57149,57151],{},[6849,57136,57137,57139],{},[974,57138,6181],{},[978,57140,4100],{},[3191,57142,258],{},[978,57144,53892],{},[3191,57146,9864],{},[978,57148,53892],{},[3191,57150,258],{},[978,57152,2553],{},[982,57154,57155],{"encoding":984},"e_3 = 300000 - 300000 = 0",[86,57157,57159,57214,57232,57250],{"className":57158,"ariaHidden":990},[989],[86,57160,57162,57165,57205,57208,57211],{"className":57161},[994],[86,57163],{"className":57164,"style":21327},[998],[86,57166,57168,57171],{"className":57167},[1003],[86,57169,6181],{"className":57170},[1003,1007],[86,57172,57174],{"className":57173},[1012],[86,57175,57177,57197],{"className":57176},[1016,3836],[86,57178,57180,57194],{"className":57179},[1020],[86,57181,57183],{"className":57182,"style":6984},[1024],[86,57184,57185,57188],{"style":6987},[86,57186],{"className":57187,"style":1032},[1031],[86,57189,57191],{"className":57190},[1036,1037,1038,1039],[86,57192,4100],{"className":57193},[1003,1039],[86,57195,3963],{"className":57196},[3962],[86,57198,57200],{"className":57199},[1020],[86,57201,57203],{"className":57202,"style":7006},[1024],[86,57204],{},[86,57206],{"className":57207,"style":3222},[3221],[86,57209,258],{"className":57210},[3226],[86,57212],{"className":57213,"style":3222},[3221],[86,57215,57217,57220,57223,57226,57229],{"className":57216},[994],[86,57218],{"className":57219,"style":9303},[998],[86,57221,53892],{"className":57222},[1003],[86,57224],{"className":57225,"style":5012},[3221],[86,57227,9864],{"className":57228},[5016],[86,57230],{"className":57231,"style":5012},[3221],[86,57233,57235,57238,57241,57244,57247],{"className":57234},[994],[86,57236],{"className":57237,"style":5994},[998],[86,57239,53892],{"className":57240},[1003],[86,57242],{"className":57243,"style":3222},[3221],[86,57245,258],{"className":57246},[3226],[86,57248],{"className":57249,"style":3222},[3221],[86,57251,57253,57256],{"className":57252},[994],[86,57254],{"className":57255,"style":5994},[998],[86,57257,2553],{"className":57258},[1003],[117,57260,57261],{"start":205},[33,57262,57263],{},"Elevamos al cuadrado y promediamos para obtener el MSE:",[86,57265,57267],{"className":57266},[3173],[86,57268,57270,57326],{"className":57269},[955],[86,57271,57273],{"className":57272},[959],[961,57274,57275],{"xmlns":963,"display":3182},[965,57276,57277,57323],{},[968,57278,57279,57281,57283,57285,57287,57293,57295,57301,57303,57309,57311,57317,57319,57321],{},[974,57280,49387],{},[974,57282,4084],{},[974,57284,7871],{},[3191,57286,258],{},[3749,57288,57289,57291],{},[978,57290,802],{},[978,57292,4100],{},[3191,57294,243],{"stretchy":3295},[971,57296,57297,57299],{},[978,57298,2553],{},[978,57300,980],{},[3191,57302,6565],{},[971,57304,57305,57307],{},[978,57306,2553],{},[978,57308,980],{},[3191,57310,6565],{},[971,57312,57313,57315],{},[978,57314,2553],{},[978,57316,980],{},[3191,57318,867],{"stretchy":3295},[3191,57320,258],{},[978,57322,2553],{},[982,57324,57325],{"encoding":984},"MSE = \\frac{1}{3} (0^2 + 0^2 + 0^2) = 0",[86,57327,57329,57353,57462,57507,57554],{"className":57328,"ariaHidden":990},[989],[86,57330,57332,57335,57338,57341,57344,57347,57350],{"className":57331},[994],[86,57333],{"className":57334,"style":3575},[998],[86,57336,49387],{"className":57337,"style":6055},[1003,1007],[86,57339,4084],{"className":57340,"style":4133},[1003,1007],[86,57342,7871],{"className":57343,"style":4133},[1003,1007],[86,57345],{"className":57346,"style":3222},[3221],[86,57348,258],{"className":57349},[3226],[86,57351],{"className":57352,"style":3222},[3221],[86,57354,57356,57359,57421,57424,57453,57456,57459],{"className":57355},[994],[86,57357],{"className":57358,"style":9549},[998],[86,57360,57362,57365,57418],{"className":57361},[1003],[86,57363],{"className":57364},[3320,3829],[86,57366,57368],{"className":57367},[3749],[86,57369,57371,57410],{"className":57370},[1016,3836],[86,57372,57374,57407],{"className":57373},[1020],[86,57375,57377,57388,57396],{"className":57376,"style":9568},[1024],[86,57378,57379,57382],{"style":3846},[86,57380],{"className":57381,"style":3850},[1031],[86,57383,57385],{"className":57384},[1003],[86,57386,4100],{"className":57387},[1003],[86,57389,57390,57393],{"style":3901},[86,57391],{"className":57392,"style":3850},[1031],[86,57394],{"className":57395,"style":3909},[3908],[86,57397,57398,57401],{"style":3912},[86,57399],{"className":57400,"style":3850},[1031],[86,57402,57404],{"className":57403},[1003],[86,57405,802],{"className":57406},[1003],[86,57408,3963],{"className":57409},[3962],[86,57411,57413],{"className":57412},[1020],[86,57414,57416],{"className":57415,"style":9620},[1024],[86,57417],{},[86,57419],{"className":57420},[3356,3829],[86,57422,243],{"className":57423},[3320],[86,57425,57427,57430],{"className":57426},[1003],[86,57428,2553],{"className":57429},[1003],[86,57431,57433],{"className":57432},[1012],[86,57434,57436],{"className":57435},[1016],[86,57437,57439],{"className":57438},[1020],[86,57440,57442],{"className":57441,"style":3236},[1024],[86,57443,57444,57447],{"style":3258},[86,57445],{"className":57446,"style":1032},[1031],[86,57448,57450],{"className":57449},[1036,1037,1038,1039],[86,57451,980],{"className":57452},[1003,1039],[86,57454],{"className":57455,"style":5012},[3221],[86,57457,6565],{"className":57458},[5016],[86,57460],{"className":57461,"style":5012},[3221],[86,57463,57465,57469,57498,57501,57504],{"className":57464},[994],[86,57466],{"className":57467,"style":57468},[998],"height:0.9474em;vertical-align:-0.0833em;",[86,57470,57472,57475],{"className":57471},[1003],[86,57473,2553],{"className":57474},[1003],[86,57476,57478],{"className":57477},[1012],[86,57479,57481],{"className":57480},[1016],[86,57482,57484],{"className":57483},[1020],[86,57485,57487],{"className":57486,"style":3236},[1024],[86,57488,57489,57492],{"style":3258},[86,57490],{"className":57491,"style":1032},[1031],[86,57493,57495],{"className":57494},[1036,1037,1038,1039],[86,57496,980],{"className":57497},[1003,1039],[86,57499],{"className":57500,"style":5012},[3221],[86,57502,6565],{"className":57503},[5016],[86,57505],{"className":57506,"style":5012},[3221],[86,57508,57510,57513,57542,57545,57548,57551],{"className":57509},[994],[86,57511],{"className":57512,"style":49667},[998],[86,57514,57516,57519],{"className":57515},[1003],[86,57517,2553],{"className":57518},[1003],[86,57520,57522],{"className":57521},[1012],[86,57523,57525],{"className":57524},[1016],[86,57526,57528],{"className":57527},[1020],[86,57529,57531],{"className":57530,"style":3236},[1024],[86,57532,57533,57536],{"style":3258},[86,57534],{"className":57535,"style":1032},[1031],[86,57537,57539],{"className":57538},[1036,1037,1038,1039],[86,57540,980],{"className":57541},[1003,1039],[86,57543,867],{"className":57544},[3356],[86,57546],{"className":57547,"style":3222},[3221],[86,57549,258],{"className":57550},[3226],[86,57552],{"className":57553,"style":3222},[3221],[86,57555,57557,57560],{"className":57556},[994],[86,57558],{"className":57559,"style":5994},[998],[86,57561,2553],{"className":57562},[1003],[12,57564,57565,57566,57569,57570,57598],{},"Para este caso un MSE de 0 nos indica que el modelo predice perfectamente los valores reales para ",[122,57567,57568],{},"este conjunto de datos de entrenamiento",". Por supuesto que en la práctica los datos reales contendrán ruido y serán aún mayores, con mas variabilidad, por lo que el epsilon ",[86,57571,57573,57586],{"className":57572},[955],[86,57574,57576],{"className":57575},[959],[961,57577,57578],{"xmlns":963},[965,57579,57580,57584],{},[968,57581,57582],{},[974,57583,47369],{},[982,57585,48343],{"encoding":984},[86,57587,57589],{"className":57588,"ariaHidden":990},[989],[86,57590,57592,57595],{"className":57591},[994],[86,57593],{"className":57594,"style":7401},[998],[86,57596,47369],{"className":57597},[1003,1007]," no será cero.",[12,57600,57601,57602],{},"Para explorar más con la regresión puedes usar este Colab de Google que contiene un ejemplo completo de regresión lineal con Python: ",[22,57603,57606],{"href":57604,"target":27,"rel":57605},"https:\u002F\u002Fcolab.research.google.com\u002Fdrive\u002F1yi8-fVw2Ak7pqYOzZsiT7NO_zccZrQir?usp=sharing",[7760,7761],"linear_regression",[43,57608],{},[323,57610,46964],{"id":57611},"clasificación",[16,57613,57614],{},[12,57615,47280,57616,61],{},[122,57617,47283],{},[12,57619,57620],{},"Un problema de clasificacion busca predecir una variable de salida categórica a partir de un conjunto de variables independientes. Por ejemplo, predecir si un correo electrónico es spam o no spam basándose en su contenido, o saber si en la foto hay un gato o un perro.",[12,57622,57623],{},"Existen tres tipos principales de clasificación:",[30,57625,57626,57632,57638],{},[33,57627,57628,57631],{},[122,57629,57630],{},"Clasificación Binaria",": Cuando hay dos clases posibles. Por ejemplo, clasificar si un paciente tiene una enfermedad (sí\u002Fno).",[33,57633,57634,57637],{},[122,57635,57636],{},"Clasificación Multiclase",": Cuando hay más de dos clases posibles. Por ejemplo, clasificar el tipo de flor (puede ser setosa, versicolor o virginica) basándose en sus características.",[33,57639,57640,57643],{},[122,57641,57642],{},"Clasificación Multietiqueta",": Cuando cada ejemplo puede pertenecer a múltiples clases, como clasificar las etiquetas de un artículo de noticias (política, economía, deportes) donde un artículo puede pertenecer a varias categorías.",[16,57645,57646],{},[12,57647,57648],{},"La diferencia entre clasificación multiclase y multietiqueta es que en la primera cada ejemplo solo puede pertenecer a una clase, mientras que en la segunda un ejemplo puede pertenecer a múltiples clases simultáneamente.",[12,57650,57651],{},"Veámos un poco más sobre la clasificación binaria. En este caso, el objetivo es encontrar una función que mapee las entradas a una de las dos clases posibles.",[12,57653,57654,57655,57658,57659,57770],{},"La pregunta que el modelo de clasificación binaria intenta responder es: ",[122,57656,57657],{},"¿Cuál es la probabilidad de que un ejemplo pertenezca a la clase 1 dado un conjunto de características?"," Esto se puede expresar matemáticamente como:\n",[86,57660,57662,57700],{"className":57661},[955],[86,57663,57665],{"className":57664},[959],[961,57666,57667],{"xmlns":963},[965,57668,57669,57697],{},[968,57670,57671,57673,57675,57677,57679,57681,57683,57685,57687,57689,57691,57693,57695],{},[974,57672,3738],{},[3191,57674,243],{"stretchy":3295},[974,57676,5464],{},[3191,57678,258],{},[978,57680,802],{},[974,57682,4804],{"mathvariant":4327},[974,57684,3189],{},[3191,57686,867],{"stretchy":3295},[3191,57688,258],{},[974,57690,6178],{},[3191,57692,243],{"stretchy":3295},[974,57694,3189],{},[3191,57696,867],{"stretchy":3295},[982,57698,57699],{"encoding":984},"P(y=1|x) = f(x)",[86,57701,57703,57727,57752],{"className":57702,"ariaHidden":990},[989],[86,57704,57706,57709,57712,57715,57718,57721,57724],{"className":57705},[994],[86,57707],{"className":57708,"style":3794},[998],[86,57710,3738],{"className":57711,"style":3537},[1003,1007],[86,57713,243],{"className":57714},[3320],[86,57716,5464],{"className":57717,"style":8109},[1003,1007],[86,57719],{"className":57720,"style":3222},[3221],[86,57722,258],{"className":57723},[3226],[86,57725],{"className":57726,"style":3222},[3221],[86,57728,57730,57733,57737,57740,57743,57746,57749],{"className":57729},[994],[86,57731],{"className":57732,"style":3794},[998],[86,57734,57736],{"className":57735},[1003],"1∣",[86,57738,3189],{"className":57739},[1003,1007],[86,57741,867],{"className":57742},[3356],[86,57744],{"className":57745,"style":3222},[3221],[86,57747,258],{"className":57748},[3226],[86,57750],{"className":57751,"style":3222},[3221],[86,57753,57755,57758,57761,57764,57767],{"className":57754},[994],[86,57756],{"className":57757,"style":3794},[998],[86,57759,6178],{"className":57760,"style":6231},[1003,1007],[86,57762,243],{"className":57763},[3320],[86,57765,3189],{"className":57766},[1003,1007],[86,57768,867],{"className":57769},[3356],"\nDonde:",[30,57772,57773,57849],{},[33,57774,57775,57848],{},[86,57776,57778,57806],{"className":57777},[955],[86,57779,57781],{"className":57780},[959],[961,57782,57783],{"xmlns":963},[965,57784,57785,57803],{},[968,57786,57787,57789,57791,57793,57795,57797,57799,57801],{},[974,57788,3738],{},[3191,57790,243],{"stretchy":3295},[974,57792,5464],{},[3191,57794,258],{},[978,57796,802],{},[974,57798,4804],{"mathvariant":4327},[974,57800,3189],{},[3191,57802,867],{"stretchy":3295},[982,57804,57805],{"encoding":984},"P(y=1|x)",[86,57807,57809,57833],{"className":57808,"ariaHidden":990},[989],[86,57810,57812,57815,57818,57821,57824,57827,57830],{"className":57811},[994],[86,57813],{"className":57814,"style":3794},[998],[86,57816,3738],{"className":57817,"style":3537},[1003,1007],[86,57819,243],{"className":57820},[3320],[86,57822,5464],{"className":57823,"style":8109},[1003,1007],[86,57825],{"className":57826,"style":3222},[3221],[86,57828,258],{"className":57829},[3226],[86,57831],{"className":57832,"style":3222},[3221],[86,57834,57836,57839,57842,57845],{"className":57835},[994],[86,57837],{"className":57838,"style":3794},[998],[86,57840,57736],{"className":57841},[1003],[86,57843,3189],{"className":57844},[1003,1007],[86,57846,867],{"className":57847},[3356]," es la probabilidad de que la clase sea 1 dado el vector de características x.",[33,57850,57851,57895],{},[86,57852,57854,57874],{"className":57853},[955],[86,57855,57857],{"className":57856},[959],[961,57858,57859],{"xmlns":963},[965,57860,57861,57871],{},[968,57862,57863,57865,57867,57869],{},[974,57864,6178],{},[3191,57866,243],{"stretchy":3295},[974,57868,3189],{},[3191,57870,867],{"stretchy":3295},[982,57872,57873],{"encoding":984},"f(x)",[86,57875,57877],{"className":57876,"ariaHidden":990},[989],[86,57878,57880,57883,57886,57889,57892],{"className":57879},[994],[86,57881],{"className":57882,"style":3794},[998],[86,57884,6178],{"className":57885,"style":6231},[1003,1007],[86,57887,243],{"className":57888},[3320],[86,57890,3189],{"className":57891},[1003,1007],[86,57893,867],{"className":57894},[3356]," es la función que mapea las características a la probabilidad.",[12,57897,57898,57899,57902],{},"El modelo más común para clasificación binaria es la ",[122,57900,57901],{},"regresión logística",", que tiene el siguiente proceso:",[117,57904,57905],{},[33,57906,57907,57908,57911],{},"Calculamos una ",[122,57909,57910],{},"combinación lineal"," de las características:",[86,57913,57915],{"className":57914},[3173],[86,57916,57918,57991],{"className":57917},[955],[86,57919,57921],{"className":57920},[959],[961,57922,57923],{"xmlns":963,"display":3182},[965,57924,57925,57988],{},[968,57926,57927,57930,57932,57938,57940,57946,57952,57954,57960,57966,57968,57970,57972,57974,57976,57982],{},[974,57928,57929],{},"z",[3191,57931,258],{},[6849,57933,57934,57936],{},[974,57935,42473],{},[978,57937,2553],{},[3191,57939,6565],{},[6849,57941,57942,57944],{},[974,57943,42473],{},[978,57945,802],{},[6849,57947,57948,57950],{},[974,57949,3189],{},[978,57951,802],{},[3191,57953,6565],{},[6849,57955,57956,57958],{},[974,57957,42473],{},[978,57959,980],{},[6849,57961,57962,57964],{},[974,57963,3189],{},[978,57965,980],{},[3191,57967,6565],{},[974,57969,61],{"mathvariant":4327},[974,57971,61],{"mathvariant":4327},[974,57973,61],{"mathvariant":4327},[3191,57975,6565],{},[6849,57977,57978,57980],{},[974,57979,42473],{},[974,57981,12],{},[6849,57983,57984,57986],{},[974,57985,3189],{},[974,57987,12],{},[982,57989,57990],{"encoding":984},"z = \\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_p x_p",[86,57992,57994,58013,58068,58163,58258,58276],{"className":57993,"ariaHidden":990},[989],[86,57995,57997,58000,58004,58007,58010],{"className":57996},[994],[86,57998],{"className":57999,"style":7401},[998],[86,58001,57929],{"className":58002,"style":58003},[1003,1007],"margin-right:0.044em;",[86,58005],{"className":58006,"style":3222},[3221],[86,58008,258],{"className":58009},[3226],[86,58011],{"className":58012,"style":3222},[3221],[86,58014,58016,58019,58059,58062,58065],{"className":58015},[994],[86,58017],{"className":58018,"style":4888},[998],[86,58020,58022,58025],{"className":58021},[1003],[86,58023,42473],{"className":58024,"style":42538},[1003,1007],[86,58026,58028],{"className":58027},[1012],[86,58029,58031,58051],{"className":58030},[1016,3836],[86,58032,58034,58048],{"className":58033},[1020],[86,58035,58037],{"className":58036,"style":6984},[1024],[86,58038,58039,58042],{"style":42553},[86,58040],{"className":58041,"style":1032},[1031],[86,58043,58045],{"className":58044},[1036,1037,1038,1039],[86,58046,2553],{"className":58047},[1003,1039],[86,58049,3963],{"className":58050},[3962],[86,58052,58054],{"className":58053},[1020],[86,58055,58057],{"className":58056,"style":7006},[1024],[86,58058],{},[86,58060],{"className":58061,"style":5012},[3221],[86,58063,6565],{"className":58064},[5016],[86,58066],{"className":58067,"style":5012},[3221],[86,58069,58071,58074,58114,58154,58157,58160],{"className":58070},[994],[86,58072],{"className":58073,"style":4888},[998],[86,58075,58077,58080],{"className":58076},[1003],[86,58078,42473],{"className":58079,"style":42538},[1003,1007],[86,58081,58083],{"className":58082},[1012],[86,58084,58086,58106],{"className":58085},[1016,3836],[86,58087,58089,58103],{"className":58088},[1020],[86,58090,58092],{"className":58091,"style":6984},[1024],[86,58093,58094,58097],{"style":42553},[86,58095],{"className":58096,"style":1032},[1031],[86,58098,58100],{"className":58099},[1036,1037,1038,1039],[86,58101,802],{"className":58102},[1003,1039],[86,58104,3963],{"className":58105},[3962],[86,58107,58109],{"className":58108},[1020],[86,58110,58112],{"className":58111,"style":7006},[1024],[86,58113],{},[86,58115,58117,58120],{"className":58116},[1003],[86,58118,3189],{"className":58119},[1003,1007],[86,58121,58123],{"className":58122},[1012],[86,58124,58126,58146],{"className":58125},[1016,3836],[86,58127,58129,58143],{"className":58128},[1020],[86,58130,58132],{"className":58131,"style":6984},[1024],[86,58133,58134,58137],{"style":6987},[86,58135],{"className":58136,"style":1032},[1031],[86,58138,58140],{"className":58139},[1036,1037,1038,1039],[86,58141,802],{"className":58142},[1003,1039],[86,58144,3963],{"className":58145},[3962],[86,58147,58149],{"className":58148},[1020],[86,58150,58152],{"className":58151,"style":7006},[1024],[86,58153],{},[86,58155],{"className":58156,"style":5012},[3221],[86,58158,6565],{"className":58159},[5016],[86,58161],{"className":58162,"style":5012},[3221],[86,58164,58166,58169,58209,58249,58252,58255],{"className":58165},[994],[86,58167],{"className":58168,"style":4888},[998],[86,58170,58172,58175],{"className":58171},[1003],[86,58173,42473],{"className":58174,"style":42538},[1003,1007],[86,58176,58178],{"className":58177},[1012],[86,58179,58181,58201],{"className":58180},[1016,3836],[86,58182,58184,58198],{"className":58183},[1020],[86,58185,58187],{"className":58186,"style":6984},[1024],[86,58188,58189,58192],{"style":42553},[86,58190],{"className":58191,"style":1032},[1031],[86,58193,58195],{"className":58194},[1036,1037,1038,1039],[86,58196,980],{"className":58197},[1003,1039],[86,58199,3963],{"className":58200},[3962],[86,58202,58204],{"className":58203},[1020],[86,58205,58207],{"className":58206,"style":7006},[1024],[86,58208],{},[86,58210,58212,58215],{"className":58211},[1003],[86,58213,3189],{"className":58214},[1003,1007],[86,58216,58218],{"className":58217},[1012],[86,58219,58221,58241],{"className":58220},[1016,3836],[86,58222,58224,58238],{"className":58223},[1020],[86,58225,58227],{"className":58226,"style":6984},[1024],[86,58228,58229,58232],{"style":6987},[86,58230],{"className":58231,"style":1032},[1031],[86,58233,58235],{"className":58234},[1036,1037,1038,1039],[86,58236,980],{"className":58237},[1003,1039],[86,58239,3963],{"className":58240},[3962],[86,58242,58244],{"className":58243},[1020],[86,58245,58247],{"className":58246,"style":7006},[1024],[86,58248],{},[86,58250],{"className":58251,"style":5012},[3221],[86,58253,6565],{"className":58254},[5016],[86,58256],{"className":58257,"style":5012},[3221],[86,58259,58261,58264,58267,58270,58273],{"className":58260},[994],[86,58262],{"className":58263,"style":14141},[998],[86,58265,4572],{"className":58266},[1003],[86,58268],{"className":58269,"style":5012},[3221],[86,58271,6565],{"className":58272},[5016],[86,58274],{"className":58275,"style":5012},[3221],[86,58277,58279,58282,58322],{"className":58278},[994],[86,58280],{"className":58281,"style":47663},[998],[86,58283,58285,58288],{"className":58284},[1003],[86,58286,42473],{"className":58287,"style":42538},[1003,1007],[86,58289,58291],{"className":58290},[1012],[86,58292,58294,58314],{"className":58293},[1016,3836],[86,58295,58297,58311],{"className":58296},[1020],[86,58298,58300],{"className":58299,"style":7171},[1024],[86,58301,58302,58305],{"style":42553},[86,58303],{"className":58304,"style":1032},[1031],[86,58306,58308],{"className":58307},[1036,1037,1038,1039],[86,58309,12],{"className":58310},[1003,1007,1039],[86,58312,3963],{"className":58313},[3962],[86,58315,58317],{"className":58316},[1020],[86,58318,58320],{"className":58319,"style":10443},[1024],[86,58321],{},[86,58323,58325,58328],{"className":58324},[1003],[86,58326,3189],{"className":58327},[1003,1007],[86,58329,58331],{"className":58330},[1012],[86,58332,58334,58354],{"className":58333},[1016,3836],[86,58335,58337,58351],{"className":58336},[1020],[86,58338,58340],{"className":58339,"style":7171},[1024],[86,58341,58342,58345],{"style":6987},[86,58343],{"className":58344,"style":1032},[1031],[86,58346,58348],{"className":58347},[1036,1037,1038,1039],[86,58349,12],{"className":58350},[1003,1007,1039],[86,58352,3963],{"className":58353},[3962],[86,58355,58357],{"className":58356},[1020],[86,58358,58360],{"className":58359,"style":10443},[1024],[86,58361],{},[117,58363,58364],{"start":192},[33,58365,58366,58367,58370],{},"Aplicamos la ",[122,58368,58369],{},"función sigmoide"," para obtener una probabilidad:",[86,58372,58374],{"className":58373},[3173],[86,58375,58377,58419],{"className":58376},[955],[86,58378,58380],{"className":58379},[959],[961,58381,58382],{"xmlns":963,"display":3182},[965,58383,58384,58416],{},[968,58385,58386,58388,58390,58392,58394,58396],{},[974,58387,9839],{},[3191,58389,243],{"stretchy":3295},[974,58391,57929],{},[3191,58393,867],{"stretchy":3295},[3191,58395,258],{},[3749,58397,58398,58400],{},[978,58399,802],{},[968,58401,58402,58404,58406],{},[978,58403,802],{},[3191,58405,6565],{},[971,58407,58408,58410],{},[974,58409,6181],{},[968,58411,58412,58414],{},[3191,58413,9864],{},[974,58415,57929],{},[982,58417,58418],{"encoding":984},"\\sigma(z) = \\frac{1}{1 + e^{-z}}",[86,58420,58422,58449],{"className":58421,"ariaHidden":990},[989],[86,58423,58425,58428,58431,58434,58437,58440,58443,58446],{"className":58424},[994],[86,58426],{"className":58427,"style":3794},[998],[86,58429,9839],{"className":58430,"style":8109},[1003,1007],[86,58432,243],{"className":58433},[3320],[86,58435,57929],{"className":58436,"style":58003},[1003,1007],[86,58438,867],{"className":58439},[3356],[86,58441],{"className":58442,"style":3222},[3221],[86,58444,258],{"className":58445},[3226],[86,58447],{"className":58448,"style":3222},[3221],[86,58450,58452,58456],{"className":58451},[994],[86,58453],{"className":58454,"style":58455},[998],"height:2.0908em;vertical-align:-0.7693em;",[86,58457,58459,58462,58561],{"className":58458},[1003],[86,58460],{"className":58461},[3320,3829],[86,58463,58465],{"className":58464},[3749],[86,58466,58468,58552],{"className":58467},[1016,3836],[86,58469,58471,58549],{"className":58470},[1020],[86,58472,58474,58530,58538],{"className":58473,"style":9568},[1024],[86,58475,58476,58479],{"style":3846},[86,58477],{"className":58478,"style":3850},[1031],[86,58480,58482,58485,58488,58491,58494],{"className":58481},[1003],[86,58483,802],{"className":58484},[1003],[86,58486],{"className":58487,"style":5012},[3221],[86,58489,6565],{"className":58490},[5016],[86,58492],{"className":58493,"style":5012},[3221],[86,58495,58497,58500],{"className":58496},[1003],[86,58498,6181],{"className":58499},[1003,1007],[86,58501,58503],{"className":58502},[1012],[86,58504,58506],{"className":58505},[1016],[86,58507,58509],{"className":58508},[1020],[86,58510,58513],{"className":58511,"style":58512},[1024],"height:0.6973em;",[86,58514,58515,58518],{"style":51308},[86,58516],{"className":58517,"style":1032},[1031],[86,58519,58521],{"className":58520},[1036,1037,1038,1039],[86,58522,58524,58527],{"className":58523},[1003,1039],[86,58525,9864],{"className":58526},[1003,1039],[86,58528,57929],{"className":58529,"style":58003},[1003,1007,1039],[86,58531,58532,58535],{"style":3901},[86,58533],{"className":58534,"style":3850},[1031],[86,58536],{"className":58537,"style":3909},[3908],[86,58539,58540,58543],{"style":3912},[86,58541],{"className":58542,"style":3850},[1031],[86,58544,58546],{"className":58545},[1003],[86,58547,802],{"className":58548},[1003],[86,58550,3963],{"className":58551},[3962],[86,58553,58555],{"className":58554},[1020],[86,58556,58559],{"className":58557,"style":58558},[1024],"height:0.7693em;",[86,58560],{},[86,58562],{"className":58563},[3356,3829],[117,58565,58566],{"start":205},[33,58567,58568],{},"Probabilidad de clase:",[86,58570,58572],{"className":58571},[3173],[86,58573,58575,58693],{"className":58574},[955],[86,58576,58578],{"className":58577},[959],[961,58579,58580],{"xmlns":963,"display":3182},[965,58581,58582,58690],{},[968,58583,58584,58586,58588,58590,58592,58594,58596,58598,58600,58602,58604,58606,58608,58610,58612],{},[974,58585,3738],{},[3191,58587,243],{"stretchy":3295},[974,58589,5464],{},[3191,58591,258],{},[978,58593,802],{},[974,58595,4804],{"mathvariant":4327},[974,58597,3189],{},[3191,58599,867],{"stretchy":3295},[3191,58601,258],{},[974,58603,9839],{},[3191,58605,243],{"stretchy":3295},[974,58607,57929],{},[3191,58609,867],{"stretchy":3295},[3191,58611,258],{},[3749,58613,58614,58616],{},[978,58615,802],{},[968,58617,58618,58620,58622],{},[978,58619,802],{},[3191,58621,6565],{},[971,58623,58624,58626],{},[974,58625,6181],{},[968,58627,58628,58630,58632,58638,58640,58646,58652,58654,58660,58666,58668,58670,58672,58674,58676,58682,58688],{},[3191,58629,9864],{},[3191,58631,243],{"stretchy":3295},[6849,58633,58634,58636],{},[974,58635,42473],{},[978,58637,2553],{},[3191,58639,6565],{},[6849,58641,58642,58644],{},[974,58643,42473],{},[978,58645,802],{},[6849,58647,58648,58650],{},[974,58649,3189],{},[978,58651,802],{},[3191,58653,6565],{},[6849,58655,58656,58658],{},[974,58657,42473],{},[978,58659,980],{},[6849,58661,58662,58664],{},[974,58663,3189],{},[978,58665,980],{},[3191,58667,6565],{},[974,58669,61],{"mathvariant":4327},[974,58671,61],{"mathvariant":4327},[974,58673,61],{"mathvariant":4327},[3191,58675,6565],{},[6849,58677,58678,58680],{},[974,58679,42473],{},[974,58681,12],{},[6849,58683,58684,58686],{},[974,58685,3189],{},[974,58687,12],{},[3191,58689,867],{"stretchy":3295},[982,58691,58692],{"encoding":984},"P(y=1|x) = \\sigma(z) = \\frac{1}{1 + e^{-(\\beta_0 + \\beta_1 x_1 + \\beta_2 x_2 + ... + \\beta_p x_p)}}",[86,58694,58696,58720,58744,58771],{"className":58695,"ariaHidden":990},[989],[86,58697,58699,58702,58705,58708,58711,58714,58717],{"className":58698},[994],[86,58700],{"className":58701,"style":3794},[998],[86,58703,3738],{"className":58704,"style":3537},[1003,1007],[86,58706,243],{"className":58707},[3320],[86,58709,5464],{"className":58710,"style":8109},[1003,1007],[86,58712],{"className":58713,"style":3222},[3221],[86,58715,258],{"className":58716},[3226],[86,58718],{"className":58719,"style":3222},[3221],[86,58721,58723,58726,58729,58732,58735,58738,58741],{"className":58722},[994],[86,58724],{"className":58725,"style":3794},[998],[86,58727,57736],{"className":58728},[1003],[86,58730,3189],{"className":58731},[1003,1007],[86,58733,867],{"className":58734},[3356],[86,58736],{"className":58737,"style":3222},[3221],[86,58739,258],{"className":58740},[3226],[86,58742],{"className":58743,"style":3222},[3221],[86,58745,58747,58750,58753,58756,58759,58762,58765,58768],{"className":58746},[994],[86,58748],{"className":58749,"style":3794},[998],[86,58751,9839],{"className":58752,"style":8109},[1003,1007],[86,58754,243],{"className":58755},[3320],[86,58757,57929],{"className":58758,"style":58003},[1003,1007],[86,58760,867],{"className":58761},[3356],[86,58763],{"className":58764,"style":3222},[3221],[86,58766,258],{"className":58767},[3226],[86,58769],{"className":58770,"style":3222},[3221],[86,58772,58774,58778],{"className":58773},[994],[86,58775],{"className":58776,"style":58777},[998],"height:2.1248em;vertical-align:-0.8034em;",[86,58779,58781,58784,59187],{"className":58780},[1003],[86,58782],{"className":58783},[3320,3829],[86,58785,58787],{"className":58786},[3749],[86,58788,58790,59178],{"className":58789},[1016,3836],[86,58791,58793,59175],{"className":58792},[1020],[86,58794,58796,59156,59164],{"className":58795,"style":9568},[1024],[86,58797,58799,58802],{"style":58798},"top:-2.2799em;",[86,58800],{"className":58801,"style":3850},[1031],[86,58803,58805,58808,58811,58814,58817],{"className":58804},[1003],[86,58806,802],{"className":58807},[1003],[86,58809],{"className":58810,"style":5012},[3221],[86,58812,6565],{"className":58813},[5016],[86,58815],{"className":58816,"style":5012},[3221],[86,58818,58820,58823],{"className":58819},[1003],[86,58821,6181],{"className":58822},[1003,1007],[86,58824,58826],{"className":58825},[1012],[86,58827,58829],{"className":58828},[1016],[86,58830,58832],{"className":58831},[1020],[86,58833,58836],{"className":58834,"style":58835},[1024],"height:0.8301em;",[86,58837,58839,58842],{"style":58838},"top:-3.0051em;margin-right:0.05em;",[86,58840],{"className":58841,"style":1032},[1031],[86,58843,58845],{"className":58844},[1036,1037,1038,1039],[86,58846,58848,58851,58854,58896,58899,58939,58979,58982,59022,59062,59065,59068,59071,59113,59153],{"className":58847},[1003,1039],[86,58849,9864],{"className":58850},[1003,1039],[86,58852,243],{"className":58853},[3320,1039],[86,58855,58857,58860],{"className":58856},[1003,1039],[86,58858,42473],{"className":58859,"style":42538},[1003,1007,1039],[86,58861,58863],{"className":58862},[1012],[86,58864,58866,58888],{"className":58865},[1016,3836],[86,58867,58869,58885],{"className":58868},[1020],[86,58870,58873],{"className":58871,"style":58872},[1024],"height:0.3173em;",[86,58874,58876,58879],{"style":58875},"top:-2.357em;margin-left:-0.0528em;margin-right:0.0714em;",[86,58877],{"className":58878,"style":11374},[1031],[86,58880,58882],{"className":58881},[1036,11378,11379,1039],[86,58883,2553],{"className":58884},[1003,1039],[86,58886,3963],{"className":58887},[3962],[86,58889,58891],{"className":58890},[1020],[86,58892,58894],{"className":58893,"style":11392},[1024],[86,58895],{},[86,58897,6565],{"className":58898},[5016,1039],[86,58900,58902,58905],{"className":58901},[1003,1039],[86,58903,42473],{"className":58904,"style":42538},[1003,1007,1039],[86,58906,58908],{"className":58907},[1012],[86,58909,58911,58931],{"className":58910},[1016,3836],[86,58912,58914,58928],{"className":58913},[1020],[86,58915,58917],{"className":58916,"style":58872},[1024],[86,58918,58919,58922],{"style":58875},[86,58920],{"className":58921,"style":11374},[1031],[86,58923,58925],{"className":58924},[1036,11378,11379,1039],[86,58926,802],{"className":58927},[1003,1039],[86,58929,3963],{"className":58930},[3962],[86,58932,58934],{"className":58933},[1020],[86,58935,58937],{"className":58936,"style":11392},[1024],[86,58938],{},[86,58940,58942,58945],{"className":58941},[1003,1039],[86,58943,3189],{"className":58944},[1003,1007,1039],[86,58946,58948],{"className":58947},[1012],[86,58949,58951,58971],{"className":58950},[1016,3836],[86,58952,58954,58968],{"className":58953},[1020],[86,58955,58957],{"className":58956,"style":58872},[1024],[86,58958,58959,58962],{"style":11370},[86,58960],{"className":58961,"style":11374},[1031],[86,58963,58965],{"className":58964},[1036,11378,11379,1039],[86,58966,802],{"className":58967},[1003,1039],[86,58969,3963],{"className":58970},[3962],[86,58972,58974],{"className":58973},[1020],[86,58975,58977],{"className":58976,"style":11392},[1024],[86,58978],{},[86,58980,6565],{"className":58981},[5016,1039],[86,58983,58985,58988],{"className":58984},[1003,1039],[86,58986,42473],{"className":58987,"style":42538},[1003,1007,1039],[86,58989,58991],{"className":58990},[1012],[86,58992,58994,59014],{"className":58993},[1016,3836],[86,58995,58997,59011],{"className":58996},[1020],[86,58998,59000],{"className":58999,"style":58872},[1024],[86,59001,59002,59005],{"style":58875},[86,59003],{"className":59004,"style":11374},[1031],[86,59006,59008],{"className":59007},[1036,11378,11379,1039],[86,59009,980],{"className":59010},[1003,1039],[86,59012,3963],{"className":59013},[3962],[86,59015,59017],{"className":59016},[1020],[86,59018,59020],{"className":59019,"style":11392},[1024],[86,59021],{},[86,59023,59025,59028],{"className":59024},[1003,1039],[86,59026,3189],{"className":59027},[1003,1007,1039],[86,59029,59031],{"className":59030},[1012],[86,59032,59034,59054],{"className":59033},[1016,3836],[86,59035,59037,59051],{"className":59036},[1020],[86,59038,59040],{"className":59039,"style":58872},[1024],[86,59041,59042,59045],{"style":11370},[86,59043],{"className":59044,"style":11374},[1031],[86,59046,59048],{"className":59047},[1036,11378,11379,1039],[86,59049,980],{"className":59050},[1003,1039],[86,59052,3963],{"className":59053},[3962],[86,59055,59057],{"className":59056},[1020],[86,59058,59060],{"className":59059,"style":11392},[1024],[86,59061],{},[86,59063,6565],{"className":59064},[5016,1039],[86,59066,4572],{"className":59067},[1003,1039],[86,59069,6565],{"className":59070},[5016,1039],[86,59072,59074,59077],{"className":59073},[1003,1039],[86,59075,42473],{"className":59076,"style":42538},[1003,1007,1039],[86,59078,59080],{"className":59079},[1012],[86,59081,59083,59104],{"className":59082},[1016,3836],[86,59084,59086,59101],{"className":59085},[1020],[86,59087,59090],{"className":59088,"style":59089},[1024],"height:0.1645em;",[86,59091,59092,59095],{"style":58875},[86,59093],{"className":59094,"style":11374},[1031],[86,59096,59098],{"className":59097},[1036,11378,11379,1039],[86,59099,12],{"className":59100},[1003,1007,1039],[86,59102,3963],{"className":59103},[3962],[86,59105,59107],{"className":59106},[1020],[86,59108,59111],{"className":59109,"style":59110},[1024],"height:0.2819em;",[86,59112],{},[86,59114,59116,59119],{"className":59115},[1003,1039],[86,59117,3189],{"className":59118},[1003,1007,1039],[86,59120,59122],{"className":59121},[1012],[86,59123,59125,59145],{"className":59124},[1016,3836],[86,59126,59128,59142],{"className":59127},[1020],[86,59129,59131],{"className":59130,"style":59089},[1024],[86,59132,59133,59136],{"style":11370},[86,59134],{"className":59135,"style":11374},[1031],[86,59137,59139],{"className":59138},[1036,11378,11379,1039],[86,59140,12],{"className":59141},[1003,1007,1039],[86,59143,3963],{"className":59144},[3962],[86,59146,59148],{"className":59147},[1020],[86,59149,59151],{"className":59150,"style":59110},[1024],[86,59152],{},[86,59154,867],{"className":59155},[3356,1039],[86,59157,59158,59161],{"style":3901},[86,59159],{"className":59160,"style":3850},[1031],[86,59162],{"className":59163,"style":3909},[3908],[86,59165,59166,59169],{"style":3912},[86,59167],{"className":59168,"style":3850},[1031],[86,59170,59172],{"className":59171},[1003],[86,59173,802],{"className":59174},[1003],[86,59176,3963],{"className":59177},[3962],[86,59179,59181],{"className":59180},[1020],[86,59182,59185],{"className":59183,"style":59184},[1024],"height:0.8034em;",[86,59186],{},[86,59188],{"className":59189},[3356,3829],[12,59191,3273],{},[30,59193,59194,59265,59461,59658],{},[33,59195,59196,52465],{},[86,59197,59199,59216],{"className":59198},[955],[86,59200,59202],{"className":59201},[959],[961,59203,59204],{"xmlns":963},[965,59205,59206,59214],{},[968,59207,59208],{},[6849,59209,59210,59212],{},[974,59211,42473],{},[978,59213,2553],{},[982,59215,48018],{"encoding":984},[86,59217,59219],{"className":59218,"ariaHidden":990},[989],[86,59220,59222,59225],{"className":59221},[994],[86,59223],{"className":59224,"style":4888},[998],[86,59226,59228,59231],{"className":59227},[1003],[86,59229,42473],{"className":59230,"style":42538},[1003,1007],[86,59232,59234],{"className":59233},[1012],[86,59235,59237,59257],{"className":59236},[1016,3836],[86,59238,59240,59254],{"className":59239},[1020],[86,59241,59243],{"className":59242,"style":6984},[1024],[86,59244,59245,59248],{"style":42553},[86,59246],{"className":59247,"style":1032},[1031],[86,59249,59251],{"className":59250},[1036,1037,1038,1039],[86,59252,2553],{"className":59253},[1003,1039],[86,59255,3963],{"className":59256},[3962],[86,59258,59260],{"className":59259},[1020],[86,59261,59263],{"className":59262,"style":7006},[1024],[86,59264],{},[33,59266,59267,48324],{},[86,59268,59270,59311],{"className":59269},[955],[86,59271,59273],{"className":59272},[959],[961,59274,59275],{"xmlns":963},[965,59276,59277,59309],{},[968,59278,59279,59285,59287,59293,59295,59297,59299,59301,59303],{},[6849,59280,59281,59283],{},[974,59282,42473],{},[978,59284,802],{},[3191,59286,291],{"separator":990},[6849,59288,59289,59291],{},[974,59290,42473],{},[978,59292,980],{},[3191,59294,291],{"separator":990},[974,59296,61],{"mathvariant":4327},[974,59298,61],{"mathvariant":4327},[974,59300,61],{"mathvariant":4327},[3191,59302,291],{"separator":990},[6849,59304,59305,59307],{},[974,59306,42473],{},[974,59308,12],{},[982,59310,48173],{"encoding":984},[86,59312,59314],{"className":59313,"ariaHidden":990},[989],[86,59315,59317,59320,59360,59363,59366,59406,59409,59412,59415,59418,59421],{"className":59316},[994],[86,59318],{"className":59319,"style":47663},[998],[86,59321,59323,59326],{"className":59322},[1003],[86,59324,42473],{"className":59325,"style":42538},[1003,1007],[86,59327,59329],{"className":59328},[1012],[86,59330,59332,59352],{"className":59331},[1016,3836],[86,59333,59335,59349],{"className":59334},[1020],[86,59336,59338],{"className":59337,"style":6984},[1024],[86,59339,59340,59343],{"style":42553},[86,59341],{"className":59342,"style":1032},[1031],[86,59344,59346],{"className":59345},[1036,1037,1038,1039],[86,59347,802],{"className":59348},[1003,1039],[86,59350,3963],{"className":59351},[3962],[86,59353,59355],{"className":59354},[1020],[86,59356,59358],{"className":59357,"style":7006},[1024],[86,59359],{},[86,59361,291],{"className":59362},[4158],[86,59364],{"className":59365,"style":4162},[3221],[86,59367,59369,59372],{"className":59368},[1003],[86,59370,42473],{"className":59371,"style":42538},[1003,1007],[86,59373,59375],{"className":59374},[1012],[86,59376,59378,59398],{"className":59377},[1016,3836],[86,59379,59381,59395],{"className":59380},[1020],[86,59382,59384],{"className":59383,"style":6984},[1024],[86,59385,59386,59389],{"style":42553},[86,59387],{"className":59388,"style":1032},[1031],[86,59390,59392],{"className":59391},[1036,1037,1038,1039],[86,59393,980],{"className":59394},[1003,1039],[86,59396,3963],{"className":59397},[3962],[86,59399,59401],{"className":59400},[1020],[86,59402,59404],{"className":59403,"style":7006},[1024],[86,59405],{},[86,59407,291],{"className":59408},[4158],[86,59410],{"className":59411,"style":4162},[3221],[86,59413,4572],{"className":59414},[1003],[86,59416,291],{"className":59417},[4158],[86,59419],{"className":59420,"style":4162},[3221],[86,59422,59424,59427],{"className":59423},[1003],[86,59425,42473],{"className":59426,"style":42538},[1003,1007],[86,59428,59430],{"className":59429},[1012],[86,59431,59433,59453],{"className":59432},[1016,3836],[86,59434,59436,59450],{"className":59435},[1020],[86,59437,59439],{"className":59438,"style":7171},[1024],[86,59440,59441,59444],{"style":42553},[86,59442],{"className":59443,"style":1032},[1031],[86,59445,59447],{"className":59446},[1036,1037,1038,1039],[86,59448,12],{"className":59449},[1003,1007,1039],[86,59451,3963],{"className":59452},[3962],[86,59454,59456],{"className":59455},[1020],[86,59457,59459],{"className":59458,"style":10443},[1024],[86,59460],{},[33,59462,59463,59657],{},[86,59464,59466,59507],{"className":59465},[955],[86,59467,59469],{"className":59468},[959],[961,59470,59471],{"xmlns":963},[965,59472,59473,59505],{},[968,59474,59475,59481,59483,59489,59491,59493,59495,59497,59499],{},[6849,59476,59477,59479],{},[974,59478,3189],{},[978,59480,802],{},[3191,59482,291],{"separator":990},[6849,59484,59485,59487],{},[974,59486,3189],{},[978,59488,980],{},[3191,59490,291],{"separator":990},[974,59492,61],{"mathvariant":4327},[974,59494,61],{"mathvariant":4327},[974,59496,61],{"mathvariant":4327},[3191,59498,291],{"separator":990},[6849,59500,59501,59503],{},[974,59502,3189],{},[974,59504,12],{},[982,59506,47843],{"encoding":984},[86,59508,59510],{"className":59509,"ariaHidden":990},[989],[86,59511,59513,59516,59556,59559,59562,59602,59605,59608,59611,59614,59617],{"className":59512},[994],[86,59514],{"className":59515,"style":47853},[998],[86,59517,59519,59522],{"className":59518},[1003],[86,59520,3189],{"className":59521},[1003,1007],[86,59523,59525],{"className":59524},[1012],[86,59526,59528,59548],{"className":59527},[1016,3836],[86,59529,59531,59545],{"className":59530},[1020],[86,59532,59534],{"className":59533,"style":6984},[1024],[86,59535,59536,59539],{"style":6987},[86,59537],{"className":59538,"style":1032},[1031],[86,59540,59542],{"className":59541},[1036,1037,1038,1039],[86,59543,802],{"className":59544},[1003,1039],[86,59546,3963],{"className":59547},[3962],[86,59549,59551],{"className":59550},[1020],[86,59552,59554],{"className":59553,"style":7006},[1024],[86,59555],{},[86,59557,291],{"className":59558},[4158],[86,59560],{"className":59561,"style":4162},[3221],[86,59563,59565,59568],{"className":59564},[1003],[86,59566,3189],{"className":59567},[1003,1007],[86,59569,59571],{"className":59570},[1012],[86,59572,59574,59594],{"className":59573},[1016,3836],[86,59575,59577,59591],{"className":59576},[1020],[86,59578,59580],{"className":59579,"style":6984},[1024],[86,59581,59582,59585],{"style":6987},[86,59583],{"className":59584,"style":1032},[1031],[86,59586,59588],{"className":59587},[1036,1037,1038,1039],[86,59589,980],{"className":59590},[1003,1039],[86,59592,3963],{"className":59593},[3962],[86,59595,59597],{"className":59596},[1020],[86,59598,59600],{"className":59599,"style":7006},[1024],[86,59601],{},[86,59603,291],{"className":59604},[4158],[86,59606],{"className":59607,"style":4162},[3221],[86,59609,4572],{"className":59610},[1003],[86,59612,291],{"className":59613},[4158],[86,59615],{"className":59616,"style":4162},[3221],[86,59618,59620,59623],{"className":59619},[1003],[86,59621,3189],{"className":59622},[1003,1007],[86,59624,59626],{"className":59625},[1012],[86,59627,59629,59649],{"className":59628},[1016,3836],[86,59630,59632,59646],{"className":59631},[1020],[86,59633,59635],{"className":59634,"style":7171},[1024],[86,59636,59637,59640],{"style":6987},[86,59638],{"className":59639,"style":1032},[1031],[86,59641,59643],{"className":59642},[1036,1037,1038,1039],[86,59644,12],{"className":59645},[1003,1007,1039],[86,59647,3963],{"className":59648},[3962],[86,59650,59652],{"className":59651},[1020],[86,59653,59655],{"className":59654,"style":10443},[1024],[86,59656],{}," son las características o variables independientes.",[33,59659,59660,57848],{},[86,59661,59663,59690],{"className":59662},[955],[86,59664,59666],{"className":59665},[959],[961,59667,59668],{"xmlns":963},[965,59669,59670,59688],{},[968,59671,59672,59674,59676,59678,59680,59682,59684,59686],{},[974,59673,3738],{},[3191,59675,243],{"stretchy":3295},[974,59677,5464],{},[3191,59679,258],{},[978,59681,802],{},[974,59683,4804],{"mathvariant":4327},[974,59685,3189],{},[3191,59687,867],{"stretchy":3295},[982,59689,57805],{"encoding":984},[86,59691,59693,59717],{"className":59692,"ariaHidden":990},[989],[86,59694,59696,59699,59702,59705,59708,59711,59714],{"className":59695},[994],[86,59697],{"className":59698,"style":3794},[998],[86,59700,3738],{"className":59701,"style":3537},[1003,1007],[86,59703,243],{"className":59704},[3320],[86,59706,5464],{"className":59707,"style":8109},[1003,1007],[86,59709],{"className":59710,"style":3222},[3221],[86,59712,258],{"className":59713},[3226],[86,59715],{"className":59716,"style":3222},[3221],[86,59718,59720,59723,59726,59729],{"className":59719},[994],[86,59721],{"className":59722,"style":3794},[998],[86,59724,57736],{"className":59725},[1003],[86,59727,3189],{"className":59728},[1003,1007],[86,59730,867],{"className":59731},[3356],[12,59733,59734],{},"Cada característica aporta evidencia a favor o en contra, imagina si la palabra \"gratis\" aparece en un correo electrónico, eso podría aumentar la probabilidad de que sea spam. Por otro lado, si la palabra \"reunión\" aparece, eso podría disminuir la probabilidad de que sea spam.",[16,59736,59737],{},[12,59738,59739],{},"Esto nos proporciona no solo una clasificación, sino también una medida de confianza en esa clasificación a través de la probabilidad calculada por la función sigmoide.",[12,59741,59742],{},"La función sigmoide transforma cualquier valor real en un valor entre 0 y 1. La fórmula como se muestra arriba es:",[86,59744,59746],{"className":59745},[3173],[86,59747,59749,59790],{"className":59748},[955],[86,59750,59752],{"className":59751},[959],[961,59753,59754],{"xmlns":963,"display":3182},[965,59755,59756,59788],{},[968,59757,59758,59760,59762,59764,59766,59768],{},[974,59759,9839],{},[3191,59761,243],{"stretchy":3295},[974,59763,57929],{},[3191,59765,867],{"stretchy":3295},[3191,59767,258],{},[3749,59769,59770,59772],{},[978,59771,802],{},[968,59773,59774,59776,59778],{},[978,59775,802],{},[3191,59777,6565],{},[971,59779,59780,59782],{},[974,59781,6181],{},[968,59783,59784,59786],{},[3191,59785,9864],{},[974,59787,57929],{},[982,59789,58418],{"encoding":984},[86,59791,59793,59820],{"className":59792,"ariaHidden":990},[989],[86,59794,59796,59799,59802,59805,59808,59811,59814,59817],{"className":59795},[994],[86,59797],{"className":59798,"style":3794},[998],[86,59800,9839],{"className":59801,"style":8109},[1003,1007],[86,59803,243],{"className":59804},[3320],[86,59806,57929],{"className":59807,"style":58003},[1003,1007],[86,59809,867],{"className":59810},[3356],[86,59812],{"className":59813,"style":3222},[3221],[86,59815,258],{"className":59816},[3226],[86,59818],{"className":59819,"style":3222},[3221],[86,59821,59823,59826],{"className":59822},[994],[86,59824],{"className":59825,"style":58455},[998],[86,59827,59829,59832,59929],{"className":59828},[1003],[86,59830],{"className":59831},[3320,3829],[86,59833,59835],{"className":59834},[3749],[86,59836,59838,59921],{"className":59837},[1016,3836],[86,59839,59841,59918],{"className":59840},[1020],[86,59842,59844,59899,59907],{"className":59843,"style":9568},[1024],[86,59845,59846,59849],{"style":3846},[86,59847],{"className":59848,"style":3850},[1031],[86,59850,59852,59855,59858,59861,59864],{"className":59851},[1003],[86,59853,802],{"className":59854},[1003],[86,59856],{"className":59857,"style":5012},[3221],[86,59859,6565],{"className":59860},[5016],[86,59862],{"className":59863,"style":5012},[3221],[86,59865,59867,59870],{"className":59866},[1003],[86,59868,6181],{"className":59869},[1003,1007],[86,59871,59873],{"className":59872},[1012],[86,59874,59876],{"className":59875},[1016],[86,59877,59879],{"className":59878},[1020],[86,59880,59882],{"className":59881,"style":58512},[1024],[86,59883,59884,59887],{"style":51308},[86,59885],{"className":59886,"style":1032},[1031],[86,59888,59890],{"className":59889},[1036,1037,1038,1039],[86,59891,59893,59896],{"className":59892},[1003,1039],[86,59894,9864],{"className":59895},[1003,1039],[86,59897,57929],{"className":59898,"style":58003},[1003,1007,1039],[86,59900,59901,59904],{"style":3901},[86,59902],{"className":59903,"style":3850},[1031],[86,59905],{"className":59906,"style":3909},[3908],[86,59908,59909,59912],{"style":3912},[86,59910],{"className":59911,"style":3850},[1031],[86,59913,59915],{"className":59914},[1003],[86,59916,802],{"className":59917},[1003],[86,59919,3963],{"className":59920},[3962],[86,59922,59924],{"className":59923},[1020],[86,59925,59927],{"className":59926,"style":58558},[1024],[86,59928],{},[86,59930],{"className":59931},[3356,3829],[12,59933,3273],{},[30,59935,59936,60411,60442],{},[33,59937,59938,59966,59967,61],{},[86,59939,59941,59954],{"className":59940},[955],[86,59942,59944],{"className":59943},[959],[961,59945,59946],{"xmlns":963},[965,59947,59948,59952],{},[968,59949,59950],{},[974,59951,57929],{},[982,59953,57929],{"encoding":984},[86,59955,59957],{"className":59956,"ariaHidden":990},[989],[86,59958,59960,59963],{"className":59959},[994],[86,59961],{"className":59962,"style":7401},[998],[86,59964,57929],{"className":59965,"style":58003},[1003,1007]," es la combinación lineal de las características, es decir, ",[86,59968,59970,60041],{"className":59969},[955],[86,59971,59973],{"className":59972},[959],[961,59974,59975],{"xmlns":963},[965,59976,59977,60039],{},[968,59978,59979,59981,59983,59989,59991,59997,60003,60005,60011,60017,60019,60021,60023,60025,60027,60033],{},[974,59980,57929],{},[3191,59982,258],{},[6849,59984,59985,59987],{},[974,59986,42473],{},[978,59988,2553],{},[3191,59990,6565],{},[6849,59992,59993,59995],{},[974,59994,42473],{},[978,59996,802],{},[6849,59998,59999,60001],{},[974,60000,3189],{},[978,60002,802],{},[3191,60004,6565],{},[6849,60006,60007,60009],{},[974,60008,42473],{},[978,60010,980],{},[6849,60012,60013,60015],{},[974,60014,3189],{},[978,60016,980],{},[3191,60018,6565],{},[974,60020,61],{"mathvariant":4327},[974,60022,61],{"mathvariant":4327},[974,60024,61],{"mathvariant":4327},[3191,60026,6565],{},[6849,60028,60029,60031],{},[974,60030,42473],{},[974,60032,12],{},[6849,60034,60035,60037],{},[974,60036,3189],{},[974,60038,12],{},[982,60040,57990],{"encoding":984},[86,60042,60044,60062,60117,60212,60307,60325],{"className":60043,"ariaHidden":990},[989],[86,60045,60047,60050,60053,60056,60059],{"className":60046},[994],[86,60048],{"className":60049,"style":7401},[998],[86,60051,57929],{"className":60052,"style":58003},[1003,1007],[86,60054],{"className":60055,"style":3222},[3221],[86,60057,258],{"className":60058},[3226],[86,60060],{"className":60061,"style":3222},[3221],[86,60063,60065,60068,60108,60111,60114],{"className":60064},[994],[86,60066],{"className":60067,"style":4888},[998],[86,60069,60071,60074],{"className":60070},[1003],[86,60072,42473],{"className":60073,"style":42538},[1003,1007],[86,60075,60077],{"className":60076},[1012],[86,60078,60080,60100],{"className":60079},[1016,3836],[86,60081,60083,60097],{"className":60082},[1020],[86,60084,60086],{"className":60085,"style":6984},[1024],[86,60087,60088,60091],{"style":42553},[86,60089],{"className":60090,"style":1032},[1031],[86,60092,60094],{"className":60093},[1036,1037,1038,1039],[86,60095,2553],{"className":60096},[1003,1039],[86,60098,3963],{"className":60099},[3962],[86,60101,60103],{"className":60102},[1020],[86,60104,60106],{"className":60105,"style":7006},[1024],[86,60107],{},[86,60109],{"className":60110,"style":5012},[3221],[86,60112,6565],{"className":60113},[5016],[86,60115],{"className":60116,"style":5012},[3221],[86,60118,60120,60123,60163,60203,60206,60209],{"className":60119},[994],[86,60121],{"className":60122,"style":4888},[998],[86,60124,60126,60129],{"className":60125},[1003],[86,60127,42473],{"className":60128,"style":42538},[1003,1007],[86,60130,60132],{"className":60131},[1012],[86,60133,60135,60155],{"className":60134},[1016,3836],[86,60136,60138,60152],{"className":60137},[1020],[86,60139,60141],{"className":60140,"style":6984},[1024],[86,60142,60143,60146],{"style":42553},[86,60144],{"className":60145,"style":1032},[1031],[86,60147,60149],{"className":60148},[1036,1037,1038,1039],[86,60150,802],{"className":60151},[1003,1039],[86,60153,3963],{"className":60154},[3962],[86,60156,60158],{"className":60157},[1020],[86,60159,60161],{"className":60160,"style":7006},[1024],[86,60162],{},[86,60164,60166,60169],{"className":60165},[1003],[86,60167,3189],{"className":60168},[1003,1007],[86,60170,60172],{"className":60171},[1012],[86,60173,60175,60195],{"className":60174},[1016,3836],[86,60176,60178,60192],{"className":60177},[1020],[86,60179,60181],{"className":60180,"style":6984},[1024],[86,60182,60183,60186],{"style":6987},[86,60184],{"className":60185,"style":1032},[1031],[86,60187,60189],{"className":60188},[1036,1037,1038,1039],[86,60190,802],{"className":60191},[1003,1039],[86,60193,3963],{"className":60194},[3962],[86,60196,60198],{"className":60197},[1020],[86,60199,60201],{"className":60200,"style":7006},[1024],[86,60202],{},[86,60204],{"className":60205,"style":5012},[3221],[86,60207,6565],{"className":60208},[5016],[86,60210],{"className":60211,"style":5012},[3221],[86,60213,60215,60218,60258,60298,60301,60304],{"className":60214},[994],[86,60216],{"className":60217,"style":4888},[998],[86,60219,60221,60224],{"className":60220},[1003],[86,60222,42473],{"className":60223,"style":42538},[1003,1007],[86,60225,60227],{"className":60226},[1012],[86,60228,60230,60250],{"className":60229},[1016,3836],[86,60231,60233,60247],{"className":60232},[1020],[86,60234,60236],{"className":60235,"style":6984},[1024],[86,60237,60238,60241],{"style":42553},[86,60239],{"className":60240,"style":1032},[1031],[86,60242,60244],{"className":60243},[1036,1037,1038,1039],[86,60245,980],{"className":60246},[1003,1039],[86,60248,3963],{"className":60249},[3962],[86,60251,60253],{"className":60252},[1020],[86,60254,60256],{"className":60255,"style":7006},[1024],[86,60257],{},[86,60259,60261,60264],{"className":60260},[1003],[86,60262,3189],{"className":60263},[1003,1007],[86,60265,60267],{"className":60266},[1012],[86,60268,60270,60290],{"className":60269},[1016,3836],[86,60271,60273,60287],{"className":60272},[1020],[86,60274,60276],{"className":60275,"style":6984},[1024],[86,60277,60278,60281],{"style":6987},[86,60279],{"className":60280,"style":1032},[1031],[86,60282,60284],{"className":60283},[1036,1037,1038,1039],[86,60285,980],{"className":60286},[1003,1039],[86,60288,3963],{"className":60289},[3962],[86,60291,60293],{"className":60292},[1020],[86,60294,60296],{"className":60295,"style":7006},[1024],[86,60297],{},[86,60299],{"className":60300,"style":5012},[3221],[86,60302,6565],{"className":60303},[5016],[86,60305],{"className":60306,"style":5012},[3221],[86,60308,60310,60313,60316,60319,60322],{"className":60309},[994],[86,60311],{"className":60312,"style":14141},[998],[86,60314,4572],{"className":60315},[1003],[86,60317],{"className":60318,"style":5012},[3221],[86,60320,6565],{"className":60321},[5016],[86,60323],{"className":60324,"style":5012},[3221],[86,60326,60328,60331,60371],{"className":60327},[994],[86,60329],{"className":60330,"style":47663},[998],[86,60332,60334,60337],{"className":60333},[1003],[86,60335,42473],{"className":60336,"style":42538},[1003,1007],[86,60338,60340],{"className":60339},[1012],[86,60341,60343,60363],{"className":60342},[1016,3836],[86,60344,60346,60360],{"className":60345},[1020],[86,60347,60349],{"className":60348,"style":7171},[1024],[86,60350,60351,60354],{"style":42553},[86,60352],{"className":60353,"style":1032},[1031],[86,60355,60357],{"className":60356},[1036,1037,1038,1039],[86,60358,12],{"className":60359},[1003,1007,1039],[86,60361,3963],{"className":60362},[3962],[86,60364,60366],{"className":60365},[1020],[86,60367,60369],{"className":60368,"style":10443},[1024],[86,60370],{},[86,60372,60374,60377],{"className":60373},[1003],[86,60375,3189],{"className":60376},[1003,1007],[86,60378,60380],{"className":60379},[1012],[86,60381,60383,60403],{"className":60382},[1016,3836],[86,60384,60386,60400],{"className":60385},[1020],[86,60387,60389],{"className":60388,"style":7171},[1024],[86,60390,60391,60394],{"style":6987},[86,60392],{"className":60393,"style":1032},[1031],[86,60395,60397],{"className":60396},[1036,1037,1038,1039],[86,60398,12],{"className":60399},[1003,1007,1039],[86,60401,3963],{"className":60402},[3962],[86,60404,60406],{"className":60405},[1020],[86,60407,60409],{"className":60408,"style":10443},[1024],[86,60410],{},[33,60412,60413,60441],{},[86,60414,60416,60429],{"className":60415},[955],[86,60417,60419],{"className":60418},[959],[961,60420,60421],{"xmlns":963},[965,60422,60423,60427],{},[968,60424,60425],{},[974,60426,6181],{},[982,60428,6181],{"encoding":984},[86,60430,60432],{"className":60431,"ariaHidden":990},[989],[86,60433,60435,60438],{"className":60434},[994],[86,60436],{"className":60437,"style":7401},[998],[86,60439,6181],{"className":60440},[1003,1007]," es el número de Euler, aproximadamente igual a 2.71828.",[33,60443,60444,60488],{},[86,60445,60447,60467],{"className":60446},[955],[86,60448,60450],{"className":60449},[959],[961,60451,60452],{"xmlns":963},[965,60453,60454,60464],{},[968,60455,60456,60458,60460,60462],{},[974,60457,9839],{},[3191,60459,243],{"stretchy":3295},[974,60461,57929],{},[3191,60463,867],{"stretchy":3295},[982,60465,60466],{"encoding":984},"\\sigma(z)",[86,60468,60470],{"className":60469,"ariaHidden":990},[989],[86,60471,60473,60476,60479,60482,60485],{"className":60472},[994],[86,60474],{"className":60475,"style":3794},[998],[86,60477,9839],{"className":60478,"style":8109},[1003,1007],[86,60480,243],{"className":60481},[3320],[86,60483,57929],{"className":60484,"style":58003},[1003,1007],[86,60486,867],{"className":60487},[3356]," es la salida de la función sigmoide, que representa la probabilidad de que la clase sea 1 dado el valor de z (rango entre 0 y 1).",[12,60490,60491,60492,60535,60536,60540],{},"Visualmente es algo así (con z en el eje X y ",[86,60493,60495,60514],{"className":60494},[955],[86,60496,60498],{"className":60497},[959],[961,60499,60500],{"xmlns":963},[965,60501,60502,60512],{},[968,60503,60504,60506,60508,60510],{},[974,60505,9839],{},[3191,60507,243],{"stretchy":3295},[974,60509,57929],{},[3191,60511,867],{"stretchy":3295},[982,60513,60466],{"encoding":984},[86,60515,60517],{"className":60516,"ariaHidden":990},[989],[86,60518,60520,60523,60526,60529,60532],{"className":60519},[994],[86,60521],{"className":60522,"style":3794},[998],[86,60524,9839],{"className":60525,"style":8109},[1003,1007],[86,60527,243],{"className":60528},[3320],[86,60530,57929],{"className":60531,"style":58003},[1003,1007],[86,60533,867],{"className":60534},[3356]," en el eje Y):\n",[1945,60537],{"alt":60538,"src":60539},"Gráfico de la función sigmoide","\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations\u002Fshared\u002Fsigmoid-function.webp",[901,60541,60542],{},"Gráfico de la Función Sigmoide",[12,60544,60545],{},"De aqui podemos sacar algunas conclusiones importantes:",[30,60547,60548,60595,60642],{},[33,60549,60550,60551,60594],{},"Cuando z es muy negativo, ",[86,60552,60554,60573],{"className":60553},[955],[86,60555,60557],{"className":60556},[959],[961,60558,60559],{"xmlns":963},[965,60560,60561,60571],{},[968,60562,60563,60565,60567,60569],{},[974,60564,9839],{},[3191,60566,243],{"stretchy":3295},[974,60568,57929],{},[3191,60570,867],{"stretchy":3295},[982,60572,60466],{"encoding":984},[86,60574,60576],{"className":60575,"ariaHidden":990},[989],[86,60577,60579,60582,60585,60588,60591],{"className":60578},[994],[86,60580],{"className":60581,"style":3794},[998],[86,60583,9839],{"className":60584,"style":8109},[1003,1007],[86,60586,243],{"className":60587},[3320],[86,60589,57929],{"className":60590,"style":58003},[1003,1007],[86,60592,867],{"className":60593},[3356]," se acerca a 0, lo que indica una baja probabilidad de que la clase sea 1.",[33,60596,60597,60598,60641],{},"Cuando z es muy positivo, ",[86,60599,60601,60620],{"className":60600},[955],[86,60602,60604],{"className":60603},[959],[961,60605,60606],{"xmlns":963},[965,60607,60608,60618],{},[968,60609,60610,60612,60614,60616],{},[974,60611,9839],{},[3191,60613,243],{"stretchy":3295},[974,60615,57929],{},[3191,60617,867],{"stretchy":3295},[982,60619,60466],{"encoding":984},[86,60621,60623],{"className":60622,"ariaHidden":990},[989],[86,60624,60626,60629,60632,60635,60638],{"className":60625},[994],[86,60627],{"className":60628,"style":3794},[998],[86,60630,9839],{"className":60631,"style":8109},[1003,1007],[86,60633,243],{"className":60634},[3320],[86,60636,57929],{"className":60637,"style":58003},[1003,1007],[86,60639,867],{"className":60640},[3356]," se acerca a 1, lo que indica una alta probabilidad de que la clase sea 1.",[33,60643,60644,60645,60688],{},"Cuando z es 0, ",[86,60646,60648,60667],{"className":60647},[955],[86,60649,60651],{"className":60650},[959],[961,60652,60653],{"xmlns":963},[965,60654,60655,60665],{},[968,60656,60657,60659,60661,60663],{},[974,60658,9839],{},[3191,60660,243],{"stretchy":3295},[974,60662,57929],{},[3191,60664,867],{"stretchy":3295},[982,60666,60466],{"encoding":984},[86,60668,60670],{"className":60669,"ariaHidden":990},[989],[86,60671,60673,60676,60679,60682,60685],{"className":60672},[994],[86,60674],{"className":60675,"style":3794},[998],[86,60677,9839],{"className":60678,"style":8109},[1003,1007],[86,60680,243],{"className":60681},[3320],[86,60683,57929],{"className":60684,"style":58003},[1003,1007],[86,60686,867],{"className":60687},[3356]," es 0.5, lo que indica una probabilidad igual de que la clase sea 0 o 1.",[12,60690,60691,60692,60695],{},"EL valor de 0.5 ",[122,60693,60694],{},"comunmente se utiliza como umbral",", de manera que:",[30,60697,60698,60769],{},[33,60699,60700,60701,60768],{},"Si ",[86,60702,60704,60729],{"className":60703},[955],[86,60705,60707],{"className":60706},[959],[961,60708,60709],{"xmlns":963},[965,60710,60711,60726],{},[968,60712,60713,60715,60717,60719,60721,60724],{},[974,60714,9839],{},[3191,60716,243],{"stretchy":3295},[974,60718,57929],{},[3191,60720,867],{"stretchy":3295},[3191,60722,60723],{},"≥",[978,60725,31150],{},[982,60727,60728],{"encoding":984},"\\sigma(z) \\geq 0.5",[86,60730,60732,60759],{"className":60731,"ariaHidden":990},[989],[86,60733,60735,60738,60741,60744,60747,60750,60753,60756],{"className":60734},[994],[86,60736],{"className":60737,"style":3794},[998],[86,60739,9839],{"className":60740,"style":8109},[1003,1007],[86,60742,243],{"className":60743},[3320],[86,60745,57929],{"className":60746,"style":58003},[1003,1007],[86,60748,867],{"className":60749},[3356],[86,60751],{"className":60752,"style":3222},[3221],[86,60754,60723],{"className":60755},[3226],[86,60757],{"className":60758,"style":3222},[3221],[86,60760,60762,60765],{"className":60761},[994],[86,60763],{"className":60764,"style":5994},[998],[86,60766,31150],{"className":60767},[1003],", se clasifica como clase 1.",[33,60770,60700,60771,60837],{},[86,60772,60774,60798],{"className":60773},[955],[86,60775,60777],{"className":60776},[959],[961,60778,60779],{"xmlns":963},[965,60780,60781,60795],{},[968,60782,60783,60785,60787,60789,60791,60793],{},[974,60784,9839],{},[3191,60786,243],{"stretchy":3295},[974,60788,57929],{},[3191,60790,867],{"stretchy":3295},[3191,60792,41317],{},[978,60794,31150],{},[982,60796,60797],{"encoding":984},"\\sigma(z) \u003C 0.5",[86,60799,60801,60828],{"className":60800,"ariaHidden":990},[989],[86,60802,60804,60807,60810,60813,60816,60819,60822,60825],{"className":60803},[994],[86,60805],{"className":60806,"style":3794},[998],[86,60808,9839],{"className":60809,"style":8109},[1003,1007],[86,60811,243],{"className":60812},[3320],[86,60814,57929],{"className":60815,"style":58003},[1003,1007],[86,60817,867],{"className":60818},[3356],[86,60820],{"className":60821,"style":3222},[3221],[86,60823,41317],{"className":60824},[3226],[86,60826],{"className":60827,"style":3222},[3221],[86,60829,60831,60834],{"className":60830},[994],[86,60832],{"className":60833,"style":5994},[998],[86,60835,31150],{"className":60836},[1003],", se clasifica como clase 0.",[16,60839,60840,60843],{},[12,60841,60842],{},"Propiedades clave:",[30,60844,60845,60848,60895],{},[33,60846,60847],{},"Rango acotado entre 0 y 1",[33,60849,60850,60851,60894],{},"Monotonía, si z aumenta, ",[86,60852,60854,60873],{"className":60853},[955],[86,60855,60857],{"className":60856},[959],[961,60858,60859],{"xmlns":963},[965,60860,60861,60871],{},[968,60862,60863,60865,60867,60869],{},[974,60864,9839],{},[3191,60866,243],{"stretchy":3295},[974,60868,57929],{},[3191,60870,867],{"stretchy":3295},[982,60872,60466],{"encoding":984},[86,60874,60876],{"className":60875,"ariaHidden":990},[989],[86,60877,60879,60882,60885,60888,60891],{"className":60878},[994],[86,60880],{"className":60881,"style":3794},[998],[86,60883,9839],{"className":60884,"style":8109},[1003,1007],[86,60886,243],{"className":60887},[3320],[86,60889,57929],{"className":60890,"style":58003},[1003,1007],[86,60892,867],{"className":60893},[3356]," también aumenta)",[33,60896,60897,60898,60964,60965,392,61017,60964,61083],{},"Asintótica, ",[86,60899,60901,60925],{"className":60900},[955],[86,60902,60904],{"className":60903},[959],[961,60905,60906],{"xmlns":963},[965,60907,60908,60922],{},[968,60909,60910,60912,60914,60916,60918,60920],{},[974,60911,9839],{},[3191,60913,243],{"stretchy":3295},[974,60915,57929],{},[3191,60917,867],{"stretchy":3295},[3191,60919,4667],{},[978,60921,802],{},[982,60923,60924],{"encoding":984},"\\sigma(z) \\to 1",[86,60926,60928,60955],{"className":60927,"ariaHidden":990},[989],[86,60929,60931,60934,60937,60940,60943,60946,60949,60952],{"className":60930},[994],[86,60932],{"className":60933,"style":3794},[998],[86,60935,9839],{"className":60936,"style":8109},[1003,1007],[86,60938,243],{"className":60939},[3320],[86,60941,57929],{"className":60942,"style":58003},[1003,1007],[86,60944,867],{"className":60945},[3356],[86,60947],{"className":60948,"style":3222},[3221],[86,60950,4667],{"className":60951},[3226],[86,60953],{"className":60954,"style":3222},[3221],[86,60956,60958,60961],{"className":60957},[994],[86,60959],{"className":60960,"style":5994},[998],[86,60962,802],{"className":60963},[1003]," cuando ",[86,60966,60968,60987],{"className":60967},[955],[86,60969,60971],{"className":60970},[959],[961,60972,60973],{"xmlns":963},[965,60974,60975,60984],{},[968,60976,60977,60979,60981],{},[974,60978,57929],{},[3191,60980,4667],{},[974,60982,60983],{"mathvariant":4327},"∞",[982,60985,60986],{"encoding":984},"z \\to \\infty",[86,60988,60990,61008],{"className":60989,"ariaHidden":990},[989],[86,60991,60993,60996,60999,61002,61005],{"className":60992},[994],[86,60994],{"className":60995,"style":7401},[998],[86,60997,57929],{"className":60998,"style":58003},[1003,1007],[86,61000],{"className":61001,"style":3222},[3221],[86,61003,4667],{"className":61004},[3226],[86,61006],{"className":61007,"style":3222},[3221],[86,61009,61011,61014],{"className":61010},[994],[86,61012],{"className":61013,"style":7401},[998],[86,61015,60983],{"className":61016},[1003],[86,61018,61020,61044],{"className":61019},[955],[86,61021,61023],{"className":61022},[959],[961,61024,61025],{"xmlns":963},[965,61026,61027,61041],{},[968,61028,61029,61031,61033,61035,61037,61039],{},[974,61030,9839],{},[3191,61032,243],{"stretchy":3295},[974,61034,57929],{},[3191,61036,867],{"stretchy":3295},[3191,61038,4667],{},[978,61040,2553],{},[982,61042,61043],{"encoding":984},"\\sigma(z) \\to 0",[86,61045,61047,61074],{"className":61046,"ariaHidden":990},[989],[86,61048,61050,61053,61056,61059,61062,61065,61068,61071],{"className":61049},[994],[86,61051],{"className":61052,"style":3794},[998],[86,61054,9839],{"className":61055,"style":8109},[1003,1007],[86,61057,243],{"className":61058},[3320],[86,61060,57929],{"className":61061,"style":58003},[1003,1007],[86,61063,867],{"className":61064},[3356],[86,61066],{"className":61067,"style":3222},[3221],[86,61069,4667],{"className":61070},[3226],[86,61072],{"className":61073,"style":3222},[3221],[86,61075,61077,61080],{"className":61076},[994],[86,61078],{"className":61079,"style":5994},[998],[86,61081,2553],{"className":61082},[1003],[86,61084,61086,61106],{"className":61085},[955],[86,61087,61089],{"className":61088},[959],[961,61090,61091],{"xmlns":963},[965,61092,61093,61103],{},[968,61094,61095,61097,61099,61101],{},[974,61096,57929],{},[3191,61098,4667],{},[3191,61100,9864],{},[974,61102,60983],{"mathvariant":4327},[982,61104,61105],{"encoding":984},"z \\to -\\infty",[86,61107,61109,61127],{"className":61108,"ariaHidden":990},[989],[86,61110,61112,61115,61118,61121,61124],{"className":61111},[994],[86,61113],{"className":61114,"style":7401},[998],[86,61116,57929],{"className":61117,"style":58003},[1003,1007],[86,61119],{"className":61120,"style":3222},[3221],[86,61122,4667],{"className":61123},[3226],[86,61125],{"className":61126,"style":3222},[3221],[86,61128,61130,61133,61136],{"className":61129},[994],[86,61131],{"className":61132,"style":14141},[998],[86,61134,9864],{"className":61135},[1003],[86,61137,60983],{"className":61138},[1003],[12,61140,61141,61144,61145,15781,61148,162],{},[122,61142,61143],{},"¿Cómo medimos el error en clasificación?"," Aquí se utilizan métricas como la ",[122,61146,61147],{},"entropía cruzada",[122,61149,61150],{},"log loss",[12,61152,61153],{},"Pérdida para una muestra:",[86,61155,61157],{"className":61156},[3173],[86,61158,61160,61234],{"className":61159},[955],[86,61161,61163],{"className":61162},[959],[961,61164,61165],{"xmlns":963,"display":3182},[965,61166,61167,61231],{},[968,61168,61169,61172,61174,61176,61178,61180,61182,61185,61187,61189,61195,61197,61199,61201,61203,61205,61207,61209,61211,61213,61215,61217,61219,61221,61227,61229],{},[974,61170,61171],{},"L",[3191,61173,258],{},[3191,61175,9864],{},[3191,61177,572],{"stretchy":3295},[974,61179,5464],{},[3191,61181,4975],{},[974,61183,61184],{},"log",[3191,61186,7250],{},[3191,61188,243],{"stretchy":3295},[3758,61190,61191,61193],{"accent":990},[974,61192,5464],{},[3191,61194,7242],{},[3191,61196,867],{"stretchy":3295},[3191,61198,6565],{},[3191,61200,243],{"stretchy":3295},[978,61202,802],{},[3191,61204,9864],{},[974,61206,5464],{},[3191,61208,867],{"stretchy":3295},[3191,61210,4975],{},[974,61212,61184],{},[3191,61214,7250],{},[3191,61216,243],{"stretchy":3295},[978,61218,802],{},[3191,61220,9864],{},[3758,61222,61223,61225],{"accent":990},[974,61224,5464],{},[3191,61226,7242],{},[3191,61228,867],{"stretchy":3295},[3191,61230,585],{"stretchy":3295},[982,61232,61233],{"encoding":984},"L = -[y \\cdot \\log(\\hat{y}) + (1 - y) \\cdot \\log(1 - \\hat{y})]",[86,61235,61237,61255,61279,61348,61369,61390,61416],{"className":61236,"ariaHidden":990},[989],[86,61238,61240,61243,61246,61249,61252],{"className":61239},[994],[86,61241],{"className":61242,"style":3575},[998],[86,61244,61171],{"className":61245},[1003,1007],[86,61247],{"className":61248,"style":3222},[3221],[86,61250,258],{"className":61251},[3226],[86,61253],{"className":61254,"style":3222},[3221],[86,61256,61258,61261,61264,61267,61270,61273,61276],{"className":61257},[994],[86,61259],{"className":61260,"style":3794},[998],[86,61262,9864],{"className":61263},[1003],[86,61265,572],{"className":61266},[3320],[86,61268,5464],{"className":61269,"style":8109},[1003,1007],[86,61271],{"className":61272,"style":5012},[3221],[86,61274,4975],{"className":61275},[5016],[86,61277],{"className":61278,"style":5012},[3221],[86,61280,61282,61285,61291,61294,61336,61339,61342,61345],{"className":61281},[994],[86,61283],{"className":61284,"style":3794},[998],[86,61286,61288,61289],{"className":61287},[7373],"lo",[86,61290,7378],{"style":7377},[86,61292,243],{"className":61293},[3320],[86,61295,61297],{"className":61296},[1003,3863],[86,61298,61300,61328],{"className":61299},[1016,3836],[86,61301,61303,61325],{"className":61302},[1020],[86,61304,61306,61314],{"className":61305,"style":3873},[1024],[86,61307,61308,61311],{"style":3876},[86,61309],{"className":61310,"style":3850},[1031],[86,61312,5464],{"className":61313,"style":8109},[1003,1007],[86,61315,61316,61319],{"style":3876},[86,61317],{"className":61318,"style":3850},[1031],[86,61320,61322],{"className":61321,"style":49979},[3891],[86,61323,7242],{"className":61324},[1003],[86,61326,3963],{"className":61327},[3962],[86,61329,61331],{"className":61330},[1020],[86,61332,61334],{"className":61333,"style":30703},[1024],[86,61335],{},[86,61337,867],{"className":61338},[3356],[86,61340],{"className":61341,"style":5012},[3221],[86,61343,6565],{"className":61344},[5016],[86,61346],{"className":61347,"style":5012},[3221],[86,61349,61351,61354,61357,61360,61363,61366],{"className":61350},[994],[86,61352],{"className":61353,"style":3794},[998],[86,61355,243],{"className":61356},[3320],[86,61358,802],{"className":61359},[1003],[86,61361],{"className":61362,"style":5012},[3221],[86,61364,9864],{"className":61365},[5016],[86,61367],{"className":61368,"style":5012},[3221],[86,61370,61372,61375,61378,61381,61384,61387],{"className":61371},[994],[86,61373],{"className":61374,"style":3794},[998],[86,61376,5464],{"className":61377,"style":8109},[1003,1007],[86,61379,867],{"className":61380},[3356],[86,61382],{"className":61383,"style":5012},[3221],[86,61385,4975],{"className":61386},[5016],[86,61388],{"className":61389,"style":5012},[3221],[86,61391,61393,61396,61401,61404,61407,61410,61413],{"className":61392},[994],[86,61394],{"className":61395,"style":3794},[998],[86,61397,61288,61399],{"className":61398},[7373],[86,61400,7378],{"style":7377},[86,61402,243],{"className":61403},[3320],[86,61405,802],{"className":61406},[1003],[86,61408],{"className":61409,"style":5012},[3221],[86,61411,9864],{"className":61412},[5016],[86,61414],{"className":61415,"style":5012},[3221],[86,61417,61419,61422,61464],{"className":61418},[994],[86,61420],{"className":61421,"style":3794},[998],[86,61423,61425],{"className":61424},[1003,3863],[86,61426,61428,61456],{"className":61427},[1016,3836],[86,61429,61431,61453],{"className":61430},[1020],[86,61432,61434,61442],{"className":61433,"style":3873},[1024],[86,61435,61436,61439],{"style":3876},[86,61437],{"className":61438,"style":3850},[1031],[86,61440,5464],{"className":61441,"style":8109},[1003,1007],[86,61443,61444,61447],{"style":3876},[86,61445],{"className":61446,"style":3850},[1031],[86,61448,61450],{"className":61449,"style":49979},[3891],[86,61451,7242],{"className":61452},[1003],[86,61454,3963],{"className":61455},[3962],[86,61457,61459],{"className":61458},[1020],[86,61460,61462],{"className":61461,"style":30703},[1024],[86,61463],{},[86,61465,61467],{"className":61466},[3356],")]",[12,61469,61470],{},"Pérdida promedio (o función de costo) para todo el conjunto de datos:",[86,61472,61474],{"className":61473},[3173],[86,61475,61477,61586],{"className":61476},[955],[86,61478,61480],{"className":61479},[959],[961,61481,61482],{"xmlns":963,"display":3182},[965,61483,61484,61583],{},[968,61485,61486,61489,61491,61493,61499,61513,61515,61521,61523,61525,61527,61529,61539,61541,61543,61545,61547,61549,61555,61557,61559,61561,61563,61565,61567,61569,61579,61581],{},[974,61487,61488],{},"J",[3191,61490,258],{},[3191,61492,9864],{},[3749,61494,61495,61497],{},[978,61496,802],{},[974,61498,6896],{},[7276,61500,61501,61503,61511],{},[3191,61502,49404],{},[968,61504,61505,61507,61509],{},[974,61506,7285],{},[3191,61508,258],{},[978,61510,802],{},[974,61512,6896],{},[3191,61514,572],{"stretchy":3295},[6849,61516,61517,61519],{},[974,61518,5464],{},[974,61520,7285],{},[3191,61522,4975],{},[974,61524,61184],{},[3191,61526,7250],{},[3191,61528,243],{"stretchy":3295},[3758,61530,61531,61537],{"accent":990},[6849,61532,61533,61535],{},[974,61534,5464],{},[974,61536,7285],{},[3191,61538,7242],{},[3191,61540,867],{"stretchy":3295},[3191,61542,6565],{},[3191,61544,243],{"stretchy":3295},[978,61546,802],{},[3191,61548,9864],{},[6849,61550,61551,61553],{},[974,61552,5464],{},[974,61554,7285],{},[3191,61556,867],{"stretchy":3295},[3191,61558,4975],{},[974,61560,61184],{},[3191,61562,7250],{},[3191,61564,243],{"stretchy":3295},[978,61566,802],{},[3191,61568,9864],{},[3758,61570,61571,61577],{"accent":990},[6849,61572,61573,61575],{},[974,61574,5464],{},[974,61576,7285],{},[3191,61578,7242],{},[3191,61580,867],{"stretchy":3295},[3191,61582,585],{"stretchy":3295},[982,61584,61585],{"encoding":984},"J = -\\frac{1}{n} \\sum_{i=1}^{n} [y_i \\cdot \\log(\\hat{y_i}) + (1 - y_i) \\cdot \\log(1 - \\hat{y_i})]",[86,61587,61589,61608,61801,61906,61927,61985,62011],{"className":61588,"ariaHidden":990},[989],[86,61590,61592,61595,61599,61602,61605],{"className":61591},[994],[86,61593],{"className":61594,"style":3575},[998],[86,61596,61488],{"className":61597,"style":61598},[1003,1007],"margin-right:0.0962em;",[86,61600],{"className":61601,"style":3222},[3221],[86,61603,258],{"className":61604},[3226],[86,61606],{"className":61607,"style":3222},[3221],[86,61609,61611,61614,61617,61679,61682,61749,61752,61792,61795,61798],{"className":61610},[994],[86,61612],{"className":61613,"style":7369},[998],[86,61615,9864],{"className":61616},[1003],[86,61618,61620,61623,61676],{"className":61619},[1003],[86,61621],{"className":61622},[3320,3829],[86,61624,61626],{"className":61625},[3749],[86,61627,61629,61668],{"className":61628},[1016,3836],[86,61630,61632,61665],{"className":61631},[1020],[86,61633,61635,61646,61654],{"className":61634,"style":9568},[1024],[86,61636,61637,61640],{"style":3846},[86,61638],{"className":61639,"style":3850},[1031],[86,61641,61643],{"className":61642},[1003],[86,61644,6896],{"className":61645},[1003,1007],[86,61647,61648,61651],{"style":3901},[86,61649],{"className":61650,"style":3850},[1031],[86,61652],{"className":61653,"style":3909},[3908],[86,61655,61656,61659],{"style":3912},[86,61657],{"className":61658,"style":3850},[1031],[86,61660,61662],{"className":61661},[1003],[86,61663,802],{"className":61664},[1003],[86,61666,3963],{"className":61667},[3962],[86,61669,61671],{"className":61670},[1020],[86,61672,61674],{"className":61673,"style":9620},[1024],[86,61675],{},[86,61677],{"className":61678},[3356,3829],[86,61680],{"className":61681,"style":4162},[3221],[86,61683,61685],{"className":61684},[7373,7391],[86,61686,61688,61741],{"className":61687},[1016,3836],[86,61689,61691,61738],{"className":61690},[1020],[86,61692,61694,61714,61724],{"className":61693,"style":7469},[1024],[86,61695,61696,61699],{"style":7472},[86,61697],{"className":61698,"style":7476},[1031],[86,61700,61702],{"className":61701},[1036,1037,1038,1039],[86,61703,61705,61708,61711],{"className":61704},[1003,1039],[86,61706,7285],{"className":61707},[1003,1007,1039],[86,61709,258],{"className":61710},[3226,1039],[86,61712,802],{"className":61713},[1003,1039],[86,61715,61716,61719],{"style":7494},[86,61717],{"className":61718,"style":7476},[1031],[86,61720,61721],{},[86,61722,49404],{"className":61723},[7373,7503,7504],[86,61725,61726,61729],{"style":7507},[86,61727],{"className":61728,"style":7476},[1031],[86,61730,61732],{"className":61731},[1036,1037,1038,1039],[86,61733,61735],{"className":61734},[1003,1039],[86,61736,6896],{"className":61737},[1003,1007,1039],[86,61739,3963],{"className":61740},[3962],[86,61742,61744],{"className":61743},[1020],[86,61745,61747],{"className":61746,"style":7529},[1024],[86,61748],{},[86,61750,572],{"className":61751},[3320],[86,61753,61755,61758],{"className":61754},[1003],[86,61756,5464],{"className":61757,"style":8109},[1003,1007],[86,61759,61761],{"className":61760},[1012],[86,61762,61764,61784],{"className":61763},[1016,3836],[86,61765,61767,61781],{"className":61766},[1020],[86,61768,61770],{"className":61769,"style":7559},[1024],[86,61771,61772,61775],{"style":20440},[86,61773],{"className":61774,"style":1032},[1031],[86,61776,61778],{"className":61777},[1036,1037,1038,1039],[86,61779,7285],{"className":61780},[1003,1007,1039],[86,61782,3963],{"className":61783},[3962],[86,61785,61787],{"className":61786},[1020],[86,61788,61790],{"className":61789,"style":7006},[1024],[86,61791],{},[86,61793],{"className":61794,"style":5012},[3221],[86,61796,4975],{"className":61797},[5016],[86,61799],{"className":61800,"style":5012},[3221],[86,61802,61804,61807,61812,61815,61894,61897,61900,61903],{"className":61803},[994],[86,61805],{"className":61806,"style":3794},[998],[86,61808,61288,61810],{"className":61809},[7373],[86,61811,7378],{"style":7377},[86,61813,243],{"className":61814},[3320],[86,61816,61818],{"className":61817},[1003,3863],[86,61819,61821,61886],{"className":61820},[1016,3836],[86,61822,61824,61883],{"className":61823},[1020],[86,61825,61827,61872],{"className":61826,"style":3873},[1024],[86,61828,61829,61832],{"style":3876},[86,61830],{"className":61831,"style":3850},[1031],[86,61833,61835,61838],{"className":61834},[1003],[86,61836,5464],{"className":61837,"style":8109},[1003,1007],[86,61839,61841],{"className":61840},[1012],[86,61842,61844,61864],{"className":61843},[1016,3836],[86,61845,61847,61861],{"className":61846},[1020],[86,61848,61850],{"className":61849,"style":7559},[1024],[86,61851,61852,61855],{"style":20440},[86,61853],{"className":61854,"style":1032},[1031],[86,61856,61858],{"className":61857},[1036,1037,1038,1039],[86,61859,7285],{"className":61860},[1003,1007,1039],[86,61862,3963],{"className":61863},[3962],[86,61865,61867],{"className":61866},[1020],[86,61868,61870],{"className":61869,"style":7006},[1024],[86,61871],{},[86,61873,61874,61877],{"style":3876},[86,61875],{"className":61876,"style":3850},[1031],[86,61878,61880],{"className":61879,"style":3892},[3891],[86,61881,7242],{"className":61882},[1003],[86,61884,3963],{"className":61885},[3962],[86,61887,61889],{"className":61888},[1020],[86,61890,61892],{"className":61891,"style":30703},[1024],[86,61893],{},[86,61895,867],{"className":61896},[3356],[86,61898],{"className":61899,"style":5012},[3221],[86,61901,6565],{"className":61902},[5016],[86,61904],{"className":61905,"style":5012},[3221],[86,61907,61909,61912,61915,61918,61921,61924],{"className":61908},[994],[86,61910],{"className":61911,"style":3794},[998],[86,61913,243],{"className":61914},[3320],[86,61916,802],{"className":61917},[1003],[86,61919],{"className":61920,"style":5012},[3221],[86,61922,9864],{"className":61923},[5016],[86,61925],{"className":61926,"style":5012},[3221],[86,61928,61930,61933,61973,61976,61979,61982],{"className":61929},[994],[86,61931],{"className":61932,"style":3794},[998],[86,61934,61936,61939],{"className":61935},[1003],[86,61937,5464],{"className":61938,"style":8109},[1003,1007],[86,61940,61942],{"className":61941},[1012],[86,61943,61945,61965],{"className":61944},[1016,3836],[86,61946,61948,61962],{"className":61947},[1020],[86,61949,61951],{"className":61950,"style":7559},[1024],[86,61952,61953,61956],{"style":20440},[86,61954],{"className":61955,"style":1032},[1031],[86,61957,61959],{"className":61958},[1036,1037,1038,1039],[86,61960,7285],{"className":61961},[1003,1007,1039],[86,61963,3963],{"className":61964},[3962],[86,61966,61968],{"className":61967},[1020],[86,61969,61971],{"className":61970,"style":7006},[1024],[86,61972],{},[86,61974,867],{"className":61975},[3356],[86,61977],{"className":61978,"style":5012},[3221],[86,61980,4975],{"className":61981},[5016],[86,61983],{"className":61984,"style":5012},[3221],[86,61986,61988,61991,61996,61999,62002,62005,62008],{"className":61987},[994],[86,61989],{"className":61990,"style":3794},[998],[86,61992,61288,61994],{"className":61993},[7373],[86,61995,7378],{"style":7377},[86,61997,243],{"className":61998},[3320],[86,62000,802],{"className":62001},[1003],[86,62003],{"className":62004,"style":5012},[3221],[86,62006,9864],{"className":62007},[5016],[86,62009],{"className":62010,"style":5012},[3221],[86,62012,62014,62017,62096],{"className":62013},[994],[86,62015],{"className":62016,"style":3794},[998],[86,62018,62020],{"className":62019},[1003,3863],[86,62021,62023,62088],{"className":62022},[1016,3836],[86,62024,62026,62085],{"className":62025},[1020],[86,62027,62029,62074],{"className":62028,"style":3873},[1024],[86,62030,62031,62034],{"style":3876},[86,62032],{"className":62033,"style":3850},[1031],[86,62035,62037,62040],{"className":62036},[1003],[86,62038,5464],{"className":62039,"style":8109},[1003,1007],[86,62041,62043],{"className":62042},[1012],[86,62044,62046,62066],{"className":62045},[1016,3836],[86,62047,62049,62063],{"className":62048},[1020],[86,62050,62052],{"className":62051,"style":7559},[1024],[86,62053,62054,62057],{"style":20440},[86,62055],{"className":62056,"style":1032},[1031],[86,62058,62060],{"className":62059},[1036,1037,1038,1039],[86,62061,7285],{"className":62062},[1003,1007,1039],[86,62064,3963],{"className":62065},[3962],[86,62067,62069],{"className":62068},[1020],[86,62070,62072],{"className":62071,"style":7006},[1024],[86,62073],{},[86,62075,62076,62079],{"style":3876},[86,62077],{"className":62078,"style":3850},[1031],[86,62080,62082],{"className":62081,"style":3892},[3891],[86,62083,7242],{"className":62084},[1003],[86,62086,3963],{"className":62087},[3962],[86,62089,62091],{"className":62090},[1020],[86,62092,62094],{"className":62093,"style":30703},[1024],[86,62095],{},[86,62097,61467],{"className":62098},[3356],[12,62100,3273],{},[30,62102,62103,62133,62233],{},[33,62104,62105,49810],{},[86,62106,62108,62121],{"className":62107},[955],[86,62109,62111],{"className":62110},[959],[961,62112,62113],{"xmlns":963},[965,62114,62115,62119],{},[968,62116,62117],{},[974,62118,6896],{},[982,62120,6896],{"encoding":984},[86,62122,62124],{"className":62123,"ariaHidden":990},[989],[86,62125,62127,62130],{"className":62126},[994],[86,62128],{"className":62129,"style":7401},[998],[86,62131,6896],{"className":62132},[1003,1007],[33,62134,62135,62204,62205,61],{},[86,62136,62138,62155],{"className":62137},[955],[86,62139,62141],{"className":62140},[959],[961,62142,62143],{"xmlns":963},[965,62144,62145,62153],{},[968,62146,62147],{},[6849,62148,62149,62151],{},[974,62150,5464],{},[974,62152,7285],{},[982,62154,46828],{"encoding":984},[86,62156,62158],{"className":62157,"ariaHidden":990},[989],[86,62159,62161,62164],{"className":62160},[994],[86,62162],{"className":62163,"style":16339},[998],[86,62165,62167,62170],{"className":62166},[1003],[86,62168,5464],{"className":62169,"style":8109},[1003,1007],[86,62171,62173],{"className":62172},[1012],[86,62174,62176,62196],{"className":62175},[1016,3836],[86,62177,62179,62193],{"className":62178},[1020],[86,62180,62182],{"className":62181,"style":7559},[1024],[86,62183,62184,62187],{"style":20440},[86,62185],{"className":62186,"style":1032},[1031],[86,62188,62190],{"className":62189},[1036,1037,1038,1039],[86,62191,7285],{"className":62192},[1003,1007,1039],[86,62194,3963],{"className":62195},[3962],[86,62197,62199],{"className":62198},[1020],[86,62200,62202],{"className":62201,"style":7006},[1024],[86,62203],{}," es la etiqueta real (0 o 1) para el ejemplo ",[86,62206,62208,62221],{"className":62207},[955],[86,62209,62211],{"className":62210},[959],[961,62212,62213],{"xmlns":963},[965,62214,62215,62219],{},[968,62216,62217],{},[974,62218,7285],{},[982,62220,7285],{"encoding":984},[86,62222,62224],{"className":62223,"ariaHidden":990},[989],[86,62225,62227,62230],{"className":62226},[994],[86,62228],{"className":62229,"style":49908},[998],[86,62231,7285],{"className":62232},[1003,1007],[33,62234,62235,62348,62349,62377],{},[86,62236,62238,62260],{"className":62237},[955],[86,62239,62241],{"className":62240},[959],[961,62242,62243],{"xmlns":963},[965,62244,62245,62257],{},[968,62246,62247],{},[3758,62248,62249,62255],{"accent":990},[6849,62250,62251,62253],{},[974,62252,5464],{},[974,62254,7285],{},[3191,62256,7242],{},[982,62258,62259],{"encoding":984},"\\hat{y_i}",[86,62261,62263],{"className":62262,"ariaHidden":990},[989],[86,62264,62266,62269],{"className":62265},[994],[86,62267],{"className":62268,"style":4888},[998],[86,62270,62272],{"className":62271},[1003,3863],[86,62273,62275,62340],{"className":62274},[1016,3836],[86,62276,62278,62337],{"className":62277},[1020],[86,62279,62281,62326],{"className":62280,"style":3873},[1024],[86,62282,62283,62286],{"style":3876},[86,62284],{"className":62285,"style":3850},[1031],[86,62287,62289,62292],{"className":62288},[1003],[86,62290,5464],{"className":62291,"style":8109},[1003,1007],[86,62293,62295],{"className":62294},[1012],[86,62296,62298,62318],{"className":62297},[1016,3836],[86,62299,62301,62315],{"className":62300},[1020],[86,62302,62304],{"className":62303,"style":7559},[1024],[86,62305,62306,62309],{"style":20440},[86,62307],{"className":62308,"style":1032},[1031],[86,62310,62312],{"className":62311},[1036,1037,1038,1039],[86,62313,7285],{"className":62314},[1003,1007,1039],[86,62316,3963],{"className":62317},[3962],[86,62319,62321],{"className":62320},[1020],[86,62322,62324],{"className":62323,"style":7006},[1024],[86,62325],{},[86,62327,62328,62331],{"style":3876},[86,62329],{"className":62330,"style":3850},[1031],[86,62332,62334],{"className":62333,"style":3892},[3891],[86,62335,7242],{"className":62336},[1003],[86,62338,3963],{"className":62339},[3962],[86,62341,62343],{"className":62342},[1020],[86,62344,62346],{"className":62345,"style":30703},[1024],[86,62347],{}," es la probabilidad predicha por el modelo para el ejemplo ",[86,62350,62352,62365],{"className":62351},[955],[86,62353,62355],{"className":62354},[959],[961,62356,62357],{"xmlns":963},[965,62358,62359,62363],{},[968,62360,62361],{},[974,62362,7285],{},[982,62364,7285],{"encoding":984},[86,62366,62368],{"className":62367,"ariaHidden":990},[989],[86,62369,62371,62374],{"className":62370},[994],[86,62372],{"className":62373,"style":49908},[998],[86,62375,7285],{"className":62376},[1003,1007]," (valor entre 0 y 1).",[12,62379,62380],{},"¿Por qué se usa la entropía cruzada?",[117,62382,62383,62386,62389],{},[33,62384,62385],{},"Penaliza más las predicciones incorrectas con alta confianza.",[33,62387,62388],{},"Es una función de pérdida convexa, lo que facilita la optimización mediante métodos como el descenso de gradiente.",[33,62390,62391],{},"Interpretación probabilística, ya que se basa en la probabilidad predicha por el modelo.",[12,62393,62394],{},"El comportamiento de la función de pérdida se muestra en la siguiente gráfica:",[12,62396,62397,62401],{},[1945,62398],{"alt":62399,"src":62400},"Gráfico de la función de pérdida de entropía cruzada","\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations\u002Fshared\u002Fcross-entropy.webp",[901,62402,62403],{},"Gráfico de la Función de Pérdida de Entropía Cruzada",[12,62405,62406],{},"La función penaliza más las predicciones incorrectas con alta confianza, lo que se refleja en la forma de la curva.",[117,62408,62409],{},[33,62410,62411],{},"Cuando la etiqueta real es 1 (y=1) (línea azul):",[30,62413,62414,62538,62613],{},[33,62415,62416,62417],{},"La fórmula se simplifica a ",[86,62418,62420,62452],{"className":62419},[955],[86,62421,62423],{"className":62422},[959],[961,62424,62425],{"xmlns":963},[965,62426,62427,62449],{},[968,62428,62429,62431,62433,62435,62437,62439,62441,62447],{},[974,62430,61171],{},[3191,62432,258],{},[3191,62434,9864],{},[974,62436,61184],{},[3191,62438,7250],{},[3191,62440,243],{"stretchy":3295},[3758,62442,62443,62445],{"accent":990},[974,62444,5464],{},[3191,62446,7242],{},[3191,62448,867],{"stretchy":3295},[982,62450,62451],{"encoding":984},"L = -\\log(\\hat{y})",[86,62453,62455,62473],{"className":62454,"ariaHidden":990},[989],[86,62456,62458,62461,62464,62467,62470],{"className":62457},[994],[86,62459],{"className":62460,"style":3575},[998],[86,62462,61171],{"className":62463},[1003,1007],[86,62465],{"className":62466,"style":3222},[3221],[86,62468,258],{"className":62469},[3226],[86,62471],{"className":62472,"style":3222},[3221],[86,62474,62476,62479,62482,62485,62490,62493,62535],{"className":62475},[994],[86,62477],{"className":62478,"style":3794},[998],[86,62480,9864],{"className":62481},[1003],[86,62483],{"className":62484,"style":4162},[3221],[86,62486,61288,62488],{"className":62487},[7373],[86,62489,7378],{"style":7377},[86,62491,243],{"className":62492},[3320],[86,62494,62496],{"className":62495},[1003,3863],[86,62497,62499,62527],{"className":62498},[1016,3836],[86,62500,62502,62524],{"className":62501},[1020],[86,62503,62505,62513],{"className":62504,"style":3873},[1024],[86,62506,62507,62510],{"style":3876},[86,62508],{"className":62509,"style":3850},[1031],[86,62511,5464],{"className":62512,"style":8109},[1003,1007],[86,62514,62515,62518],{"style":3876},[86,62516],{"className":62517,"style":3850},[1031],[86,62519,62521],{"className":62520,"style":49979},[3891],[86,62522,7242],{"className":62523},[1003],[86,62525,3963],{"className":62526},[3962],[86,62528,62530],{"className":62529},[1020],[86,62531,62533],{"className":62532,"style":30703},[1024],[86,62534],{},[86,62536,867],{"className":62537},[3356],[33,62539,60700,62540,62612],{},[86,62541,62543,62561],{"className":62542},[955],[86,62544,62546],{"className":62545},[959],[961,62547,62548],{"xmlns":963},[965,62549,62550,62558],{},[968,62551,62552],{},[3758,62553,62554,62556],{"accent":990},[974,62555,5464],{},[3191,62557,7242],{},[982,62559,62560],{"encoding":984},"\\hat{y}",[86,62562,62564],{"className":62563,"ariaHidden":990},[989],[86,62565,62567,62570],{"className":62566},[994],[86,62568],{"className":62569,"style":4888},[998],[86,62571,62573],{"className":62572},[1003,3863],[86,62574,62576,62604],{"className":62575},[1016,3836],[86,62577,62579,62601],{"className":62578},[1020],[86,62580,62582,62590],{"className":62581,"style":3873},[1024],[86,62583,62584,62587],{"style":3876},[86,62585],{"className":62586,"style":3850},[1031],[86,62588,5464],{"className":62589,"style":8109},[1003,1007],[86,62591,62592,62595],{"style":3876},[86,62593],{"className":62594,"style":3850},[1031],[86,62596,62598],{"className":62597,"style":49979},[3891],[86,62599,7242],{"className":62600},[1003],[86,62602,3963],{"className":62603},[3962],[86,62605,62607],{"className":62606},[1020],[86,62608,62610],{"className":62609,"style":30703},[1024],[86,62611],{}," se acerca a 1, la pérdida se acerca a 0 (buena predicción).",[33,62614,60700,62615,62686],{},[86,62616,62618,62635],{"className":62617},[955],[86,62619,62621],{"className":62620},[959],[961,62622,62623],{"xmlns":963},[965,62624,62625,62633],{},[968,62626,62627],{},[3758,62628,62629,62631],{"accent":990},[974,62630,5464],{},[3191,62632,7242],{},[982,62634,62560],{"encoding":984},[86,62636,62638],{"className":62637,"ariaHidden":990},[989],[86,62639,62641,62644],{"className":62640},[994],[86,62642],{"className":62643,"style":4888},[998],[86,62645,62647],{"className":62646},[1003,3863],[86,62648,62650,62678],{"className":62649},[1016,3836],[86,62651,62653,62675],{"className":62652},[1020],[86,62654,62656,62664],{"className":62655,"style":3873},[1024],[86,62657,62658,62661],{"style":3876},[86,62659],{"className":62660,"style":3850},[1031],[86,62662,5464],{"className":62663,"style":8109},[1003,1007],[86,62665,62666,62669],{"style":3876},[86,62667],{"className":62668,"style":3850},[1031],[86,62670,62672],{"className":62671,"style":49979},[3891],[86,62673,7242],{"className":62674},[1003],[86,62676,3963],{"className":62677},[3962],[86,62679,62681],{"className":62680},[1020],[86,62682,62684],{"className":62683,"style":30703},[1024],[86,62685],{}," se acerca a 0, la pérdida se dispara a infinito (mala predicción).",[117,62688,62689],{"start":192},[33,62690,62691],{},"Cuando la etiqueta real es 0 (y=0) (línea roja):",[30,62693,62694,62839,62913],{},[33,62695,62416,62696],{},[86,62697,62699,62735],{"className":62698},[955],[86,62700,62702],{"className":62701},[959],[961,62703,62704],{"xmlns":963},[965,62705,62706,62732],{},[968,62707,62708,62710,62712,62714,62716,62718,62720,62722,62724,62730],{},[974,62709,61171],{},[3191,62711,258],{},[3191,62713,9864],{},[974,62715,61184],{},[3191,62717,7250],{},[3191,62719,243],{"stretchy":3295},[978,62721,802],{},[3191,62723,9864],{},[3758,62725,62726,62728],{"accent":990},[974,62727,5464],{},[3191,62729,7242],{},[3191,62731,867],{"stretchy":3295},[982,62733,62734],{"encoding":984},"L = -\\log(1 - \\hat{y})",[86,62736,62738,62756,62788],{"className":62737,"ariaHidden":990},[989],[86,62739,62741,62744,62747,62750,62753],{"className":62740},[994],[86,62742],{"className":62743,"style":3575},[998],[86,62745,61171],{"className":62746},[1003,1007],[86,62748],{"className":62749,"style":3222},[3221],[86,62751,258],{"className":62752},[3226],[86,62754],{"className":62755,"style":3222},[3221],[86,62757,62759,62762,62765,62768,62773,62776,62779,62782,62785],{"className":62758},[994],[86,62760],{"className":62761,"style":3794},[998],[86,62763,9864],{"className":62764},[1003],[86,62766],{"className":62767,"style":4162},[3221],[86,62769,61288,62771],{"className":62770},[7373],[86,62772,7378],{"style":7377},[86,62774,243],{"className":62775},[3320],[86,62777,802],{"className":62778},[1003],[86,62780],{"className":62781,"style":5012},[3221],[86,62783,9864],{"className":62784},[5016],[86,62786],{"className":62787,"style":5012},[3221],[86,62789,62791,62794,62836],{"className":62790},[994],[86,62792],{"className":62793,"style":3794},[998],[86,62795,62797],{"className":62796},[1003,3863],[86,62798,62800,62828],{"className":62799},[1016,3836],[86,62801,62803,62825],{"className":62802},[1020],[86,62804,62806,62814],{"className":62805,"style":3873},[1024],[86,62807,62808,62811],{"style":3876},[86,62809],{"className":62810,"style":3850},[1031],[86,62812,5464],{"className":62813,"style":8109},[1003,1007],[86,62815,62816,62819],{"style":3876},[86,62817],{"className":62818,"style":3850},[1031],[86,62820,62822],{"className":62821,"style":49979},[3891],[86,62823,7242],{"className":62824},[1003],[86,62826,3963],{"className":62827},[3962],[86,62829,62831],{"className":62830},[1020],[86,62832,62834],{"className":62833,"style":30703},[1024],[86,62835],{},[86,62837,867],{"className":62838},[3356],[33,62840,60700,62841,62912],{},[86,62842,62844,62861],{"className":62843},[955],[86,62845,62847],{"className":62846},[959],[961,62848,62849],{"xmlns":963},[965,62850,62851,62859],{},[968,62852,62853],{},[3758,62854,62855,62857],{"accent":990},[974,62856,5464],{},[3191,62858,7242],{},[982,62860,62560],{"encoding":984},[86,62862,62864],{"className":62863,"ariaHidden":990},[989],[86,62865,62867,62870],{"className":62866},[994],[86,62868],{"className":62869,"style":4888},[998],[86,62871,62873],{"className":62872},[1003,3863],[86,62874,62876,62904],{"className":62875},[1016,3836],[86,62877,62879,62901],{"className":62878},[1020],[86,62880,62882,62890],{"className":62881,"style":3873},[1024],[86,62883,62884,62887],{"style":3876},[86,62885],{"className":62886,"style":3850},[1031],[86,62888,5464],{"className":62889,"style":8109},[1003,1007],[86,62891,62892,62895],{"style":3876},[86,62893],{"className":62894,"style":3850},[1031],[86,62896,62898],{"className":62897,"style":49979},[3891],[86,62899,7242],{"className":62900},[1003],[86,62902,3963],{"className":62903},[3962],[86,62905,62907],{"className":62906},[1020],[86,62908,62910],{"className":62909,"style":30703},[1024],[86,62911],{}," se acerca a 0, la pérdida se acerca a 0 (buena predicción).",[33,62914,60700,62915,62986],{},[86,62916,62918,62935],{"className":62917},[955],[86,62919,62921],{"className":62920},[959],[961,62922,62923],{"xmlns":963},[965,62924,62925,62933],{},[968,62926,62927],{},[3758,62928,62929,62931],{"accent":990},[974,62930,5464],{},[3191,62932,7242],{},[982,62934,62560],{"encoding":984},[86,62936,62938],{"className":62937,"ariaHidden":990},[989],[86,62939,62941,62944],{"className":62940},[994],[86,62942],{"className":62943,"style":4888},[998],[86,62945,62947],{"className":62946},[1003,3863],[86,62948,62950,62978],{"className":62949},[1016,3836],[86,62951,62953,62975],{"className":62952},[1020],[86,62954,62956,62964],{"className":62955,"style":3873},[1024],[86,62957,62958,62961],{"style":3876},[86,62959],{"className":62960,"style":3850},[1031],[86,62962,5464],{"className":62963,"style":8109},[1003,1007],[86,62965,62966,62969],{"style":3876},[86,62967],{"className":62968,"style":3850},[1031],[86,62970,62972],{"className":62971,"style":49979},[3891],[86,62973,7242],{"className":62974},[1003],[86,62976,3963],{"className":62977},[3962],[86,62979,62981],{"className":62980},[1020],[86,62982,62984],{"className":62983,"style":30703},[1024],[86,62985],{}," se acerca a 1, la pérdida se dispara a infinito (mala predicción).",[12,62988,62989],{},"La naturaleza logarítmica de la función es la que garantiza que el modelo sea penalizado severamente cuando se muestra \"seguro pero equivocado\", lo que obliga al modelo a ajustar sus pesos de forma más agresiva para mejorar las predicciones.",[46,62991,62993],{"id":62992},"validación-y-optimización","Validación y Optimización",[323,62995,62997],{"id":62996},"métricas-de-evaluación","Métricas de Evaluación",[12,62999,63000,63001,63003],{},"Para ",[122,63002,47275],{},", las métricas comunes incluyen:",[30,63005,63006,63012,63018,63024],{},[33,63007,63008,63011],{},[122,63009,63010],{},"Error Cuadrático Medio (MSE)",": Promedio de los cuadrados de las diferencias entre los valores reales y las predicciones.",[33,63013,63014,63017],{},[122,63015,63016],{},"Error Raíz Cuadrático Medio (RMSE)",": Raíz cuadrada del MSE, que tiene la misma unidad que la variable dependiente.",[33,63019,63020,63023],{},[122,63021,63022],{},"Coeficiente de Determinación (R²)",": Proporción de la varianza en la variable dependiente que es explicada por el modelo.",[33,63025,63026,63029],{},[122,63027,63028],{},"Error Absoluto Medio (MAE)",": Promedio de las diferencias absolutas entre los valores reales y las predicciones.",[12,63031,63000,63032,63003],{},[122,63033,57611],{},[30,63035,63036,63042,63048,63053],{},[33,63037,63038,63041],{},[122,63039,63040],{},"Exactitud (Accuracy)",": Proporción de predicciones correctas sobre el total de ejemplos.",[33,63043,63044,63047],{},[122,63045,63046],{},"Precisión (Precision)",": Proporción de verdaderos positivos sobre el total de predicciones positivas.",[33,63049,63050,63052],{},[122,63051,45370],{},": Proporción de verdaderos positivos sobre el total de ejemplos reales positivos.",[33,63054,63055,63058],{},[122,63056,63057],{},"F1 Score",": Media armónica de la precisión y el recall, que proporciona una medida equilibrada entre ambos.",[16,63060,63061],{},[12,63062,63063],{},"La elección de la métrica adecuada depende del contexto del problema y de las consecuencias de los errores de clasificación. Por ejemplo, en un problema de detección de fraude, es más importante minimizar los falsos negativos (no detectar un fraude) que los falsos positivos (marcar una transacción legítima como fraude), por lo que el recall podría ser una métrica más relevante que la precisión.",[323,63065,63067],{"id":63066},"optimización","Optimización",[12,63069,63070,63071,63074],{},"La optimización de modelos de machine learning se refiere al proceso de ajustar los parámetros del modelo para ",[122,63072,63073],{},"minimizar la función de pérdida",". Esto se puede lograr mediante técnicas como el descenso de gradiente, que iterativamente ajusta los pesos del modelo en la dirección que reduce la pérdida.",[12,63076,63077],{},"El descenso de gradiente se puede expresar matemáticamente como:",[86,63079,63081],{"className":63080},[3173],[86,63082,63084,63118],{"className":63083},[955],[86,63085,63087],{"className":63086},[959],[961,63088,63089],{"xmlns":963,"display":3182},[965,63090,63091,63115],{},[968,63092,63093,63096,63098,63100,63102,63104,63107,63109,63111,63113],{},[974,63094,63095],{},"θ",[3191,63097,258],{},[974,63099,63095],{},[3191,63101,9864],{},[974,63103,10574],{},[974,63105,63106],{"mathvariant":4327},"∇",[974,63108,61488],{},[3191,63110,243],{"stretchy":3295},[974,63112,63095],{},[3191,63114,867],{"stretchy":3295},[982,63116,63117],{"encoding":984},"\\theta = \\theta - \\alpha \\nabla J(\\theta)",[86,63119,63121,63139,63157],{"className":63120,"ariaHidden":990},[989],[86,63122,63124,63127,63130,63133,63136],{"className":63123},[994],[86,63125],{"className":63126,"style":3873},[998],[86,63128,63095],{"className":63129,"style":6235},[1003,1007],[86,63131],{"className":63132,"style":3222},[3221],[86,63134,258],{"className":63135},[3226],[86,63137],{"className":63138,"style":3222},[3221],[86,63140,63142,63145,63148,63151,63154],{"className":63141},[994],[86,63143],{"className":63144,"style":42893},[998],[86,63146,63095],{"className":63147,"style":6235},[1003,1007],[86,63149],{"className":63150,"style":5012},[3221],[86,63152,9864],{"className":63153},[5016],[86,63155],{"className":63156,"style":5012},[3221],[86,63158,63160,63163,63166,63169,63172,63175,63178],{"className":63159},[994],[86,63161],{"className":63162,"style":3794},[998],[86,63164,10574],{"className":63165,"style":10771},[1003,1007],[86,63167,63106],{"className":63168},[1003],[86,63170,61488],{"className":63171,"style":61598},[1003,1007],[86,63173,243],{"className":63174},[3320],[86,63176,63095],{"className":63177,"style":6235},[1003,1007],[86,63179,867],{"className":63180},[3356],[12,63182,3273],{},[30,63184,63185,63217,63248],{},[33,63186,63187,63216],{},[86,63188,63190,63204],{"className":63189},[955],[86,63191,63193],{"className":63192},[959],[961,63194,63195],{"xmlns":963},[965,63196,63197,63201],{},[968,63198,63199],{},[974,63200,63095],{},[982,63202,63203],{"encoding":984},"\\theta",[86,63205,63207],{"className":63206,"ariaHidden":990},[989],[86,63208,63210,63213],{"className":63209},[994],[86,63211],{"className":63212,"style":3873},[998],[86,63214,63095],{"className":63215,"style":6235},[1003,1007]," representa los parámetros del modelo (por ejemplo, los coeficientes en regresión).",[33,63218,63219,63247],{},[86,63220,63222,63235],{"className":63221},[955],[86,63223,63225],{"className":63224},[959],[961,63226,63227],{"xmlns":963},[965,63228,63229,63233],{},[968,63230,63231],{},[974,63232,10574],{},[982,63234,10904],{"encoding":984},[86,63236,63238],{"className":63237,"ariaHidden":990},[989],[86,63239,63241,63244],{"className":63240},[994],[86,63242],{"className":63243,"style":7401},[998],[86,63245,10574],{"className":63246,"style":10771},[1003,1007]," es la tasa de aprendizaje, que controla el tamaño de los pasos que se dan en cada iteración.",[33,63249,63250,63299],{},[86,63251,63253,63275],{"className":63252},[955],[86,63254,63256],{"className":63255},[959],[961,63257,63258],{"xmlns":963},[965,63259,63260,63272],{},[968,63261,63262,63264,63266,63268,63270],{},[974,63263,63106],{"mathvariant":4327},[974,63265,61488],{},[3191,63267,243],{"stretchy":3295},[974,63269,63095],{},[3191,63271,867],{"stretchy":3295},[982,63273,63274],{"encoding":984},"\\nabla J(\\theta)",[86,63276,63278],{"className":63277,"ariaHidden":990},[989],[86,63279,63281,63284,63287,63290,63293,63296],{"className":63280},[994],[86,63282],{"className":63283,"style":3794},[998],[86,63285,63106],{"className":63286},[1003],[86,63288,61488],{"className":63289,"style":61598},[1003,1007],[86,63291,243],{"className":63292},[3320],[86,63294,63095],{"className":63295,"style":6235},[1003,1007],[86,63297,867],{"className":63298},[3356]," es el gradiente de la función de pérdida con respecto a los parámetros, que indica la dirección de mayor aumento de la pérdida.",[12,63301,63302],{},"El proceso de optimización continúa hasta que se alcanza un criterio de convergencia, como un número máximo de iteraciones o una mejora mínima en la función de pérdida.",[30,63304,63305,63340,63394],{},[33,63306,63307,63308,606,63311,63339],{},"Posee una ",[122,63309,63310],{},"tasa de aprendizaje",[86,63312,63314,63327],{"className":63313},[955],[86,63315,63317],{"className":63316},[959],[961,63318,63319],{"xmlns":963},[965,63320,63321,63325],{},[968,63322,63323],{},[974,63324,10574],{},[982,63326,10904],{"encoding":984},[86,63328,63330],{"className":63329,"ariaHidden":990},[989],[86,63331,63333,63336],{"className":63332},[994],[86,63334],{"className":63335,"style":7401},[998],[86,63337,10574],{"className":63338,"style":10771},[1003,1007],") que controla el tamaño de los pasos que se dan en cada iteración (típicamente un valor pequeño como 0.01 o 0.001).",[33,63341,1243,63342,606,63345,63393],{},[122,63343,63344],{},"gradiente",[86,63346,63348,63369],{"className":63347},[955],[86,63349,63351],{"className":63350},[959],[961,63352,63353],{"xmlns":963},[965,63354,63355,63367],{},[968,63356,63357,63359,63361,63363,63365],{},[974,63358,63106],{"mathvariant":4327},[974,63360,61488],{},[3191,63362,243],{"stretchy":3295},[974,63364,63095],{},[3191,63366,867],{"stretchy":3295},[982,63368,63274],{"encoding":984},[86,63370,63372],{"className":63371,"ariaHidden":990},[989],[86,63373,63375,63378,63381,63384,63387,63390],{"className":63374},[994],[86,63376],{"className":63377,"style":3794},[998],[86,63379,63106],{"className":63380},[1003],[86,63382,61488],{"className":63383,"style":61598},[1003,1007],[86,63385,243],{"className":63386},[3320],[86,63388,63095],{"className":63389,"style":6235},[1003,1007],[86,63391,867],{"className":63392},[3356],") es un vector que contiene las derivadas parciales de la función de pérdida con respecto a cada parámetro, indicando la dirección de mayor aumento de la pérdida.",[33,63395,63396,63397,63400],{},"El proceso de optimización continúa hasta que se alcanza un criterio de ",[122,63398,63399],{},"convergencia",", como un número máximo de iteraciones o una mejora mínima en la función de pérdida.",[12,63402,63403],{},"Gráficamente:",[12,63405,63406,63410],{},[1945,63407],{"alt":63408,"src":63409},"Gráfico del proceso de optimización con descenso de gradiente","\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations\u002Fshared\u002Fgradient-descent.webp",[901,63411,63412],{},"Optimización con Descenso de Gradiente",[117,63414,63415,63418,63421,63424],{},[33,63416,63417],{},"Se inicia con un punto aleatorio en la función de pérdida (INITIAL POINT).",[33,63419,63420],{},"Se calcula el gradiente en ese punto, que indica la dirección de mayor aumento de la pérdida.",[33,63422,63423],{},"Se actualizan los parámetros del modelo en la dirección opuesta al gradiente, con un paso controlado por la tasa de aprendizaje (LEARNING RATE \u002F STEP SIZE).",[33,63425,63426],{},"Este proceso se repite iterativamente hasta que se alcanza un mínimo local o global de la función de pérdida, lo que indica que el modelo ha sido optimizado.",[12,63428,63429],{},"La tasa de aprendizaje es crucial para el éxito del proceso de optimización:",[30,63431,63432,63442,63451],{},[33,63433,63434,63437,63438,63441],{},[122,63435,63436],{},"DIVERGENCIA",": Si la tasa de aprendizaje es demasiado ",[122,63439,63440],{},"alta",", el modelo puede divergir, saltando por encima del mínimo y aumentando la pérdida.",[33,63443,63444,63437,63447,63450],{},[122,63445,63446],{},"CONVERGENCIA LENTA",[122,63448,63449],{},"baja",", el proceso de optimización puede ser muy lento, tardando mucho tiempo en converger o quedándose atrapado en un mínimo local.",[33,63452,63453,63456],{},[122,63454,63455],{},"CONVERGENCIA ÓPTIMA",": Una tasa de aprendizaje adecuada permite que el modelo converja de manera eficiente hacia un mínimo global o local, optimizando la función de pérdida de manera efectiva.",[46,63458,63460],{"id":63459},"el-proceso-de-machine-learning","El Proceso de Machine Learning",[12,63462,63463],{},"Podemos resumir el proceso de ML en:",[117,63465,63466,63477,63488,63499,63509],{},[33,63467,63468,63471,63472],{},[122,63469,63470],{},"Paradigma de aprendizaje",": Elegir el tipo de aprendizaje (supervisado, no supervisado, por refuerzo) según el problema a resolver.\n",[30,63473,63474],{},[33,63475,63476],{},"Define el tipo de problema y datos disponibles.",[33,63478,63479,63482,63483],{},[122,63480,63481],{},"Modelo matemático",": Seleccionar un modelo adecuado (regresión, clasificación, clustering) y entender su formulación matemática.\n",[30,63484,63485],{},[33,63486,63487],{},"Establece la relación matemática entre entrada y salida.",[33,63489,63490,63493,63494],{},[122,63491,63492],{},"Función de pérdida\u002Fcosto",": Definir una función de pérdida que mida el error del modelo y que se pueda optimizar.\n",[30,63495,63496],{},[33,63497,63498],{},"Cuántifica que tan malo es el modelo en sus predicciones.",[33,63500,63501,63503,63504],{},[122,63502,63067],{},": Utilizar técnicas como el descenso de gradiente para ajustar los parámetros del modelo y minimizar la función de pérdida.\n",[30,63505,63506],{},[33,63507,63508],{},"Encuentra los mejores parámetros para que el modelo haga buenas predicciones.",[33,63510,63511,63513,63514],{},[122,63512,46063],{},": Medir el rendimiento del modelo utilizando métricas adecuadas para el tipo de problema (MSE para regresión, precisión\u002Frecall para clasificación, etc.).\n",[30,63515,63516],{},[33,63517,63518],{},"Valida el desempeño del modelo y su capacidad de generalización a datos no vistos.",{"title":169,"searchDepth":205,"depth":205,"links":63520},[63521,63526,63530,63534],{"id":46310,"depth":192,"text":46311,"children":63522},[63523,63524,63525],{"id":46337,"depth":205,"text":46338},{"id":46984,"depth":205,"text":46985},{"id":47218,"depth":205,"text":47219},{"id":47261,"depth":192,"text":47262,"children":63527},[63528,63529],{"id":47275,"depth":205,"text":46970},{"id":57611,"depth":205,"text":46964},{"id":62992,"depth":192,"text":62993,"children":63531},[63532,63533],{"id":62996,"depth":205,"text":62997},{"id":63066,"depth":205,"text":63067},{"id":63459,"depth":192,"text":63460},"2026-04-06","\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations\u002Fshared\u002Fml-paradigms.webp",{},"\u002Fblog\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations",{"title":44608,"description":46296},{"loc":63541,"priority":2259,"lastmod":63535},"\u002Fes\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations","machine-learning-paradigms-and-mathematical-foundations","blog\u002Fblog\u002Fmachine-learning-paradigms-and-mathematical-foundations","Tipos de aprendizaje automático, algoritmos comunes y fundamentos matemáticos esenciales para entender cómo funcionan los modelos de machine learning.",[2264,3624,63546,63547,47283,63548,63549],"matemáticas para machine learning","fundamentos de aprendizaje automático","aprendizaje no supervisado","aprendizaje por refuerzo","NVoE-6RT6irWWCfKu_SRjAAOYBzQ5KVM2ms2EU9-xzo",{"id":63552,"title":46303,"author":7,"body":63553,"date":64179,"description":63557,"extension":2250,"image":64180,"lastmod":64179,"meta":64181,"navigation":208,"order":192,"path":64182,"seo":64183,"sitemap":64184,"slug":64186,"stem":64187,"summary":64188,"tags":64189,"__hash__":64191},"content_es\u002Fblog\u002Fblog\u002Fmachine-learning-fundamentals.md",{"type":9,"value":63554,"toc":64170},[63555,63558,63560,63562,63566,63580,63583,63607,63610,63624,63626,63630,63633,63701,63703,63707,63710,63819,63821,63924,63926,63969,63989,63991,63995,63998,64051,64055,64058,64067,64070,64081,64094,64096,64100,64126,64136,64138,64142,64145,64165,64167],[12,63556,63557],{},"Esta es la primera parte de una serie de artículos donde exploraremos el aprendizaje automático, desde sus conceptos básicos hasta redes neuronales y la creación de un modelo de machine learning. En esta primera parte, nos centraremos en los fundamentos del aprendizaje automático, incluyendo qué es, sus tipos y algunos algoritmos comunes.",[40,63559],{},[43,63561],{},[46,63563,63565],{"id":63564},"inteligencia-artificial-y-machine-learning","Inteligencia Artificial y Machine Learning",[12,63567,63568,63569,93,63571,392,63574,63577,63578,61],{},"Te despiertas un día, abres Netflix y te encuentras recomendada exactamente la serie que querías ver. Luego, abres Google escribes algo y el buscador completa tu frase antes de que termines de teclear. ¿Cómo hacen esto? La respuesta es: Inteligencia Artificial. La IA, es una disciplina enfocada en desarrollar sistemas capaces de realizar tareas que normalmente requieren inteligencia humana, como ",[122,63570,2520],{},[122,63572,63573],{},"razonar",[122,63575,63576],{},"percibir"," nuestro entorno, asi como ",[122,63579,15492],{},[12,63581,63582],{},"Existen tres tipos de IA:",[30,63584,63585,63591,63597],{},[33,63586,63587,63590],{},[122,63588,63589],{},"IA débil o estrecha (Artificial Narrow Intelligence o ANI)",": Es la IA que tenemos hoy en día. Está diseñada para realizar tareas específicas, como reconocimiento de voz, recomendaciones de productos o traducción automática. No tiene conciencia ni comprensión real, simplemente sigue algoritmos y patrones predefinidos. Los LLM como GPT, Claude o Gemini, son ejemplos de IA débil, ya que están diseñados para procesar y generar texto, \"solamente\" son modelos estadisticos que predicen texto, y  no tienen una comprensión profunda del mundo ni pueden realizar tareas fuera de su ámbito específico. Aunque parecen inteligentes, en realidad solo están imitando patrones de lenguaje basados en los datos con los que fueron entrenados.",[33,63592,63593,63596],{},[122,63594,63595],{},"IA general (Artifical General Intelligence o AGI)",": Es una IA hipotética que tendría la capacidad de entender, aprender y aplicar conocimientos en una amplia variedad de tareas, similar a la inteligencia humana. Aún no existe, pero es un objetivo a largo plazo en el campo de la IA.",[33,63598,63599,63602,63603,63606],{},[122,63600,63601],{},"IA superinteligente (Artificial Superintelligence o ASI)",": Es una IA que superaría la inteligencia humana en todos los aspectos, incluyendo creatividad, resolución de problemas y toma de decisiones. Es un concepto ",[122,63604,63605],{},"teórico"," que plantea muchas preguntas éticas y filosóficas sobre el futuro de la humanidad.",[12,63608,63609],{},"¿Dónde entra el Machine Learning? Es muy común confundir la IA con el Machine Learning, pero no son exactamente lo mismo. Podemos decir que la Inteligencia Artificial es un gran paraguas conceptual, y debajo de ese paraguas se encuentra el Machine Learning, un subcampo específico que permite a las computadoras aprender automáticamente a partir de datos, sin necesidad de que un humano las programe paso a paso.",[16,63611,63612,63615],{},[12,63613,63614],{},"Recursos recomendados:",[30,63616,63617],{},[33,63618,63619],{},[22,63620,63623],{"href":63621,"rel":63622},"https:\u002F\u002Fyoutu.be\u002FdKqwnCKrpVI?si=g6qqFa_1G_M5P3LS",[26],"Inteligencia Artificial vs Machine Learning vs Deep Learning | Machine Learning 101",[43,63625],{},[46,63627,63629],{"id":63628},"subcampos-de-la-ia","Subcampos de la IA",[12,63631,63632],{},"Dentro del gran paraguas de la IA, hay varios subcampos que se especializan en diferentes aspectos de la inteligencia artificial:",[30,63634,63635,63641,63647,63653,63659,63665,63671,63677,63683,63689,63695],{},[33,63636,63637,63640],{},[122,63638,63639],{},"Aprendizaje Automático (Machine Learning)",": Se centra en desarrollar algoritmos que permiten a las máquinas aprender de los datos y mejorar su rendimiento con el tiempo sin ser explícitamente programadas para cada tarea específica.",[33,63642,63643,63646],{},[122,63644,63645],{},"Aprendizaje Profundo (Deep Learning)",": Es una rama del aprendizaje automático que utiliza redes neuronales profundas para modelar y resolver problemas complejos. Es especialmente efectivo en tareas como reconocimiento de voz, visión por computadora y procesamiento del lenguaje natural.",[33,63648,63649,63652],{},[122,63650,63651],{},"Procesamiento del Lenguaje Natural (Natural Language Processing o NLP)",": Se enfoca en la interacción entre las computadoras y el lenguaje humano, permitiendo a las máquinas entender, interpretar y generar texto de manera natural. Es lo que hace posible que los chatbots como ChatGPT puedan mantener conversaciones coherentes con los usuarios.",[33,63654,63655,63658],{},[122,63656,63657],{},"Visión por Computadora (Computer Vision)",": Se ocupa de permitir que las máquinas comprendan y procesen imágenes y videos. Esto es fundamental para aplicaciones como el reconocimiento facial, la conducción autónoma y la detección de objetos.",[33,63660,63661,63664],{},[122,63662,63663],{},"Robótica",": Se dedica al diseño y construcción de robots que pueden realizar tareas físicas en el mundo real, desde la fabricación hasta la asistencia médica.",[33,63666,63667,63670],{},[122,63668,63669],{},"Sistemas Expertos",": Son programas que imitan la toma de decisiones de un experto humano en un dominio específico, utilizando reglas y lógica para resolver problemas complejos.",[33,63672,63673,63676],{},[122,63674,63675],{},"Razonamiento Automático",": Se enfoca en inferir conclusiones lógicas a partir de reglas formales, no es lo mismo que el aprendizaje automático, este campo incluye lógica simbólica, resolución de problemas y planificación automática.",[33,63678,63679,63682],{},[122,63680,63681],{},"Agentes Inteligentes",": Son sistemas que pueden percibir su entorno, razonar sobre él y tomar decisiones para alcanzar objetivos específicos. Pueden ser tan simples como un chatbot o tan complejos como un sistema de conducción autónoma (puede usar ML, reglas simples, razonamiento lógico, etc).",[33,63684,63685,63688],{},[122,63686,63687],{},"IA Distribuida",": Se refiere a sistemas de IA que operan en múltiples dispositivos o nodos, colaborando para resolver problemas de manera más eficiente. Esto es especialmente relevante en aplicaciones como el Internet de las Cosas (IoT) y la computación en la nube.",[33,63690,63691,63694],{},[122,63692,63693],{},"IA Explicable (XAI)",": Se centra en desarrollar modelos de IA que sean transparentes y comprensibles para los humanos, permitiendo a los usuarios entender cómo y por qué la IA toma ciertas decisiones.",[33,63696,63697,63700],{},[122,63698,63699],{},"Ética y Gobernanza de la IA",": Se ocupa de las implicaciones éticas, legales y sociales del desarrollo y uso de la IA, abordando temas como la privacidad, la equidad, la transparencia.",[43,63702],{},[46,63704,63706],{"id":63705},"como-aprende-una-máquina","Como aprende una máquina",[12,63708,63709],{},"Todo depende de los datos que le demos:",[30,63711,63712],{},[33,63713,63714,63716,63717,63720,63721,63724,63725,63727,63728,63774,63776,63777,63779,63780,63792,63794,63795,63801,63802,63804,63805],{},[122,63715,46338],{},": Aquí le damos a la máquina ejemplos claros con las respuestas correctas ya \"etiquetadas\". Por ejemplo, si queremos que la IA ayude en un diagnóstico médico, le damos miles de historiales médicos donde ya sabemos qué paciente estaba ",[122,63718,63719],{},"enfermo"," y qué paciente estaba ",[122,63722,63723],{},"sano",".\nLa máquina aprende a reconocer patrones en esos datos para poder predecir el diagnóstico de nuevos pacientes basándose en lo que ha aprendido.",[43152,63726],{},"Un ejemplo sencillo sería algo así:",[461,63729,63730,63745],{},[464,63731,63732],{},[467,63733,63734,63736,63739,63742],{},[470,63735,19849],{},[470,63737,63738],{},"Síntomas",[470,63740,63741],{},"Resultado de Pruebas",[470,63743,63744],{},"Diagnóstico",[480,63746,63747,63761],{},[467,63748,63749,63752,63755,63758],{},[485,63750,63751],{},"45",[485,63753,63754],{},"Fiebre, Tos",[485,63756,63757],{},"Positivo",[485,63759,63760],{},"Enfermo",[467,63762,63763,63765,63768,63771],{},[485,63764,16271],{},[485,63766,63767],{},"Dolor de cabeza",[485,63769,63770],{},"Negativo",[485,63772,63773],{},"Sano",[43152,63775],{},"La etiqueta aquí es el \"Diagnóstico\", y la máquina aprende a asociar las características (Edad, Síntomas, Resultado de Pruebas) con esa etiqueta para hacer predicciones futuras.",[43152,63778],{},"Dentro del aprendizaje supervisado, hay dos tipos principales de tareas:",[30,63781,63782,63787],{},[33,63783,63784,63786],{},[122,63785,46964],{},": Donde la máquina asigna una etiqueta a cada ejemplo. Como clasificar correos electrónicos como \"spam\" o \"no spam\".",[33,63788,63789,63791],{},[122,63790,46970],{},": Donde la máquina predice un valor continuo. Por ejemplo, predecir el precio de una casa basándose en características como el tamaño, la ubicación y el número de habitaciones.",[43152,63793],{},"Basicamente si la respuesta que queremos predecir es una categoría (o una ",[22,63796,63800],{"href":63797,"target":27,"rel":63798,"ariaLabel":63799},"https:\u002F\u002Fwww.probabilidadyestadistica.net\u002Fvariable-discreta",[7760,7761],"LinkedIn","variable discreta","), es clasificación, si la respuesta representa una cantidad medible en una escala continua, es regresión.\nY el requisito para que el aprendizaje supervisado funcione bien es tener un conjunto de datos grande y representativo, con etiquetas precisas. Si los datos son escasos o las etiquetas son incorrectas, la máquina no podrá aprender correctamente y sus predicciones serán inexactas.",[43152,63803],{},"Ejemplos de aplicaciones de ML son:",[30,63806,63807,63810,63813,63816],{},[33,63808,63809],{},"Detección de fraudes en transacciones financieras (clasificación)",[33,63811,63812],{},"Predicción de precios de acciones (regresión)",[33,63814,63815],{},"Reconocimiento de imágenes (clasificación)",[33,63817,63818],{},"Análisis de sentimientos en redes sociales (clasificación)",[43,63820],{},[30,63822,63823],{},[33,63824,63825,63827,63828,63830,63831,63870,63872,63873,63921,63923],{},[122,63826,46985],{},": Imagina que te sueltan en un país desconocido y tienes que deducir cómo funciona la sociedad solo observando, es algo similar. Aquí, la máquina recibe datos sin etiquetas y debe encontrar patrones ocultos por sí sola. El sistema tendrá que analizar similitudes, diferencias y comportamientos para encontrar agrupaciones o patrones inusuales. No hay un \"profesor\" que le diga si está bien o mal.",[43152,63829],{},"Técnicas principales:",[117,63832,63833,63850,63864],{},[33,63834,63835,63838,63839],{},[122,63836,63837],{},"Clustering (Agrupamiento)",": Agrupa datos similares entre si.\nSe usa típicamente para segmentación de clientes, agrupar documentos por tema y organización automática de imágenes, etc. Algunos algoritmos:\n",[30,63840,63841,63844,63847],{},[33,63842,63843],{},"K-means clustering",[33,63845,63846],{},"DBSCAN",[33,63848,63849],{},"Hierarchical clustering",[33,63851,63852,63855,63856],{},[122,63853,63854],{},"Reducción de dimensionalidad",": Este busca reducir la cantidad de variables manteniendo la información importante. Usado para visualizar datos complejos y preparar datos para otros modelos.\n",[30,63857,63858,63861],{},[33,63859,63860],{},"Principal Component Analysis (PCA)",[33,63862,63863],{},"t-SNE",[33,63865,63866,63869],{},[122,63867,63868],{},"Detección de anomalías",": Identifica datos que se comportan diferente del resto. Útil para detectar fraudes, fallos en sistemas y comportamientos sospechosos.",[43152,63871],{},"Un ejemplo sencillo sería:",[461,63874,63875,63887],{},[464,63876,63877],{},[467,63878,63879,63881,63884],{},[470,63880,19849],{},[470,63882,63883],{},"Ingresos Anuales",[470,63885,63886],{},"Gastos Mensuales",[480,63888,63889,63899,63910],{},[467,63890,63891,63893,63896],{},[485,63892,19872],{},[485,63894,63895],{},"$30,000",[485,63897,63898],{},"$1,000",[467,63900,63901,63904,63907],{},[485,63902,63903],{},"40",[485,63905,63906],{},"$80,000",[485,63908,63909],{},"$3,000",[467,63911,63912,63915,63918],{},[485,63913,63914],{},"60",[485,63916,63917],{},"$50,000",[485,63919,63920],{},"$2,000",[43152,63922],{},"La máquina podría agrupar a los clientes en segmentos basados en sus ingresos y gastos, sin que le digamos explícitamente qué grupos existen.\nCon esto podemos identificar patrones de consumo, como por ejemplo, que los clientes jóvenes tienden a gastar menos que los clientes de mediana edad, o que hay un grupo de clientes con ingresos altos pero gastos bajos, lo que podría indicar un segmento de ahorro.",[43,63925],{},[30,63927,63928],{},[33,63929,63930,63932,63933,61,63938,63940,63941,63963,63965,63966],{},[122,63931,47219],{},": Piensa en cómo entrenas a una mascota con premios. La máquina (el agente) toma decisiones en un entorno y recibe \"recompensas\" o \"penalizaciones\". Así es como los sistemas de conducción autónoma de Tesla o los robots aprenden a navegar por el mundo físico. Un ejemplo que me gusta es el de un video donde ",[22,63934,63937],{"href":63935,"target":27,"rel":63936},"https:\u002F\u002Fyoutu.be\u002FPKDMGPf-PEA?si=tAEMO3cETdPrvi_t",[7760,7761],"entrenan a un agente para jugar Geometry Dash",[43152,63939],{},"En este tipo de aprendizaje se tienen cuatro componentes principales:",[117,63942,63943,63948,63953,63958],{},[33,63944,63945,63947],{},[122,63946,47229],{},": Es el sistema que toma decisiones y aprende a través de la interacción con el entorno. Puede ser un robot, un programa de computadora o cualquier sistema que pueda percibir su entorno y actuar sobre él.",[33,63949,63950,63952],{},[122,63951,47235],{},": Es el mundo en el que el agente opera. Puede ser un entorno físico, como un robot en una habitación, o un entorno virtual, como un videojuego.",[33,63954,63955,63957],{},[122,63956,47241],{},": Es la señal que el agente recibe después de tomar una acción. Puede ser positiva (recompensa) o negativa (penalización) y sirve para guiar el aprendizaje del agente.",[33,63959,63960,63962],{},[122,63961,47247],{},": Es la estrategia que el agente utiliza para decidir qué acción tomar en función de su estado actual y de las recompensas que ha recibido en el pasado.",[43152,63964],{},"Básicamente siguen un flujo como el siguiente:",[7793,63967],{"content":63968},"graph TD\n A[Agente] -->|Toma acción| B(Entorno)\n B -->|Proporciona recompensa| C[Recompensa]\n C -->|Actualiza política| A",[16,63970,63971,63973],{},[12,63972,63614],{},[30,63974,63975,63982],{},[33,63976,63977],{},[22,63978,63981],{"href":63979,"rel":63980},"https:\u002F\u002Fyoutu.be\u002FoT3arRRB2Cw?si=ykU9KQjQLxdn9ggj",[26],"¿Qué es el Aprendizaje Supervisado y No Supervisado? | DotCSV",[33,63983,63984],{},[22,63985,63988],{"href":63986,"rel":63987},"https:\u002F\u002Fyoutu.be\u002FqBtB-xcJp4c?si=c2GuJBCFPorKGN44",[26],"El APRENDIZAJE POR REFUERZO: la guía DEFINITIVA",[43,63990],{},[46,63992,63994],{"id":63993},"pipeline-de-un-proyecto-de-ia","Pipeline de un proyecto de IA",[12,63996,63997],{},"Un proyecto de IA generalmente sigue un proceso estructurado que incluye varias etapas clave:",[117,63999,64000,64005,64011,64017,64023,64029,64035,64040,64045],{},[33,64001,64002,64004],{},[122,64003,45720],{},": Es fundamental entender claramente el problema que se quiere resolver y los objetivos del proyecto. Esto incluye identificar las preguntas que se quieren responder, los resultados esperados y las métricas de éxito.",[33,64006,64007,64010],{},[122,64008,64009],{},"Recolección de datos",": Se recopilan los datos necesarios para entrenar el modelo de IA. Esto puede incluir datos estructurados (como bases de datos) o no estructurados (como texto, imágenes o videos). Es importante asegurarse de que los datos sean de alta calidad y representativos del problema que se quiere resolver.",[33,64012,64013,64016],{},[122,64014,64015],{},"Preprocesamiento de datos",": Los datos recopilados a menudo necesitan ser limpiados y transformados antes de ser utilizados para entrenar el modelo. Esto puede incluir la eliminación de valores faltantes, la normalización de datos, la codificación de variables categóricas y la división de los datos en conjuntos de entrenamiento y prueba.",[33,64018,64019,64022],{},[122,64020,64021],{},"Selección del modelo",": Se elige el algoritmo de aprendizaje automático más adecuado para el problema en cuestión. Esto puede depender de la naturaleza de los datos, la complejidad del problema y los recursos disponibles.",[33,64024,64025,64028],{},[122,64026,64027],{},"Entrenamiento del modelo",": Se utiliza el conjunto de datos de entrenamiento para entrenar el modelo de IA. Durante esta etapa, el modelo aprende a partir de los datos y ajusta sus parámetros para minimizar el error en las predicciones.",[33,64030,64031,64034],{},[122,64032,64033],{},"Evaluación del modelo",": Se evalúa el rendimiento del modelo utilizando el conjunto de prueba. Se utilizan métricas específicas para medir la precisión, la exactitud, la sensibilidad y otras características del modelo, dependiendo del tipo de problema (clasificación, regresión, etc.).",[33,64036,64037,64039],{},[122,64038,1452],{},": Si el rendimiento del modelo no es satisfactorio, se pueden ajustar los hiperparámetros del modelo para mejorar su rendimiento. Esto puede incluir cambiar la arquitectura del modelo, ajustar la tasa de aprendizaje o modificar otros parámetros específicos del algoritmo.",[33,64041,64042,64044],{},[122,64043,46140],{},": Una vez que el modelo ha sido entrenado y evaluado, se implementa en un entorno de producción donde puede ser utilizado para hacer predicciones en tiempo real o procesar nuevos datos.",[33,64046,64047,64050],{},[122,64048,64049],{},"Mantenimiento y actualización",": Después de la implementación, es importante monitorear el rendimiento del modelo y actualizarlo regularmente para asegurarse de que siga siendo efectivo a medida que cambian los datos y las condiciones del entorno.",[46,64052,64054],{"id":64053},"memorizar-vs-aprender","Memorizar vs Aprender",[12,64056,64057],{},"Cuando hablamos de aprendizaje, ya sea humano o de máquinas, existe un concepto crucial que debemos entender: memorizar no es lo mismo que aprender.",[12,64059,64060,64063,64064,64066],{},[122,64061,64062],{},"Memorizar"," es como copiar y pegar información sin realmente entenderla. Por ejemplo, si memorizas la fórmula del área de un círculo (A = πr²) sin comprender qué significa cada parte, no podrás aplicarla correctamente en diferentes contextos. La memoria te salva en lo inmediato, pero no te da la capacidad de adaptarte a nuevas situaciones o resolver problemas que no has visto antes, en cambio, ",[122,64065,2520],{}," implica comprender los conceptos que están detrás y ser capaz de aplicarlos en situaciones nuevas.",[12,64068,64069],{},"En el mundo del aprendizaje automático, una máquina que solo memoriza los datos de entrenamiento puede tener un rendimiento excelente en esos datos específicos, pero luego fallar estrepitosamente cuando se utiliza en entornos reales. Por eso, en machine learning, el verdadero objetivo no es memorizar patrones específicos, sino generalizar: aprender reglas y relaciones que funcionen más allá de los ejemplos vistos.",[12,64071,64072,64073,64076,64077,64080],{},"Pero aprender tampoco es sencillo, a veces, las máquinas sufren de ",[122,64074,64075],{},"Overfitting"," (sobreajuste), que ocurre cuando un modelo \"memoriza\" los datos de entrenamiento a la perfección, pero fracasa rotundamente cuando se enfrenta a datos nuevos en el mundo real. Es exactamente igual que un estudiante que memoriza las respuestas de un examen sin entender realmente los conceptos. Por el contrario, si el modelo es demasiado simple y no aprende nada, sufre de ",[122,64078,64079],{},"Underfitting"," (subajuste), como un estudiante que no estudió lo suficiente.",[16,64082,64083,64085],{},[12,64084,63614],{},[30,64086,64087],{},[33,64088,64089],{},[22,64090,64093],{"href":64091,"rel":64092},"https:\u002F\u002Fyoutu.be\u002Fo3DztvnfAJg?si=lorMlPZqLAMa-EV3",[26],"Subajuste y sobreajuste: explicados",[43,64095],{},[46,64097,64099],{"id":64098},"los-componentes-de-un-sistema-de-ia","Los componentes de un sistema de IA",[30,64101,64102,64114,64120],{},[33,64103,64104,64107,64108,64113],{},[122,64105,64106],{},"Datos",": Son la base de cualquier sistema de IA. Sin datos, no hay aprendizaje. Deben ser de alta calidad, relevantes y representativos del problema que se quiere resolver. Con un alto volumen y con el menor ",[22,64109,64112],{"href":64110,"target":27,"rel":64111},"https:\u002F\u002Fwww.innovatiana.com\u002Fes\u002Fpost\u002Fbias-estimation-in-machine-learning",[7760,7761],"sesgo"," posible.",[33,64115,64116,64119],{},[122,64117,64118],{},"Algoritmos",": Son las recetas que la máquina sigue para aprender de los datos. Hay muchos tipos de algoritmos, cada uno con sus propias fortalezas y debilidades, y deben ser seleccionados cuidadosamente según el problema específico que se quiere resolver, configurados y ajustados para obtener el mejor rendimiento posible.",[33,64121,64122,64125],{},[122,64123,64124],{},"Infraestructura",": Es el hardware y software necesario para procesar los datos y ejecutar los algoritmos. Esto incluye desde servidores (CPU, GPU, TPU) hasta plataformas de computación en la nube y herramientas de desarrollo (AWS, Azure, GCP), asi como almacenamiento de datos y sistemas de gestión de bases de datos.",[12,64127,64128,64129,64131,64132,64135],{},"A parte de estos componentes, tenemos la ",[122,64130,46062],{},", que es el proceso de medir el rendimiento del modelo de IA para asegurarse de que está funcionando correctamente y cumpliendo con los objetivos establecidos, asi como el rol de la ",[122,64133,64134],{},"ética y gobernanza",", que es fundamental para considerar las implicaciones éticas y sociales.",[43,64137],{},[46,64139,64141],{"id":64140},"la-ética-en-la-ia","La ética en la IA",[12,64143,64144],{},"A medida que la inteligencia artificial se vuelve más omnipresente en nuestras vidas, es crucial considerar las implicaciones éticas de su uso. Los modelos de machine learning pueden perpetuar sesgos existentes en los datos, lo que puede llevar a decisiones injustas o discriminatorias. Por ejemplo, si un modelo de contratación se entrena con datos históricos que reflejan prejuicios de género o raza, es probable que el modelo reproduzca esos sesgos en sus recomendaciones. Además, la privacidad de los datos es una preocupación importante. Es fundamental asegurarse de que los datos utilizados se recopilen y manejen de manera ética, respetando la privacidad y los derechos de las personas.",[30,64146,64147,64153,64159],{},[33,64148,64149,64152],{},[122,64150,64151],{},"Transparencia",": Los sistemas deben ser comprensibles y auditables para que los usuarios puedan entender cómo funcionan y por qué toman ciertas decisiones, una solución a esto es la IA explicable (XAI).",[33,64154,64155,64158],{},[122,64156,64157],{},"Explicabilidad",": Los modelos de IA deben ser capaces de explicar sus decisiones de manera clara y comprensible para los usuarios, lo que ayuda a generar confianza y permite a los usuarios entender las razones detrás de las recomendaciones o acciones del sistema.",[33,64160,64161,64164],{},[122,64162,64163],{},"Responsabilidad",": Se debe establecer claramente quién es responsable de las decisiones tomadas por los sistemas de IA, especialmente en casos donde las decisiones pueden tener un impacto significativo en la vida de las personas. Aqui entran en juego los marcos legales y regulaciones que deben ser desarrollados para garantizar que las empresas y desarrolladores de IA sean responsables de sus creaciones.",[43,64166],{},[12,64168,64169],{},"Hasta aquí la primera parte de esta serie de artículos sobre aprendizaje automático. En la próxima parte, exploraremos algunos paradigmas de machine learning y ciertos fundamentos matemáticos que son esenciales para entender cómo funcionan los algoritmos.",{"title":169,"searchDepth":205,"depth":205,"links":64171},[64172,64173,64174,64175,64176,64177,64178],{"id":63564,"depth":192,"text":63565},{"id":63628,"depth":192,"text":63629},{"id":63705,"depth":192,"text":63706},{"id":63993,"depth":192,"text":63994},{"id":64053,"depth":192,"text":64054},{"id":64098,"depth":192,"text":64099},{"id":64140,"depth":192,"text":64141},"2026-03-30","\u002Fblog\u002Fmachine-learning-fundamentals\u002Fshared\u002Fml-fundamentals.webp",{},"\u002Fblog\u002Fblog\u002Fmachine-learning-fundamentals",{"title":46303,"description":63557},{"loc":64185,"priority":2259,"lastmod":64179},"\u002Fes\u002Fblog\u002Fmachine-learning-fundamentals","machine-learning-fundamentals","blog\u002Fblog\u002Fmachine-learning-fundamentals","Conceptos básicos para iniciar en el mundo del aprendizaje automático",[3625,3624,168,2265,2264,64190,47283,63548,63549],"fundamentos de machine learning","TBmlULvtaevuJ8SHhCIz2odUSxS19FSSzJgs83U7Mc0",{"id":64193,"title":64194,"author":7,"body":64195,"date":70623,"description":64199,"extension":2250,"image":70624,"lastmod":70625,"meta":70626,"navigation":208,"order":175,"path":70627,"seo":70628,"sitemap":70629,"slug":70631,"stem":70632,"summary":70633,"tags":70634,"__hash__":70639},"content_es\u002Fblog\u002Fblog\u002Fgetting-started-vue-vite.md","Comenzando con Vue 3 y Vite",{"type":9,"value":64196,"toc":70603},[64197,64200,64202,64204,64208,64211,64249,64252,64262,64264,64268,64276,64279,64282,64284,64288,64291,64308,64318,64327,64330,64339,64342,64351,64354,64431,64434,64442,64462,64465,64468,64471,64479,64484,64497,64502,64514,64519,64534,64539,64553,64562,64569,64596,64599,64607,64616,64618,64622,64625,64874,64881,64889,64902,64906,64984,64988,64991,65001,65393,65403,65408,65900,65907,65914,65921,65932,65934,65938,65947,66144,66147,66208,66215,66463,66480,66486,66833,66846,66851,67101,67129,67132,67159,67167,67176,67187,67189,67192,67194,67198,67201,67204,67210,67420,67434,67779,67794,67797,67817,67823,67825,67829,67832,67839,67845,68104,68119,68125,68347,68356,68673,68679,68682,68705,68709,68719,68729,68738,68742,68748,68793,68796,68819,68823,68830,68837,68840,68871,68874,68876,68880,68887,68900,68903,68978,68988,68994,68997,69020,69022,69026,69035,69044,69047,69065,69071,69319,69326,69367,69374,69614,69621,69633,69638,70238,70244,70251,70264,70266,70270,70273,70278,70291,70300,70306,70311,70326,70348,70360,70380,70398,70417,70422,70434,70444,70449,70484,70487,70490,70499,70502,70525,70528,70544,70546,70550,70553,70593,70595,70598,70600],[12,64198,64199],{},"En esta guía, exploraremos cómo iniciar un proyecto moderno con Vue 3 y Vite, explicaremos la estructura del proyecto, como funciona una aplicación Vue, el router, Pinia, los composables, veremos algunas buenas prácticas para desarrollar aplicaciones escalables y mantenibles, y como extra publicaremos el proyecto en GitHub y veremos cómo instalar Tailwind CSS v4 para obtener estilos rápidos y responsivos.",[40,64201],{},[43,64203],{},[46,64205,64207],{"id":64206},"configurando-el-entorno","Configurando el entorno",[12,64209,64210],{},"Antes de continuar, debemos tener:",[30,64212,64213,64226,64233,64241],{},[33,64214,64215,64216,64219,64220,64225],{},"Node.js, cualquier versión ",[122,64217,64218],{},"LTS",". Recomiendo acostumbrarse a utilizar ",[22,64221,64224],{"target":27,"href":64222,"rel":64223},"https:\u002F\u002Fgithub.com\u002Fcoreybutler\u002Fnvm-windows",[7760,7761],"nvm"," para manejar múltiples versiones de Node.",[33,64227,64228,64229,64232],{},"Un gestor de paquetes (aquí usaremos ",[145,64230,64231],{},"npm",", que ya se instala con Node.js).",[33,64234,64235,64240],{},[22,64236,64239],{"target":27,"href":64237,"rel":64238},"https:\u002F\u002Fcode.visualstudio.com\u002F",[7760,7761],"VS Code"," actualizado",[33,64242,64243,64248],{},[22,64244,64247],{"target":27,"href":64245,"rel":64246},"https:\u002F\u002Fwww.desarrollolibre.net\u002Fblog\u002Fprogramacion-basica\u002Fla-guia-de-git-que-nunca-tuve",[7760,7761],"Git configurado"," correctamente",[12,64250,64251],{},"Además, instala la extensión oficial de Vue.js para VS Code:",[30,64253,64254],{},[33,64255,64256,64261],{},[22,64257,64260],{"target":27,"href":64258,"rel":64259},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=Vue.volar",[7760,7761],"Vue.js (Volar)",".\nMás adelante exploraremos otros plugins útiles como ESLint, Prettier y Tailwind CSS IntelliSense.",[43,64263],{},[46,64265,64267],{"id":64266},"javascript-o-typescript","¿JavaScript o TypeScript?",[12,64269,64270,64271,61],{},"Vue 3 tiene un soporte bastante bueno para TypeScript, puedes usarlo teniendo en cuenta la ",[22,64272,64275],{"target":27,"href":64273,"rel":64274},"https:\u002F\u002Fvuejs.org\u002Fguide\u002Ftypescript\u002Foverview.html",[7760,7761],"guía de uso oficial",[12,64277,64278],{},"No necesitas usar TypeScript en todos tus proyectos, especialmente si estás comenzando o solo quieres experimentar. Asi que mi recomendación es que valores tu contexto, la aplicación y tu equipo (si estás trabajando en uno).",[12,64280,64281],{},"En esta guía usaremos JavaScript para mantener las cosas simples.",[43,64283],{},[46,64285,64287],{"id":64286},"creando-el-proyecto-con-vite","Creando el proyecto con Vite",[12,64289,64290],{},"La forma más rápida de iniciar un proyecto Vue 3 con Vite es usando el comando (puedes ejecutarlo en cualquier carpeta donde quieras crear el proyecto, utiliza la terminal integrada de VS Code o tu terminal favorita):",[164,64292,64296],{"className":64293,"code":64294,"language":64295,"meta":169,"style":169},"language-bash shiki shiki-themes vitesse-light vitesse-dark","npm create vue@latest\n","bash",[145,64297,64298],{"__ignoreMap":169},[86,64299,64300,64302,64305],{"class":174,"line":175},[86,64301,64231],{"class":239},[86,64303,64304],{"class":579}," create",[86,64306,64307],{"class":579}," vue@latest\n",[12,64309,64310,64311,64314,64315,64317],{},"Si es primera vez que lo usas, te preguntará si deseas instalar el paquete ",[145,64312,64313],{},"create-vue",". Responde que sí (escribimos ",[145,64316,5464],{}," y damos ENTER).",[12,64319,64320,64324],{},[1945,64321],{"alt":64322,"src":64323},"Instalando create-vue","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Finstall-create-vue-package.webp",[901,64325,64326],{},"Instalando paquete: create-vue",[12,64328,64329],{},"Nos preguntará por el nombre del proyecto, escribe el nombre que quieras:",[12,64331,64332,64336],{},[1945,64333],{"alt":64334,"src":64335},"Nombre del proyecto","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fproject-name.webp",[901,64337,64338],{},"Asígnale un nombre a tu proyecto",[12,64340,64341],{},"Luego selecciona las opciones que necesites:",[12,64343,64344,64348],{},[1945,64345],{"alt":64346,"src":64347},"Opciones del proyecto","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fproject-options.webp",[901,64349,64350],{},"Features disponibles al crear una app Vue",[12,64352,64353],{},"Vamos punto por punto (tal como se muestra en la imagen, nos movemos con las flechas y seleccionamos con la barra espaciadora):",[117,64355,64356,64362,64373,64385,64391,64397,64419,64425],{},[33,64357,64358,64361],{},[122,64359,64360],{},"TypeScript",": como mencionamos antes, usaremos JavaScript, así que ignoramos.",[33,64363,64364,64367,64368,61],{},[122,64365,64366],{},"JSX Support",": no usaremos ",[22,64369,64372],{"target":27,"href":64370,"rel":64371},"https:\u002F\u002Fkinsta.com\u002Fes\u002Fblog\u002Fque-es-jsx\u002F",[7760,7761],"JSX",[33,64374,64375,64378,64379,64384],{},[122,64376,64377],{},"Router (SPA development)",": Vue Router es esencial para trabajar con Vue como SPA (Single Page Application). No ahondaremos en temas de ",[22,64380,64383],{"target":27,"href":64381,"rel":64382},"https:\u002F\u002Fwww.geeksforgeeks.org\u002Fblogs\u002Fspa-vs-mpa-which-one-is-better-for-you\u002F",[7760,7761],"SPA vs MPA",", solo ten presente que Vue funciona como una SPA por defecto. Selecciona esta opción.",[33,64386,64387,64390],{},[122,64388,64389],{},"Pinia (state management)",": es la librería oficial para el manejo de estado. Nos ayudará a manejar datos compartidos entre componentes. Selecciona esta opción.",[33,64392,64393,64396],{},[122,64394,64395],{},"Vitest (unit testing)",": es el framework de testing recomendado para proyectos con Vite. No lo usaremos en esta guía.",[33,64398,64399,64402,64403,93,64408,15781,64413,64418],{},[122,64400,64401],{},"End-to-End Testing",": nos permitirá elegir e integrar una herramienta para pruebas E2E (",[22,64404,64407],{"target":27,"href":64405,"rel":64406},"https:\u002F\u002Fplaywright.dev\u002F",[7760,7761],"Playwright",[22,64409,64412],{"target":27,"href":64410,"rel":64411},"https:\u002F\u002Fwww.cypress.io\u002F",[7760,7761],"Cypress",[22,64414,64417],{"target":27,"href":64415,"rel":64416},"https:\u002F\u002Fnightwatchjs.org\u002F",[7760,7761],"Nightwatch","). No lo usaremos en esta guía.",[33,64420,64421,64424],{},[122,64422,64423],{},"ESLint (error prevention)",": es una herramienta para mantener la calidad del código, ayudando a detectar errores y mantener un estilo consistente. Recomiendo mucho su uso, aunque es importante personalizarlo según tu equipo y proyecto. La seleccionaremos para explorarla un poco más adelante.",[33,64426,64427,64430],{},[122,64428,64429],{},"Prettier (code formatting)",": es una herramienta para formatear el código automáticamente. En este caso la seleccionaremos también para explorarla.",[12,64432,64433],{},"Presionamos ENTER y ahora nos preguntará sobre algunas features experimentales de Vite:",[12,64435,64436,64440],{},[1945,64437],{"alt":64438,"src":64439},"Features experimentales de Vite","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fproject-experimental-options.webp",[901,64441,64438],{},[117,64443,64444,64456],{},[33,64445,64446,64449,64450,64455],{},[122,64447,64448],{},"Oxlint",": es un nuevo linter, parte de ",[22,64451,64454],{"target":27,"href":64452,"rel":64453},"https:\u002F\u002Foxc.rs\u002F",[7760,7761],"OXC",", una nueva colección de herramientas de javascript escritas en Rust, Oxlint es en extremo rápido y promete bastante, sin embargo como se menciona en su web, aún tiene sus detalles, así que por ahora recomiendo seguir usando ESLint. Ignoramos esta opción.",[33,64457,64458,64461],{},[122,64459,64460],{},"rolldown vite (experimental)",": Rolldown-vite es una bifurcación de Vite que utiliza Rolldown en lugar de Rollup y esbuild, con el objetivo de obtener el máximo rendimiento. Pronto se convertirá en el paquete por defecto, por ahora ignoremos esta opción.",[12,64463,64464],{},"Continuamos presionando ENTER.",[12,64466,64467],{},"Nos preguntará si queremos empezar con un proyecto totalmente en blanco o con ejemplos. Si es tu primera vez, te recomiendo seleccionar \"No\" para que puedas ver una estructura básica con ejemplos. Esa será la opción que seleccionaremos aquí.",[12,64469,64470],{},"Vite creará la estructura inicial del proyecto y nos dará algunos comandos útiles, vamos ejecutando uno por uno:",[12,64472,64473,64477],{},[1945,64474],{"alt":64475,"src":64476},"Proyecto creado","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fproject-created.webp",[901,64478,64475],{},[117,64480,64481],{},[33,64482,64483],{},"Primero navegamos a la carpeta del proyecto:",[164,64485,64487],{"className":64293,"code":64486,"language":64295,"meta":169,"style":169},"cd nombre-del-proyecto\n",[145,64488,64489],{"__ignoreMap":169},[86,64490,64491,64494],{"class":174,"line":175},[86,64492,64493],{"class":812},"cd",[86,64495,64496],{"class":579}," nombre-del-proyecto\n",[117,64498,64499],{"start":192},[33,64500,64501],{},"Instalamos las dependencias (esto puede tardar unos minutos dependiendo de tu conexión):",[164,64503,64505],{"className":64293,"code":64504,"language":64295,"meta":169,"style":169},"npm install\n",[145,64506,64507],{"__ignoreMap":169},[86,64508,64509,64511],{"class":174,"line":175},[86,64510,64231],{"class":239},[86,64512,64513],{"class":579}," install\n",[117,64515,64516],{"start":205},[33,64517,64518],{},"Este comando es para correr Prettier, no tendrá ningún efecto porque no hemos modificado nada aún, pero es bueno tenerlo presente:",[164,64520,64522],{"className":64293,"code":64521,"language":64295,"meta":169,"style":169},"npm run format\n",[145,64523,64524],{"__ignoreMap":169},[86,64525,64526,64528,64531],{"class":174,"line":175},[86,64527,64231],{"class":239},[86,64529,64530],{"class":579}," run",[86,64532,64533],{"class":579}," format\n",[117,64535,64536],{"start":212},[33,64537,64538],{},"Finalmente, iniciamos el servidor de desarrollo:",[164,64540,64542],{"className":64293,"code":64541,"language":64295,"meta":169,"style":169},"npm run dev\n",[145,64543,64544],{"__ignoreMap":169},[86,64545,64546,64548,64550],{"class":174,"line":175},[86,64547,64231],{"class":239},[86,64549,64530],{"class":579},[86,64551,64552],{"class":579}," dev\n",[12,64554,64555,64559],{},[1945,64556],{"alt":64557,"src":64558},"Servidor de desarrollo corriendo","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fdev-server-running.webp",[901,64560,64561],{},"Servidor de desarrollo levantado",[12,64563,64564,64565,64568],{},"Vite corre el servidor de desarrollo en ",[145,64566,64567],{},"http:\u002F\u002Flocalhost:5173\u002F"," (el puerto puede variar si el 5173 ya está en uso (5174, 5175, etc.) ).",[16,64570,64571,64574,64588],{},[12,64572,64573],{},"El puerto 5173 es un guiño al propio Vite:",[30,64575,64576,64579,64582,64585],{},[33,64577,64578],{},"5 = V",[33,64580,64581],{},"1 = I",[33,64583,64584],{},"7 = T",[33,64586,64587],{},"3 = E",[12,64589,64590,64591,61],{},"Aunque más allá de eso, Vite utiliza el puerto 5173 porque es poco habitual en entornos de desarrollo, lo que reduce la probabilidad de conflictos con otros servidores locales. Vía ",[22,64592,64595],{"target":27,"href":64593,"rel":64594},"https:\u002F\u002Fmedium.com\u002F@bishakhghosh0\u002Fwhy-localhost-5173-is-every-frontend-developers-best-friend-b3bb5b6fb1db",[7760,7761],"Why localhost:5173 is Every Frontend Developer’s Best Friend",[12,64597,64598],{},"Si entramos a esa URL en nuestro navegador, veremos la app Vue corriendo:",[12,64600,64601,64605],{},[1945,64602],{"alt":64603,"src":64604},"App Vue corriendo","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fvue-app-running.webp",[901,64606,64603],{},[12,64608,64609,64610,64615],{},"El equipo de Vue comparte varios recursos oficiales para aprender más sobre el framework, comenzando por la ",[22,64611,64614],{"target":27,"href":64612,"rel":64613},"https:\u002F\u002Fvuejs.org\u002Fguide\u002Fintroduction.html",[7760,7761],"documentación oficial",". Explora cada enlace para aprender y conocer sobre todo el ecosistema.",[43,64617],{},[46,64619,64621],{"id":64620},"estructura-del-proyecto","Estructura del proyecto",[12,64623,64624],{},"Pasemos a ver la estructura inicial, abre el proyecto en tu editor de código favorito (recomiendo VS Code):",[164,64626,64628],{"className":64293,"code":64627,"language":64295,"meta":169,"style":169},"my-vue-app\u002F\n├── .vscode\u002F              # (Si estás en VS Code) Configuración de Visual Studio Code\n├── node_modules\u002F         # Dependencias del proyecto, generadas al instalar los paquetes\n├── public\u002F               # Archivos estáticos\n├── src\u002F                  # Código fuente de la aplicación\n│   ├── assets\u002F           # Recursos como imágenes y estilos\n│   ├── components\u002F       # Componentes Vue reutilizables\n│   ├── router\u002F           # Configuración de Vue Router\n│   ├── store\u002F            # Configuración de Pinia\n│   ├── views\u002F            # Vistas para las rutas\n│   ├── App.vue           # Componente raíz de la aplicación\n│   └── main.js           # Punto de entrada de la aplicación\n├── .editorconfig         # Configuración de EditorConfig\n├── .gitattributes        # Configuración de Git\n├── .gitignore            # Archivos y carpetas ignoradas por Git\n├── .prettierrc.json      # Configuración de Prettier\n├── eslint.config.js      # Configuración de ESLint\n├── index.html            # Archivo HTML principal\n├── jsconfig.json         # Configuración de JavaScript para el editor\n├── package-lock.json     # Versiones exactas de las dependencias (autogenerado)\n├── package.json          # Información del proyecto y scripts\n├── README.md             # Documentación del proyecto\n└── vite.config.js        # Configuración de Vite\n",[145,64629,64630,64635,64646,64656,64666,64676,64690,64702,64714,64726,64738,64750,64763,64773,64783,64793,64803,64813,64823,64833,64843,64853,64863],{"__ignoreMap":169},[86,64631,64632],{"class":174,"line":175},[86,64633,64634],{"class":239},"my-vue-app\u002F\n",[86,64636,64637,64640,64643],{"class":174,"line":192},[86,64638,64639],{"class":239},"├──",[86,64641,64642],{"class":579}," .vscode\u002F",[86,64644,64645],{"class":1360},"              # (Si estás en VS Code) Configuración de Visual Studio Code\n",[86,64647,64648,64650,64653],{"class":174,"line":205},[86,64649,64639],{"class":239},[86,64651,64652],{"class":579}," node_modules\u002F",[86,64654,64655],{"class":1360},"         # Dependencias del proyecto, generadas al instalar los paquetes\n",[86,64657,64658,64660,64663],{"class":174,"line":212},[86,64659,64639],{"class":239},[86,64661,64662],{"class":579}," public\u002F",[86,64664,64665],{"class":1360},"               # Archivos estáticos\n",[86,64667,64668,64670,64673],{"class":174,"line":227},[86,64669,64639],{"class":239},[86,64671,64672],{"class":579}," src\u002F",[86,64674,64675],{"class":1360},"                  # Código fuente de la aplicación\n",[86,64677,64678,64681,64684,64687],{"class":174,"line":232},[86,64679,64680],{"class":239},"│",[86,64682,64683],{"class":579},"   ├──",[86,64685,64686],{"class":579}," assets\u002F",[86,64688,64689],{"class":1360},"           # Recursos como imágenes y estilos\n",[86,64691,64692,64694,64696,64699],{"class":174,"line":252},[86,64693,64680],{"class":239},[86,64695,64683],{"class":579},[86,64697,64698],{"class":579}," components\u002F",[86,64700,64701],{"class":1360},"       # Componentes Vue reutilizables\n",[86,64703,64704,64706,64708,64711],{"class":174,"line":276},[86,64705,64680],{"class":239},[86,64707,64683],{"class":579},[86,64709,64710],{"class":579}," router\u002F",[86,64712,64713],{"class":1360},"           # Configuración de Vue Router\n",[86,64715,64716,64718,64720,64723],{"class":174,"line":315},[86,64717,64680],{"class":239},[86,64719,64683],{"class":579},[86,64721,64722],{"class":579}," store\u002F",[86,64724,64725],{"class":1360},"            # Configuración de Pinia\n",[86,64727,64728,64730,64732,64735],{"class":174,"line":3665},[86,64729,64680],{"class":239},[86,64731,64683],{"class":579},[86,64733,64734],{"class":579}," views\u002F",[86,64736,64737],{"class":1360},"            # Vistas para las rutas\n",[86,64739,64740,64742,64744,64747],{"class":174,"line":13256},[86,64741,64680],{"class":239},[86,64743,64683],{"class":579},[86,64745,64746],{"class":579}," App.vue",[86,64748,64749],{"class":1360},"           # Componente raíz de la aplicación\n",[86,64751,64752,64754,64757,64760],{"class":174,"line":13286},[86,64753,64680],{"class":239},[86,64755,64756],{"class":579},"   └──",[86,64758,64759],{"class":579}," main.js",[86,64761,64762],{"class":1360},"           # Punto de entrada de la aplicación\n",[86,64764,64765,64767,64770],{"class":174,"line":13291},[86,64766,64639],{"class":239},[86,64768,64769],{"class":579}," .editorconfig",[86,64771,64772],{"class":1360},"         # Configuración de EditorConfig\n",[86,64774,64775,64777,64780],{"class":174,"line":13308},[86,64776,64639],{"class":239},[86,64778,64779],{"class":579}," .gitattributes",[86,64781,64782],{"class":1360},"        # Configuración de Git\n",[86,64784,64785,64787,64790],{"class":174,"line":13334},[86,64786,64639],{"class":239},[86,64788,64789],{"class":579}," .gitignore",[86,64791,64792],{"class":1360},"            # Archivos y carpetas ignoradas por Git\n",[86,64794,64795,64797,64800],{"class":174,"line":13359},[86,64796,64639],{"class":239},[86,64798,64799],{"class":579}," .prettierrc.json",[86,64801,64802],{"class":1360},"      # Configuración de Prettier\n",[86,64804,64805,64807,64810],{"class":174,"line":13385},[86,64806,64639],{"class":239},[86,64808,64809],{"class":579}," eslint.config.js",[86,64811,64812],{"class":1360},"      # Configuración de ESLint\n",[86,64814,64815,64817,64820],{"class":174,"line":13390},[86,64816,64639],{"class":239},[86,64818,64819],{"class":579}," index.html",[86,64821,64822],{"class":1360},"            # Archivo HTML principal\n",[86,64824,64825,64827,64830],{"class":174,"line":13396},[86,64826,64639],{"class":239},[86,64828,64829],{"class":579}," jsconfig.json",[86,64831,64832],{"class":1360},"         # Configuración de JavaScript para el editor\n",[86,64834,64835,64837,64840],{"class":174,"line":3615},[86,64836,64639],{"class":239},[86,64838,64839],{"class":579}," package-lock.json",[86,64841,64842],{"class":1360},"     # Versiones exactas de las dependencias (autogenerado)\n",[86,64844,64845,64847,64850],{"class":174,"line":2254},[86,64846,64639],{"class":239},[86,64848,64849],{"class":579}," package.json",[86,64851,64852],{"class":1360},"          # Información del proyecto y scripts\n",[86,64854,64855,64857,64860],{"class":174,"line":13492},[86,64856,64639],{"class":239},[86,64858,64859],{"class":579}," README.md",[86,64861,64862],{"class":1360},"             # Documentación del proyecto\n",[86,64864,64865,64868,64871],{"class":174,"line":13545},[86,64866,64867],{"class":239},"└──",[86,64869,64870],{"class":579}," vite.config.js",[86,64872,64873],{"class":1360},"        # Configuración de Vite\n",[12,64875,64876,64877,64880],{},"La estructura puede variar ligeramente dependiendo de las opciones seleccionadas al crear el proyecto (por ejemplo, si se incluye o no ESLint o Pinia). Además, si estás usando VS Code es probable que veas la carpeta ",[145,64878,64879],{},".vscode\u002F"," con configuraciones específicas para el editor y que algunos archivos los veas \"agrupados\":",[12,64882,64883,64887],{},[1945,64884],{"alt":64885,"src":64886},"Estructura del proyecto en VS Code","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fproject-structure-nested.webp",[901,64888,64885],{},[12,64890,64891,64892,64895,64896,64898,64899,61],{},"Esto es solo una forma visual que tiene VS Code para organizar los archivos, puedes mostrarlos individualmente (opción que prefiero) cambiando el valor de ",[145,64893,64894],{},"\"explorer.fileNesting.enabled\""," a ",[145,64897,3295],{}," en el archivo ",[145,64900,64901],{},".vscode\\settings.json",[323,64903,64905],{"id":64904},"entendiendo-las-carpetas-principales","Entendiendo las carpetas principales",[30,64907,64908,64914],{},[33,64909,64910,64913],{},[145,64911,64912],{},"public\u002F",": Aquí van los archivos estáticos que no serán procesados por Vite. Puedes colocar imágenes, fuentes u otros recursos que necesites servir directamente.",[33,64915,64916,64919,64920],{},[145,64917,64918],{},"src\u002F",": Esta es la carpeta más importante, contiene todo el código fuente de tu aplicación. Aquí tenemos:\n",[30,64921,64922,64928,64934,64946,64962,64972,64978],{},[33,64923,64924,64927],{},[145,64925,64926],{},"assets\u002F",": Aquí van los recursos como imágenes, fuentes y estilos CSS.",[33,64929,64930,64933],{},[145,64931,64932],{},"components\u002F",": Aquí van los componentes Vue globales, reutilizables, que puedes usar en diferentes partes de tu aplicación, por ejemplo, botones, tarjetas, modales, etc.",[33,64935,64936,64939,64940,64945],{},[145,64937,64938],{},"router\u002F",": Aquí va la configuración de ",[22,64941,64944],{"href":64942,"target":27,"rel":64943},"https:\u002F\u002Frouter.vuejs.org\u002F",[7760,7761],"Vue Router",", donde defines las rutas de tu aplicación y cómo se navega entre ellas, así como la posible configuración de guards, lazy loading, etc.",[33,64947,64948,64939,64951,64956,64957],{},[145,64949,64950],{},"store\u002F",[22,64952,64955],{"href":64953,"target":27,"rel":64954},"https:\u002F\u002Fpinia.vuejs.org\u002F",[7760,7761],"Pinia",", donde defines el ",[22,64958,64961],{"href":64959,"target":27,"rel":64960},"https:\u002F\u002Fkinsta.com\u002Fes\u002Fblog\u002Fvue-pinia\u002F",[7760,7761],"estado global de tu aplicación. ",[33,64963,64964,64967,64968,64971],{},[145,64965,64966],{},"views\u002F",": Aquí van las vistas principales que corresponden a las rutas definidas en Vue Router. Cada vista generalmente representa una página completa, caso contrario a los componentes que son partes más pequeñas y reutilizables. A final todos son archivos ",[145,64969,64970],{},".vue",", por lo que la diferencia radica en su propósito y uso.",[33,64973,64974,64977],{},[145,64975,64976],{},"App.vue",": Este es el componente raíz de tu aplicación, donde se monta todo (ya explicaremos más adelante).",[33,64979,64980,64983],{},[145,64981,64982],{},"main.js",": Este es el punto de entrada de tu aplicación, donde se inicializa Vue, se configuran los plugins (como Vue Router y Pinia) y se monta la aplicación en el DOM.",[323,64985,64987],{"id":64986},"es-suficiente-esta-estructura","¿Es suficiente esta estructura?",[12,64989,64990],{},"Es una estructura básica que por ahora está bien. A medida que tu aplicación crezca normalmente se busca organizar mejor el código. Aquí hay dos propuestas:",[30,64992,64993],{},[33,64994,64995,64996,392,64998,65000],{},"Crear subcarpetas por módulo\u002Ffuncionalidad dentro de las distintas carpetas, como ",[145,64997,64932],{},[145,64999,64966],{},". Por ejemplo:",[164,65002,65004],{"className":64293,"code":65003,"language":64295,"meta":169,"style":169},"my-vue-app\u002F\n├── src\u002F\n│   ├── assets\u002F\n│   ├── components\u002F\n│   │   ├── auth\u002F\n│   │   │   ├── LoginForm.vue\n│   │   │   └── RegisterForm.vue\n│   │   ├── dashboard\u002F\n│   │   │   ├── StatsCard.vue\n│   │   │   └── ChartWidget.vue\n│   │   └── shared\u002F\n│   │       ├── BaseButton.vue\n│   │       └── BaseModal.vue\n│   │\n│   ├── views\u002F\n│   │   ├── auth\u002F\n│   │   │   ├── LoginView.vue\n│   │   │   └── RegisterView.vue\n│   │   ├── dashboard\u002F\n│   │   │   └── DashboardView.vue\n│   │   └── home\u002F\n│   │       └── HomeView.vue\n│   │\n│   ├── store\u002F\n│   │   ├── auth\u002F\n│   │   │   └── auth.store.js\n│   │   ├── dashboard\u002F\n│   │   │   └── dashboard.store.js\n│   │   └── shared\u002F\n│   │       └── ui.store.js\n│   │\n│   ├── router\u002F\n│   │   ├── auth.routes.js\n│   │   ├── dashboard.routes.js\n│   │   └── index.js\n│   │\n│   ├── ...\n├── ...\n",[145,65005,65006,65010,65017,65026,65035,65047,65060,65073,65084,65097,65110,65121,65133,65145,65152,65161,65171,65184,65197,65207,65220,65231,65242,65248,65257,65267,65280,65290,65303,65313,65324,65330,65339,65350,65361,65372,65378,65387],{"__ignoreMap":169},[86,65007,65008],{"class":174,"line":175},[86,65009,64634],{"class":239},[86,65011,65012,65014],{"class":174,"line":192},[86,65013,64639],{"class":239},[86,65015,65016],{"class":579}," src\u002F\n",[86,65018,65019,65021,65023],{"class":174,"line":205},[86,65020,64680],{"class":239},[86,65022,64683],{"class":579},[86,65024,65025],{"class":579}," assets\u002F\n",[86,65027,65028,65030,65032],{"class":174,"line":212},[86,65029,64680],{"class":239},[86,65031,64683],{"class":579},[86,65033,65034],{"class":579}," components\u002F\n",[86,65036,65037,65039,65042,65044],{"class":174,"line":227},[86,65038,64680],{"class":239},[86,65040,65041],{"class":579},"   │",[86,65043,64683],{"class":579},[86,65045,65046],{"class":579}," auth\u002F\n",[86,65048,65049,65051,65053,65055,65057],{"class":174,"line":232},[86,65050,64680],{"class":239},[86,65052,65041],{"class":579},[86,65054,65041],{"class":579},[86,65056,64683],{"class":579},[86,65058,65059],{"class":579}," LoginForm.vue\n",[86,65061,65062,65064,65066,65068,65070],{"class":174,"line":252},[86,65063,64680],{"class":239},[86,65065,65041],{"class":579},[86,65067,65041],{"class":579},[86,65069,64756],{"class":579},[86,65071,65072],{"class":579}," RegisterForm.vue\n",[86,65074,65075,65077,65079,65081],{"class":174,"line":276},[86,65076,64680],{"class":239},[86,65078,65041],{"class":579},[86,65080,64683],{"class":579},[86,65082,65083],{"class":579}," dashboard\u002F\n",[86,65085,65086,65088,65090,65092,65094],{"class":174,"line":315},[86,65087,64680],{"class":239},[86,65089,65041],{"class":579},[86,65091,65041],{"class":579},[86,65093,64683],{"class":579},[86,65095,65096],{"class":579}," StatsCard.vue\n",[86,65098,65099,65101,65103,65105,65107],{"class":174,"line":3665},[86,65100,64680],{"class":239},[86,65102,65041],{"class":579},[86,65104,65041],{"class":579},[86,65106,64756],{"class":579},[86,65108,65109],{"class":579}," ChartWidget.vue\n",[86,65111,65112,65114,65116,65118],{"class":174,"line":13256},[86,65113,64680],{"class":239},[86,65115,65041],{"class":579},[86,65117,64756],{"class":579},[86,65119,65120],{"class":579}," shared\u002F\n",[86,65122,65123,65125,65127,65130],{"class":174,"line":13286},[86,65124,64680],{"class":239},[86,65126,65041],{"class":579},[86,65128,65129],{"class":579},"       ├──",[86,65131,65132],{"class":579}," BaseButton.vue\n",[86,65134,65135,65137,65139,65142],{"class":174,"line":13291},[86,65136,64680],{"class":239},[86,65138,65041],{"class":579},[86,65140,65141],{"class":579},"       └──",[86,65143,65144],{"class":579}," BaseModal.vue\n",[86,65146,65147,65149],{"class":174,"line":13308},[86,65148,64680],{"class":239},[86,65150,65151],{"class":579},"   │\n",[86,65153,65154,65156,65158],{"class":174,"line":13334},[86,65155,64680],{"class":239},[86,65157,64683],{"class":579},[86,65159,65160],{"class":579}," views\u002F\n",[86,65162,65163,65165,65167,65169],{"class":174,"line":13359},[86,65164,64680],{"class":239},[86,65166,65041],{"class":579},[86,65168,64683],{"class":579},[86,65170,65046],{"class":579},[86,65172,65173,65175,65177,65179,65181],{"class":174,"line":13385},[86,65174,64680],{"class":239},[86,65176,65041],{"class":579},[86,65178,65041],{"class":579},[86,65180,64683],{"class":579},[86,65182,65183],{"class":579}," LoginView.vue\n",[86,65185,65186,65188,65190,65192,65194],{"class":174,"line":13390},[86,65187,64680],{"class":239},[86,65189,65041],{"class":579},[86,65191,65041],{"class":579},[86,65193,64756],{"class":579},[86,65195,65196],{"class":579}," RegisterView.vue\n",[86,65198,65199,65201,65203,65205],{"class":174,"line":13396},[86,65200,64680],{"class":239},[86,65202,65041],{"class":579},[86,65204,64683],{"class":579},[86,65206,65083],{"class":579},[86,65208,65209,65211,65213,65215,65217],{"class":174,"line":3615},[86,65210,64680],{"class":239},[86,65212,65041],{"class":579},[86,65214,65041],{"class":579},[86,65216,64756],{"class":579},[86,65218,65219],{"class":579}," DashboardView.vue\n",[86,65221,65222,65224,65226,65228],{"class":174,"line":2254},[86,65223,64680],{"class":239},[86,65225,65041],{"class":579},[86,65227,64756],{"class":579},[86,65229,65230],{"class":579}," home\u002F\n",[86,65232,65233,65235,65237,65239],{"class":174,"line":13492},[86,65234,64680],{"class":239},[86,65236,65041],{"class":579},[86,65238,65141],{"class":579},[86,65240,65241],{"class":579}," HomeView.vue\n",[86,65243,65244,65246],{"class":174,"line":13545},[86,65245,64680],{"class":239},[86,65247,65151],{"class":579},[86,65249,65250,65252,65254],{"class":174,"line":13550},[86,65251,64680],{"class":239},[86,65253,64683],{"class":579},[86,65255,65256],{"class":579}," store\u002F\n",[86,65258,65259,65261,65263,65265],{"class":174,"line":13566},[86,65260,64680],{"class":239},[86,65262,65041],{"class":579},[86,65264,64683],{"class":579},[86,65266,65046],{"class":579},[86,65268,65269,65271,65273,65275,65277],{"class":174,"line":13591},[86,65270,64680],{"class":239},[86,65272,65041],{"class":579},[86,65274,65041],{"class":579},[86,65276,64756],{"class":579},[86,65278,65279],{"class":579}," auth.store.js\n",[86,65281,65282,65284,65286,65288],{"class":174,"line":13616},[86,65283,64680],{"class":239},[86,65285,65041],{"class":579},[86,65287,64683],{"class":579},[86,65289,65083],{"class":579},[86,65291,65292,65294,65296,65298,65300],{"class":174,"line":13641},[86,65293,64680],{"class":239},[86,65295,65041],{"class":579},[86,65297,65041],{"class":579},[86,65299,64756],{"class":579},[86,65301,65302],{"class":579}," dashboard.store.js\n",[86,65304,65305,65307,65309,65311],{"class":174,"line":37784},[86,65306,64680],{"class":239},[86,65308,65041],{"class":579},[86,65310,64756],{"class":579},[86,65312,65120],{"class":579},[86,65314,65315,65317,65319,65321],{"class":174,"line":37795},[86,65316,64680],{"class":239},[86,65318,65041],{"class":579},[86,65320,65141],{"class":579},[86,65322,65323],{"class":579}," ui.store.js\n",[86,65325,65326,65328],{"class":174,"line":37807},[86,65327,64680],{"class":239},[86,65329,65151],{"class":579},[86,65331,65332,65334,65336],{"class":174,"line":37822},[86,65333,64680],{"class":239},[86,65335,64683],{"class":579},[86,65337,65338],{"class":579}," router\u002F\n",[86,65340,65341,65343,65345,65347],{"class":174,"line":37837},[86,65342,64680],{"class":239},[86,65344,65041],{"class":579},[86,65346,64683],{"class":579},[86,65348,65349],{"class":579}," auth.routes.js\n",[86,65351,65352,65354,65356,65358],{"class":174,"line":37852},[86,65353,64680],{"class":239},[86,65355,65041],{"class":579},[86,65357,64683],{"class":579},[86,65359,65360],{"class":579}," dashboard.routes.js\n",[86,65362,65363,65365,65367,65369],{"class":174,"line":37867},[86,65364,64680],{"class":239},[86,65366,65041],{"class":579},[86,65368,64756],{"class":579},[86,65370,65371],{"class":579}," index.js\n",[86,65373,65374,65376],{"class":174,"line":37882},[86,65375,64680],{"class":239},[86,65377,65151],{"class":579},[86,65379,65380,65382,65384],{"class":174,"line":37887},[86,65381,64680],{"class":239},[86,65383,64683],{"class":579},[86,65385,65386],{"class":579}," ...\n",[86,65388,65389,65391],{"class":174,"line":37911},[86,65390,64639],{"class":239},[86,65392,65386],{"class":579},[12,65394,65395,65398,65399,65402],{},[122,65396,65397],{},"Puedes usar un enfoque similar a este"," en apps pequeñas o medianas, con poca gente trabajando, en las que quieres un poco más de orden sin complicarte demasiado y sin cambiar demasiado la estructura original que propone Vue. ",[122,65400,65401],{},"La limitante"," es que a medida que la app crece, puede volverse difícil manejar dependencias entre módulos y mantener el código organizado, porque todo está disperso en varias carpetas.",[30,65404,65405],{},[33,65406,65407],{},"En otros casos, puedes optar por una estructura basada en funcionalidades o módulos, donde cada uno tiene su propia carpeta que contiene componentes, vistas, y lógica relacionada. Por ejemplo:",[164,65409,65411],{"className":64293,"code":65410,"language":64295,"meta":169,"style":169},"my-vue-app\u002F\n├── src\u002F\n│   ├── modules\u002F\n│   │   ├── auth\u002F                     # Si el módulo es pequeño, puedes omitir la división en carpetas\n│   │   │   ├── components\u002F\n│   │   │   │   └── LoginForm.vue\n│   │   │   ├── views\u002F\n│   │   │   │   └── LoginView.vue\n│   │   │   ├── store\u002F\n│   │   │   │   └── auth.store.js\n│   │   │   ├── router\u002F\n│   │   │   │   └── auth.routes.js\n│   │   │   └── index.js\n│   │   │\n│   │   ├── dashboard\u002F\n│   │   │   ├── components\u002F\n│   │   │   ├── views\u002F\n│   │   │   ├── store\u002F\n│   │   │   ├── router\u002F\n│   │   │   └── index.js\n│   │   │\n│   │   └── users\u002F\n│   │       ├── components\u002F\n│   │       ├── views\u002F\n│   │       ├── store\u002F\n│   │       ├── router\u002F\n│   │       └── index.js\n│   │\n│   ├── shared\u002F\n│   │   ├── components\u002F\n│   │   │   ├── BaseButton.vue\n│   │   │   └── BaseModal.vue\n│   │   ├── composables\u002F\n│   │   │   └── useFetch.js\n│   │   ├── store\u002F\n│   │   │   └── ui.store.js\n│   │   ├── utils\u002F\n│   │   │   └── formatDate.js\n│   │   └── constants\u002F\n│   │       └── roles.js\n│   │\n│   ├── router\u002F\n│   │   └── index.js                # Archivo principal del router que importa las rutas de los módulos\n│   │                               # (los guards van aquí)\n│   ├── ...\n├── ...\n",[145,65412,65413,65417,65423,65432,65446,65458,65472,65484,65498,65510,65524,65536,65550,65562,65570,65580,65592,65604,65616,65628,65640,65648,65659,65669,65679,65689,65699,65709,65715,65723,65733,65745,65757,65768,65781,65791,65803,65814,65827,65838,65849,65855,65863,65877,65886,65894],{"__ignoreMap":169},[86,65414,65415],{"class":174,"line":175},[86,65416,64634],{"class":239},[86,65418,65419,65421],{"class":174,"line":192},[86,65420,64639],{"class":239},[86,65422,65016],{"class":579},[86,65424,65425,65427,65429],{"class":174,"line":205},[86,65426,64680],{"class":239},[86,65428,64683],{"class":579},[86,65430,65431],{"class":579}," modules\u002F\n",[86,65433,65434,65436,65438,65440,65443],{"class":174,"line":212},[86,65435,64680],{"class":239},[86,65437,65041],{"class":579},[86,65439,64683],{"class":579},[86,65441,65442],{"class":579}," auth\u002F",[86,65444,65445],{"class":1360},"                     # Si el módulo es pequeño, puedes omitir la división en carpetas\n",[86,65447,65448,65450,65452,65454,65456],{"class":174,"line":227},[86,65449,64680],{"class":239},[86,65451,65041],{"class":579},[86,65453,65041],{"class":579},[86,65455,64683],{"class":579},[86,65457,65034],{"class":579},[86,65459,65460,65462,65464,65466,65468,65470],{"class":174,"line":232},[86,65461,64680],{"class":239},[86,65463,65041],{"class":579},[86,65465,65041],{"class":579},[86,65467,65041],{"class":579},[86,65469,64756],{"class":579},[86,65471,65059],{"class":579},[86,65473,65474,65476,65478,65480,65482],{"class":174,"line":252},[86,65475,64680],{"class":239},[86,65477,65041],{"class":579},[86,65479,65041],{"class":579},[86,65481,64683],{"class":579},[86,65483,65160],{"class":579},[86,65485,65486,65488,65490,65492,65494,65496],{"class":174,"line":276},[86,65487,64680],{"class":239},[86,65489,65041],{"class":579},[86,65491,65041],{"class":579},[86,65493,65041],{"class":579},[86,65495,64756],{"class":579},[86,65497,65183],{"class":579},[86,65499,65500,65502,65504,65506,65508],{"class":174,"line":315},[86,65501,64680],{"class":239},[86,65503,65041],{"class":579},[86,65505,65041],{"class":579},[86,65507,64683],{"class":579},[86,65509,65256],{"class":579},[86,65511,65512,65514,65516,65518,65520,65522],{"class":174,"line":3665},[86,65513,64680],{"class":239},[86,65515,65041],{"class":579},[86,65517,65041],{"class":579},[86,65519,65041],{"class":579},[86,65521,64756],{"class":579},[86,65523,65279],{"class":579},[86,65525,65526,65528,65530,65532,65534],{"class":174,"line":13256},[86,65527,64680],{"class":239},[86,65529,65041],{"class":579},[86,65531,65041],{"class":579},[86,65533,64683],{"class":579},[86,65535,65338],{"class":579},[86,65537,65538,65540,65542,65544,65546,65548],{"class":174,"line":13286},[86,65539,64680],{"class":239},[86,65541,65041],{"class":579},[86,65543,65041],{"class":579},[86,65545,65041],{"class":579},[86,65547,64756],{"class":579},[86,65549,65349],{"class":579},[86,65551,65552,65554,65556,65558,65560],{"class":174,"line":13291},[86,65553,64680],{"class":239},[86,65555,65041],{"class":579},[86,65557,65041],{"class":579},[86,65559,64756],{"class":579},[86,65561,65371],{"class":579},[86,65563,65564,65566,65568],{"class":174,"line":13308},[86,65565,64680],{"class":239},[86,65567,65041],{"class":579},[86,65569,65151],{"class":579},[86,65571,65572,65574,65576,65578],{"class":174,"line":13334},[86,65573,64680],{"class":239},[86,65575,65041],{"class":579},[86,65577,64683],{"class":579},[86,65579,65083],{"class":579},[86,65581,65582,65584,65586,65588,65590],{"class":174,"line":13359},[86,65583,64680],{"class":239},[86,65585,65041],{"class":579},[86,65587,65041],{"class":579},[86,65589,64683],{"class":579},[86,65591,65034],{"class":579},[86,65593,65594,65596,65598,65600,65602],{"class":174,"line":13385},[86,65595,64680],{"class":239},[86,65597,65041],{"class":579},[86,65599,65041],{"class":579},[86,65601,64683],{"class":579},[86,65603,65160],{"class":579},[86,65605,65606,65608,65610,65612,65614],{"class":174,"line":13390},[86,65607,64680],{"class":239},[86,65609,65041],{"class":579},[86,65611,65041],{"class":579},[86,65613,64683],{"class":579},[86,65615,65256],{"class":579},[86,65617,65618,65620,65622,65624,65626],{"class":174,"line":13396},[86,65619,64680],{"class":239},[86,65621,65041],{"class":579},[86,65623,65041],{"class":579},[86,65625,64683],{"class":579},[86,65627,65338],{"class":579},[86,65629,65630,65632,65634,65636,65638],{"class":174,"line":3615},[86,65631,64680],{"class":239},[86,65633,65041],{"class":579},[86,65635,65041],{"class":579},[86,65637,64756],{"class":579},[86,65639,65371],{"class":579},[86,65641,65642,65644,65646],{"class":174,"line":2254},[86,65643,64680],{"class":239},[86,65645,65041],{"class":579},[86,65647,65151],{"class":579},[86,65649,65650,65652,65654,65656],{"class":174,"line":13492},[86,65651,64680],{"class":239},[86,65653,65041],{"class":579},[86,65655,64756],{"class":579},[86,65657,65658],{"class":579}," users\u002F\n",[86,65660,65661,65663,65665,65667],{"class":174,"line":13545},[86,65662,64680],{"class":239},[86,65664,65041],{"class":579},[86,65666,65129],{"class":579},[86,65668,65034],{"class":579},[86,65670,65671,65673,65675,65677],{"class":174,"line":13550},[86,65672,64680],{"class":239},[86,65674,65041],{"class":579},[86,65676,65129],{"class":579},[86,65678,65160],{"class":579},[86,65680,65681,65683,65685,65687],{"class":174,"line":13566},[86,65682,64680],{"class":239},[86,65684,65041],{"class":579},[86,65686,65129],{"class":579},[86,65688,65256],{"class":579},[86,65690,65691,65693,65695,65697],{"class":174,"line":13591},[86,65692,64680],{"class":239},[86,65694,65041],{"class":579},[86,65696,65129],{"class":579},[86,65698,65338],{"class":579},[86,65700,65701,65703,65705,65707],{"class":174,"line":13616},[86,65702,64680],{"class":239},[86,65704,65041],{"class":579},[86,65706,65141],{"class":579},[86,65708,65371],{"class":579},[86,65710,65711,65713],{"class":174,"line":13641},[86,65712,64680],{"class":239},[86,65714,65151],{"class":579},[86,65716,65717,65719,65721],{"class":174,"line":37784},[86,65718,64680],{"class":239},[86,65720,64683],{"class":579},[86,65722,65120],{"class":579},[86,65724,65725,65727,65729,65731],{"class":174,"line":37795},[86,65726,64680],{"class":239},[86,65728,65041],{"class":579},[86,65730,64683],{"class":579},[86,65732,65034],{"class":579},[86,65734,65735,65737,65739,65741,65743],{"class":174,"line":37807},[86,65736,64680],{"class":239},[86,65738,65041],{"class":579},[86,65740,65041],{"class":579},[86,65742,64683],{"class":579},[86,65744,65132],{"class":579},[86,65746,65747,65749,65751,65753,65755],{"class":174,"line":37822},[86,65748,64680],{"class":239},[86,65750,65041],{"class":579},[86,65752,65041],{"class":579},[86,65754,64756],{"class":579},[86,65756,65144],{"class":579},[86,65758,65759,65761,65763,65765],{"class":174,"line":37837},[86,65760,64680],{"class":239},[86,65762,65041],{"class":579},[86,65764,64683],{"class":579},[86,65766,65767],{"class":579}," composables\u002F\n",[86,65769,65770,65772,65774,65776,65778],{"class":174,"line":37852},[86,65771,64680],{"class":239},[86,65773,65041],{"class":579},[86,65775,65041],{"class":579},[86,65777,64756],{"class":579},[86,65779,65780],{"class":579}," useFetch.js\n",[86,65782,65783,65785,65787,65789],{"class":174,"line":37867},[86,65784,64680],{"class":239},[86,65786,65041],{"class":579},[86,65788,64683],{"class":579},[86,65790,65256],{"class":579},[86,65792,65793,65795,65797,65799,65801],{"class":174,"line":37882},[86,65794,64680],{"class":239},[86,65796,65041],{"class":579},[86,65798,65041],{"class":579},[86,65800,64756],{"class":579},[86,65802,65323],{"class":579},[86,65804,65805,65807,65809,65811],{"class":174,"line":37887},[86,65806,64680],{"class":239},[86,65808,65041],{"class":579},[86,65810,64683],{"class":579},[86,65812,65813],{"class":579}," utils\u002F\n",[86,65815,65816,65818,65820,65822,65824],{"class":174,"line":37911},[86,65817,64680],{"class":239},[86,65819,65041],{"class":579},[86,65821,65041],{"class":579},[86,65823,64756],{"class":579},[86,65825,65826],{"class":579}," formatDate.js\n",[86,65828,65829,65831,65833,65835],{"class":174,"line":37934},[86,65830,64680],{"class":239},[86,65832,65041],{"class":579},[86,65834,64756],{"class":579},[86,65836,65837],{"class":579}," constants\u002F\n",[86,65839,65840,65842,65844,65846],{"class":174,"line":37957},[86,65841,64680],{"class":239},[86,65843,65041],{"class":579},[86,65845,65141],{"class":579},[86,65847,65848],{"class":579}," roles.js\n",[86,65850,65851,65853],{"class":174,"line":37980},[86,65852,64680],{"class":239},[86,65854,65151],{"class":579},[86,65856,65857,65859,65861],{"class":174,"line":38008},[86,65858,64680],{"class":239},[86,65860,64683],{"class":579},[86,65862,65338],{"class":579},[86,65864,65865,65867,65869,65871,65874],{"class":174,"line":38013},[86,65866,64680],{"class":239},[86,65868,65041],{"class":579},[86,65870,64756],{"class":579},[86,65872,65873],{"class":579}," index.js",[86,65875,65876],{"class":1360},"                # Archivo principal del router que importa las rutas de los módulos\n",[86,65878,65879,65881,65883],{"class":174,"line":38019},[86,65880,64680],{"class":239},[86,65882,65041],{"class":579},[86,65884,65885],{"class":1360},"                               # (los guards van aquí)\n",[86,65887,65888,65890,65892],{"class":174,"line":38067},[86,65889,64680],{"class":239},[86,65891,64683],{"class":579},[86,65893,65386],{"class":579},[86,65895,65896,65898],{"class":174,"line":38156},[86,65897,64639],{"class":239},[86,65899,65386],{"class":579},[12,65901,65902,65903,65906],{},"Cada módulo o funcionalidad concentra ",[122,65904,65905],{},"todo lo que necesita en un solo lugar",", lo que simplifica la navegación y facilita el mantenimiento del código. Este enfoque resulta especialmente beneficioso en aplicaciones grandes o complejas.",[12,65908,65909,65910,65913],{},"La carpeta ",[145,65911,65912],{},"shared\u002F"," nos sirve para almacenar componentes, composables, utilidades y constantes que son reutilizables en toda la aplicación (solo ten cuidado de no sobrecargarla).",[12,65915,65916,65917,65920],{},"La base de este enfoque consiste en dividir la aplicación en módulos independientes dentro de ",[145,65918,65919],{},"\u002Fsrc\u002Fmodules",", cada uno con su propia estructura interna.",[16,65922,65923],{},[12,65924,65925,65926,65931],{},"Al final, la elección depende del tamaño y complejidad de tu proyecto, así como de las ",[122,65927,65928],{},[901,65929,65930],{},"preferencias de tu equipo",", asi que no hay una única forma correcta de hacerlo. Estos son solo ejemplos para inspirarte.",[43,65933],{},[46,65935,65937],{"id":65936},"entendiendo-como-se-monta-la-app-vue","Entendiendo como se monta la app Vue",[12,65939,65940,65941,65944,65945,162],{},"El punto de entrada de la aplicación Vue en sí, es el archivo ",[145,65942,65943],{},"src\u002Fmain.js",", aquí es donde se inicializa, se configuran los plugins y se monta en el DOM. Si vemos el archivo ",[145,65946,65943],{},[164,65948,65952],{"className":65949,"code":65950,"language":65951,"meta":169,"style":169},"language-javascript shiki shiki-themes vitesse-light vitesse-dark","import '.\u002Fassets\u002Fmain.css';\n\nimport { createApp } from 'vue';\nimport { createPinia } from 'pinia';\n\nimport App from '.\u002FApp.vue';\nimport router from '.\u002Frouter';\n\nconst app = createApp(App);\n\napp.use(createPinia());\napp.use(router);\n\napp.mount('#app');\n","javascript",[145,65953,65954,65968,65972,65997,66019,66023,66041,66059,66063,66083,66087,66105,66120,66124],{"__ignoreMap":169},[86,65955,65956,65958,65960,65963,65965],{"class":174,"line":175},[86,65957,179],{"class":178},[86,65959,11970],{"class":575},[86,65961,65962],{"class":579},".\u002Fassets\u002Fmain.css",[86,65964,10971],{"class":575},[86,65966,65967],{"class":219},";\n",[86,65969,65970],{"class":174,"line":192},[86,65971,209],{"emptyLinePlaceholder":208},[86,65973,65974,65976,65979,65982,65985,65988,65990,65993,65995],{"class":174,"line":205},[86,65975,179],{"class":178},[86,65977,65978],{"class":219}," {",[86,65980,65981],{"class":304}," createApp",[86,65983,65984],{"class":219}," }",[86,65986,65987],{"class":178}," from",[86,65989,11970],{"class":575},[86,65991,65992],{"class":579},"vue",[86,65994,10971],{"class":575},[86,65996,65967],{"class":219},[86,65998,65999,66001,66003,66006,66008,66010,66012,66015,66017],{"class":174,"line":212},[86,66000,179],{"class":178},[86,66002,65978],{"class":219},[86,66004,66005],{"class":304}," createPinia",[86,66007,65984],{"class":219},[86,66009,65987],{"class":178},[86,66011,11970],{"class":575},[86,66013,66014],{"class":579},"pinia",[86,66016,10971],{"class":575},[86,66018,65967],{"class":219},[86,66020,66021],{"class":174,"line":227},[86,66022,209],{"emptyLinePlaceholder":208},[86,66024,66025,66027,66030,66032,66034,66037,66039],{"class":174,"line":232},[86,66026,179],{"class":178},[86,66028,66029],{"class":304}," App",[86,66031,65987],{"class":178},[86,66033,11970],{"class":575},[86,66035,66036],{"class":579},".\u002FApp.vue",[86,66038,10971],{"class":575},[86,66040,65967],{"class":219},[86,66042,66043,66045,66048,66050,66052,66055,66057],{"class":174,"line":252},[86,66044,179],{"class":178},[86,66046,66047],{"class":304}," router",[86,66049,65987],{"class":178},[86,66051,11970],{"class":575},[86,66053,66054],{"class":579},".\u002Frouter",[86,66056,10971],{"class":575},[86,66058,65967],{"class":219},[86,66060,66061],{"class":174,"line":276},[86,66062,209],{"emptyLinePlaceholder":208},[86,66064,66065,66068,66071,66073,66075,66077,66080],{"class":174,"line":315},[86,66066,66067],{"class":235},"const",[86,66069,66070],{"class":304}," app",[86,66072,220],{"class":219},[86,66074,65981],{"class":239},[86,66076,243],{"class":219},[86,66078,66079],{"class":304},"App",[86,66081,66082],{"class":219},");\n",[86,66084,66085],{"class":174,"line":3665},[86,66086,209],{"emptyLinePlaceholder":208},[86,66088,66089,66092,66094,66097,66099,66102],{"class":174,"line":13256},[86,66090,66091],{"class":304},"app",[86,66093,61],{"class":219},[86,66095,66096],{"class":239},"use",[86,66098,243],{"class":219},[86,66100,66101],{"class":239},"createPinia",[86,66103,66104],{"class":219},"());\n",[86,66106,66107,66109,66111,66113,66115,66118],{"class":174,"line":13286},[86,66108,66091],{"class":304},[86,66110,61],{"class":219},[86,66112,66096],{"class":239},[86,66114,243],{"class":219},[86,66116,66117],{"class":304},"router",[86,66119,66082],{"class":219},[86,66121,66122],{"class":174,"line":13291},[86,66123,209],{"emptyLinePlaceholder":208},[86,66125,66126,66128,66130,66133,66135,66137,66140,66142],{"class":174,"line":13308},[86,66127,66091],{"class":304},[86,66129,61],{"class":219},[86,66131,66132],{"class":239},"mount",[86,66134,243],{"class":219},[86,66136,10971],{"class":575},[86,66138,66139],{"class":579},"#app",[86,66141,10971],{"class":575},[86,66143,66082],{"class":219},[12,66145,66146],{},"Aquí estamos haciendo lo siguiente:",[117,66148,66149,66156,66165,66170,66176,66186,66193,66199],{},[33,66150,66151,66152,66155],{},"Importamos los estilos globales desde ",[145,66153,66154],{},"main.css",". Este archivo contiene cualquier estilo que quieras aplicar globalmente.",[33,66157,66158,66159,392,66162,66164],{},"Importamos las funciones ",[145,66160,66161],{},"createApp",[145,66163,66101],{}," para crear nuevas instancias de Vue y Pinia.",[33,66166,66167,66168,61],{},"Importamos el componente raíz ",[145,66169,64976],{},[33,66171,66172,66173,61],{},"Importamos la configuración de nuestras rutas desde ",[145,66174,66175],{},"src\u002Frouter\u002Findex.js",[33,66177,66178,66179,66182,66183,66185],{},"Creamos la instancia de la aplicación con ",[145,66180,66181],{},"createApp(App)",", pasando el componente raíz ",[145,66184,66079],{}," como argumento, indicando que este será el punto de partida de nuestra aplicación Vue, básicamente le estamos diciendo a Vue: \"Aquí está el componente principal, toda la aplicación la construirás a partir de él\".",[33,66187,66188,66189,66192],{},"Usamos ",[145,66190,66191],{},"app.use(createPinia())"," para registrar la instancia de Pinia, habilitando el manejo de estado global en nuestra aplicación.",[33,66194,66188,66195,66198],{},[145,66196,66197],{},"app.use(router)"," para registrar la instancia de Vue Router y habilitar la navegación entre vistas.",[33,66200,66201,66202,66204,66205,61],{},"Finalmente, montamos la aplicación Vue en el elemento del DOM con el id ",[145,66203,66091],{}," usando ",[145,66206,66207],{},"app.mount('#app')",[12,66209,66210,66211,66214],{},"Ahora, abre el archivo ",[145,66212,66213],{},"index.html"," ubicado en la raíz del proyecto:",[164,66216,66220],{"className":66217,"code":66218,"language":66219,"meta":169,"style":169},"language-html shiki shiki-themes vitesse-light vitesse-dark","\u003C!DOCTYPE html>\n\u003Chtml lang=\"\">\n  \u003Chead>\n    \u003Cmeta charset=\"UTF-8\" \u002F>\n    \u003Clink rel=\"icon\" href=\"\u002Ffavicon.ico\" \u002F>\n    \u003Cmeta name=\"viewport\" content=\"width=device-width, initial-scale=1.0\" \u002F>\n    \u003Ctitle>Vite App\u003C\u002Ftitle>\n  \u003C\u002Fhead>\n  \u003Cbody>\n    \u003Cdiv id=\"app\">\u003C\u002Fdiv>\n    \u003Cscript type=\"module\" src=\"\u002Fsrc\u002Fmain.js\">\u003C\u002Fscript>\n  \u003C\u002Fbody>\n\u003C\u002Fhtml>\n","html",[145,66221,66222,66235,66251,66260,66283,66316,66348,66367,66376,66385,66410,66447,66455],{"__ignoreMap":169},[86,66223,66224,66227,66230,66233],{"class":174,"line":175},[86,66225,66226],{"class":219},"\u003C!",[86,66228,66229],{"class":178},"DOCTYPE",[86,66231,66232],{"class":304}," html",[86,66234,41330],{"class":219},[86,66236,66237,66239,66241,66244,66246,66249],{"class":174,"line":192},[86,66238,41317],{"class":219},[86,66240,66219],{"class":178},[86,66242,66243],{"class":304}," lang",[86,66245,258],{"class":219},[86,66247,66248],{"class":575},"\"\"",[86,66250,41330],{"class":219},[86,66252,66253,66256,66258],{"class":174,"line":205},[86,66254,66255],{"class":219},"  \u003C",[86,66257,33285],{"class":178},[86,66259,41330],{"class":219},[86,66261,66262,66265,66268,66271,66273,66275,66278,66280],{"class":174,"line":212},[86,66263,66264],{"class":219},"    \u003C",[86,66266,66267],{"class":178},"meta",[86,66269,66270],{"class":304}," charset",[86,66272,258],{"class":219},[86,66274,576],{"class":575},[86,66276,66277],{"class":579},"UTF-8",[86,66279,576],{"class":575},[86,66281,66282],{"class":219}," \u002F>\n",[86,66284,66285,66287,66290,66293,66295,66297,66300,66302,66305,66307,66309,66312,66314],{"class":174,"line":227},[86,66286,66264],{"class":219},[86,66288,66289],{"class":178},"link",[86,66291,66292],{"class":304}," rel",[86,66294,258],{"class":219},[86,66296,576],{"class":575},[86,66298,66299],{"class":579},"icon",[86,66301,576],{"class":575},[86,66303,66304],{"class":304}," href",[86,66306,258],{"class":219},[86,66308,576],{"class":575},[86,66310,66311],{"class":579},"\u002Ffavicon.ico",[86,66313,576],{"class":575},[86,66315,66282],{"class":219},[86,66317,66318,66320,66322,66325,66327,66329,66332,66334,66337,66339,66341,66344,66346],{"class":174,"line":232},[86,66319,66264],{"class":219},[86,66321,66267],{"class":178},[86,66323,66324],{"class":304}," name",[86,66326,258],{"class":219},[86,66328,576],{"class":575},[86,66330,66331],{"class":579},"viewport",[86,66333,576],{"class":575},[86,66335,66336],{"class":304}," content",[86,66338,258],{"class":219},[86,66340,576],{"class":575},[86,66342,66343],{"class":579},"width=device-width, initial-scale=1.0",[86,66345,576],{"class":575},[86,66347,66282],{"class":219},[86,66349,66350,66352,66354,66357,66360,66363,66365],{"class":174,"line":252},[86,66351,66264],{"class":219},[86,66353,34801],{"class":178},[86,66355,66356],{"class":219},">",[86,66358,66359],{"class":182},"Vite App",[86,66361,66362],{"class":219},"\u003C\u002F",[86,66364,34801],{"class":178},[86,66366,41330],{"class":219},[86,66368,66369,66372,66374],{"class":174,"line":276},[86,66370,66371],{"class":219},"  \u003C\u002F",[86,66373,33285],{"class":178},[86,66375,41330],{"class":219},[86,66377,66378,66380,66383],{"class":174,"line":315},[86,66379,66255],{"class":219},[86,66381,66382],{"class":178},"body",[86,66384,41330],{"class":219},[86,66386,66387,66389,66392,66395,66397,66399,66401,66403,66406,66408],{"class":174,"line":3665},[86,66388,66264],{"class":219},[86,66390,66391],{"class":178},"div",[86,66393,66394],{"class":304}," id",[86,66396,258],{"class":219},[86,66398,576],{"class":575},[86,66400,66091],{"class":579},[86,66402,576],{"class":575},[86,66404,66405],{"class":219},">\u003C\u002F",[86,66407,66391],{"class":178},[86,66409,41330],{"class":219},[86,66411,66412,66414,66417,66420,66422,66424,66427,66429,66432,66434,66436,66439,66441,66443,66445],{"class":174,"line":13256},[86,66413,66264],{"class":219},[86,66415,66416],{"class":178},"script",[86,66418,66419],{"class":304}," type",[86,66421,258],{"class":219},[86,66423,576],{"class":575},[86,66425,66426],{"class":579},"module",[86,66428,576],{"class":575},[86,66430,66431],{"class":304}," src",[86,66433,258],{"class":219},[86,66435,576],{"class":575},[86,66437,66438],{"class":579},"\u002Fsrc\u002Fmain.js",[86,66440,576],{"class":575},[86,66442,66405],{"class":219},[86,66444,66416],{"class":178},[86,66446,41330],{"class":219},[86,66448,66449,66451,66453],{"class":174,"line":13286},[86,66450,66371],{"class":219},[86,66452,66382],{"class":178},[86,66454,41330],{"class":219},[86,66456,66457,66459,66461],{"class":174,"line":13291},[86,66458,66362],{"class":219},[86,66460,66219],{"class":178},[86,66462,41330],{"class":219},[12,66464,66465,66466,66469,66470,66472,66473,66476,66477,66479],{},"Aquí vemos que el archivo HTML tiene un ",[145,66467,66468],{},"\u003Cdiv>"," con el id ",[145,66471,66091],{},", que es donde Vue montará nuestra aplicación. El ",[145,66474,66475],{},"\u003Cscript>"," que le sigue carga nuestro archivo ",[145,66478,64982],{},", que es donde inicializamos todo.",[12,66481,66482,66483,162],{},"Abre el archivo ",[145,66484,66485],{},"src\u002FApp.vue",[164,66487,66490],{"className":66488,"code":66489,"language":65992,"meta":169,"style":169},"language-vue shiki shiki-themes vitesse-light vitesse-dark","\u003Cscript setup>\nimport { RouterLink, RouterView } from 'vue-router';\nimport HelloWorld from '.\u002Fcomponents\u002FHelloWorld.vue';\n\u003C\u002Fscript>\n\n\u003Ctemplate>\n  \u003Cheader>\n    \u003Cimg alt=\"Vue logo\" class=\"logo\" src=\"@\u002Fassets\u002Flogo.svg\" width=\"125\" height=\"125\" \u002F>\n\n    \u003Cdiv class=\"wrapper\">\n      \u003CHelloWorld msg=\"You did it!\" \u002F>\n\n      \u003Cnav>\n        \u003CRouterLink to=\"\u002F\">Home\u003C\u002FRouterLink>\n        \u003CRouterLink to=\"\u002Fabout\">About\u003C\u002FRouterLink>\n      \u003C\u002Fnav>\n    \u003C\u002Fdiv>\n  \u003C\u002Fheader>\n\n  \u003CRouterView \u002F>\n\u003C\u002Ftemplate>\n\n\u003Cstyle scoped>\n\u002F* Estilos CSS *\u002F\n\u003C\u002Fstyle>\n",[145,66491,66492,66503,66530,66548,66556,66560,66569,66578,66643,66647,66666,66688,66692,66701,66730,66758,66767,66776,66784,66788,66797,66805,66809,66820,66825],{"__ignoreMap":169},[86,66493,66494,66496,66498,66501],{"class":174,"line":175},[86,66495,41317],{"class":219},[86,66497,66416],{"class":178},[86,66499,66500],{"class":304}," setup",[86,66502,41330],{"class":219},[86,66504,66505,66507,66509,66512,66514,66517,66519,66521,66523,66526,66528],{"class":174,"line":192},[86,66506,179],{"class":178},[86,66508,65978],{"class":219},[86,66510,66511],{"class":304}," RouterLink",[86,66513,291],{"class":219},[86,66515,66516],{"class":304}," RouterView",[86,66518,65984],{"class":219},[86,66520,65987],{"class":178},[86,66522,11970],{"class":575},[86,66524,66525],{"class":579},"vue-router",[86,66527,10971],{"class":575},[86,66529,65967],{"class":219},[86,66531,66532,66534,66537,66539,66541,66544,66546],{"class":174,"line":205},[86,66533,179],{"class":178},[86,66535,66536],{"class":304}," HelloWorld",[86,66538,65987],{"class":178},[86,66540,11970],{"class":575},[86,66542,66543],{"class":579},".\u002Fcomponents\u002FHelloWorld.vue",[86,66545,10971],{"class":575},[86,66547,65967],{"class":219},[86,66549,66550,66552,66554],{"class":174,"line":212},[86,66551,66362],{"class":219},[86,66553,66416],{"class":178},[86,66555,41330],{"class":219},[86,66557,66558],{"class":174,"line":227},[86,66559,209],{"emptyLinePlaceholder":208},[86,66561,66562,66564,66567],{"class":174,"line":232},[86,66563,41317],{"class":219},[86,66565,66566],{"class":178},"template",[86,66568,41330],{"class":219},[86,66570,66571,66573,66576],{"class":174,"line":252},[86,66572,66255],{"class":219},[86,66574,66575],{"class":178},"header",[86,66577,41330],{"class":219},[86,66579,66580,66582,66584,66587,66589,66591,66594,66596,66599,66601,66603,66606,66608,66610,66612,66614,66617,66619,66622,66624,66626,66629,66631,66633,66635,66637,66639,66641],{"class":174,"line":276},[86,66581,66264],{"class":219},[86,66583,1945],{"class":178},[86,66585,66586],{"class":304}," alt",[86,66588,258],{"class":219},[86,66590,576],{"class":575},[86,66592,66593],{"class":579},"Vue logo",[86,66595,576],{"class":575},[86,66597,66598],{"class":304}," class",[86,66600,258],{"class":219},[86,66602,576],{"class":575},[86,66604,66605],{"class":579},"logo",[86,66607,576],{"class":575},[86,66609,66431],{"class":304},[86,66611,258],{"class":219},[86,66613,576],{"class":575},[86,66615,66616],{"class":579},"@\u002Fassets\u002Flogo.svg",[86,66618,576],{"class":575},[86,66620,66621],{"class":304}," width",[86,66623,258],{"class":219},[86,66625,576],{"class":575},[86,66627,66628],{"class":579},"125",[86,66630,576],{"class":575},[86,66632,34993],{"class":304},[86,66634,258],{"class":219},[86,66636,576],{"class":575},[86,66638,66628],{"class":579},[86,66640,576],{"class":575},[86,66642,66282],{"class":219},[86,66644,66645],{"class":174,"line":315},[86,66646,209],{"emptyLinePlaceholder":208},[86,66648,66649,66651,66653,66655,66657,66659,66662,66664],{"class":174,"line":3665},[86,66650,66264],{"class":219},[86,66652,66391],{"class":178},[86,66654,66598],{"class":304},[86,66656,258],{"class":219},[86,66658,576],{"class":575},[86,66660,66661],{"class":579},"wrapper",[86,66663,576],{"class":575},[86,66665,41330],{"class":219},[86,66667,66668,66671,66674,66677,66679,66681,66684,66686],{"class":174,"line":13256},[86,66669,66670],{"class":219},"      \u003C",[86,66672,66673],{"class":178},"HelloWorld",[86,66675,66676],{"class":304}," msg",[86,66678,258],{"class":219},[86,66680,576],{"class":575},[86,66682,66683],{"class":579},"You did it!",[86,66685,576],{"class":575},[86,66687,66282],{"class":219},[86,66689,66690],{"class":174,"line":13286},[86,66691,209],{"emptyLinePlaceholder":208},[86,66693,66694,66696,66699],{"class":174,"line":13291},[86,66695,66670],{"class":219},[86,66697,66698],{"class":178},"nav",[86,66700,41330],{"class":219},[86,66702,66703,66706,66709,66711,66713,66715,66717,66719,66721,66724,66726,66728],{"class":174,"line":13308},[86,66704,66705],{"class":219},"        \u003C",[86,66707,66708],{"class":178},"RouterLink",[86,66710,41346],{"class":304},[86,66712,258],{"class":219},[86,66714,576],{"class":575},[86,66716,16555],{"class":579},[86,66718,576],{"class":575},[86,66720,66356],{"class":219},[86,66722,66723],{"class":182},"Home",[86,66725,66362],{"class":219},[86,66727,66708],{"class":178},[86,66729,41330],{"class":219},[86,66731,66732,66734,66736,66738,66740,66742,66745,66747,66749,66752,66754,66756],{"class":174,"line":13334},[86,66733,66705],{"class":219},[86,66735,66708],{"class":178},[86,66737,41346],{"class":304},[86,66739,258],{"class":219},[86,66741,576],{"class":575},[86,66743,66744],{"class":579},"\u002Fabout",[86,66746,576],{"class":575},[86,66748,66356],{"class":219},[86,66750,66751],{"class":182},"About",[86,66753,66362],{"class":219},[86,66755,66708],{"class":178},[86,66757,41330],{"class":219},[86,66759,66760,66763,66765],{"class":174,"line":13359},[86,66761,66762],{"class":219},"      \u003C\u002F",[86,66764,66698],{"class":178},[86,66766,41330],{"class":219},[86,66768,66769,66772,66774],{"class":174,"line":13385},[86,66770,66771],{"class":219},"    \u003C\u002F",[86,66773,66391],{"class":178},[86,66775,41330],{"class":219},[86,66777,66778,66780,66782],{"class":174,"line":13390},[86,66779,66371],{"class":219},[86,66781,66575],{"class":178},[86,66783,41330],{"class":219},[86,66785,66786],{"class":174,"line":13396},[86,66787,209],{"emptyLinePlaceholder":208},[86,66789,66790,66792,66795],{"class":174,"line":3615},[86,66791,66255],{"class":219},[86,66793,66794],{"class":178},"RouterView",[86,66796,66282],{"class":219},[86,66798,66799,66801,66803],{"class":174,"line":2254},[86,66800,66362],{"class":219},[86,66802,66566],{"class":178},[86,66804,41330],{"class":219},[86,66806,66807],{"class":174,"line":13492},[86,66808,209],{"emptyLinePlaceholder":208},[86,66810,66811,66813,66815,66818],{"class":174,"line":13545},[86,66812,41317],{"class":219},[86,66814,2218],{"class":178},[86,66816,66817],{"class":304}," scoped",[86,66819,41330],{"class":219},[86,66821,66822],{"class":174,"line":13550},[86,66823,66824],{"class":1360},"\u002F* Estilos CSS *\u002F\n",[86,66826,66827,66829,66831],{"class":174,"line":13566},[86,66828,66362],{"class":219},[86,66830,2218],{"class":178},[86,66832,41330],{"class":219},[12,66834,66835,66836,66838,66839,66841,66842,66845],{},"Aquí vemos que ",[145,66837,64976],{}," contiene un encabezado (header) con un logo, un componente ",[145,66840,66673],{},", y un menú de navegación con enlaces a las rutas definidas. El ",[145,66843,66844],{},"\u003CRouterView \u002F>"," es donde se renderizarán las vistas correspondientes según la ruta actual, gracias a Vue Router.",[12,66847,66848,66849,162],{},"Exploremos la configuración del router. Abre el archivo ",[145,66850,66175],{},[164,66852,66854],{"className":65949,"code":66853,"language":65951,"meta":169,"style":169},"import { createRouter, createWebHistory } from 'vue-router';\nimport HomeView from '..\u002Fviews\u002FHomeView.vue';\n\nconst router = createRouter({\n  history: createWebHistory(import.meta.env.BASE_URL),\n  routes: [\n    {\n      path: '\u002F',\n      name: 'home',\n      component: HomeView,\n    },\n    {\n      path: '\u002Fabout',\n      name: 'about',\n      \u002F* Esta ruta usa lazy loading *\u002F\n      component: () => import('..\u002Fviews\u002FAboutView.vue'),\n    },\n  ],\n});\n\nexport default router;\n",[145,66855,66856,66882,66900,66904,66916,66945,66955,66960,66975,66991,67002,67007,67011,67025,67040,67045,67071,67075,67080,67085,67089],{"__ignoreMap":169},[86,66857,66858,66860,66862,66865,66867,66870,66872,66874,66876,66878,66880],{"class":174,"line":175},[86,66859,179],{"class":178},[86,66861,65978],{"class":219},[86,66863,66864],{"class":304}," createRouter",[86,66866,291],{"class":219},[86,66868,66869],{"class":304}," createWebHistory",[86,66871,65984],{"class":219},[86,66873,65987],{"class":178},[86,66875,11970],{"class":575},[86,66877,66525],{"class":579},[86,66879,10971],{"class":575},[86,66881,65967],{"class":219},[86,66883,66884,66886,66889,66891,66893,66896,66898],{"class":174,"line":192},[86,66885,179],{"class":178},[86,66887,66888],{"class":304}," HomeView",[86,66890,65987],{"class":178},[86,66892,11970],{"class":575},[86,66894,66895],{"class":579},"..\u002Fviews\u002FHomeView.vue",[86,66897,10971],{"class":575},[86,66899,65967],{"class":219},[86,66901,66902],{"class":174,"line":205},[86,66903,209],{"emptyLinePlaceholder":208},[86,66905,66906,66908,66910,66912,66914],{"class":174,"line":212},[86,66907,66067],{"class":235},[86,66909,66047],{"class":304},[86,66911,220],{"class":219},[86,66913,66864],{"class":239},[86,66915,44326],{"class":219},[86,66917,66918,66921,66923,66925,66927,66929,66931,66933,66935,66938,66940,66943],{"class":174,"line":227},[86,66919,66920],{"class":812},"  history",[86,66922,162],{"class":219},[86,66924,66869],{"class":239},[86,66926,243],{"class":219},[86,66928,179],{"class":178},[86,66930,61],{"class":219},[86,66932,66267],{"class":812},[86,66934,61],{"class":219},[86,66936,66937],{"class":304},"env",[86,66939,61],{"class":219},[86,66941,66942],{"class":304},"BASE_URL",[86,66944,1412],{"class":219},[86,66946,66947,66950,66952],{"class":174,"line":232},[86,66948,66949],{"class":812},"  routes",[86,66951,162],{"class":219},[86,66953,66954],{"class":219}," [\n",[86,66956,66957],{"class":174,"line":252},[86,66958,66959],{"class":219},"    {\n",[86,66961,66962,66965,66967,66969,66971,66973],{"class":174,"line":276},[86,66963,66964],{"class":812},"      path",[86,66966,162],{"class":219},[86,66968,11970],{"class":575},[86,66970,16555],{"class":579},[86,66972,10971],{"class":575},[86,66974,1111],{"class":219},[86,66976,66977,66980,66982,66984,66987,66989],{"class":174,"line":315},[86,66978,66979],{"class":812},"      name",[86,66981,162],{"class":219},[86,66983,11970],{"class":575},[86,66985,66986],{"class":579},"home",[86,66988,10971],{"class":575},[86,66990,1111],{"class":219},[86,66992,66993,66996,66998,67000],{"class":174,"line":3665},[86,66994,66995],{"class":812},"      component",[86,66997,162],{"class":219},[86,66999,66888],{"class":304},[86,67001,1111],{"class":219},[86,67003,67004],{"class":174,"line":13256},[86,67005,67006],{"class":219},"    },\n",[86,67008,67009],{"class":174,"line":13286},[86,67010,66959],{"class":219},[86,67012,67013,67015,67017,67019,67021,67023],{"class":174,"line":13291},[86,67014,66964],{"class":812},[86,67016,162],{"class":219},[86,67018,11970],{"class":575},[86,67020,66744],{"class":579},[86,67022,10971],{"class":575},[86,67024,1111],{"class":219},[86,67026,67027,67029,67031,67033,67036,67038],{"class":174,"line":13308},[86,67028,66979],{"class":812},[86,67030,162],{"class":219},[86,67032,11970],{"class":575},[86,67034,67035],{"class":579},"about",[86,67037,10971],{"class":575},[86,67039,1111],{"class":219},[86,67041,67042],{"class":174,"line":13334},[86,67043,67044],{"class":1360},"      \u002F* Esta ruta usa lazy loading *\u002F\n",[86,67046,67047,67049,67051,67054,67057,67060,67062,67064,67067,67069],{"class":174,"line":13359},[86,67048,66995],{"class":239},[86,67050,162],{"class":219},[86,67052,67053],{"class":219}," ()",[86,67055,67056],{"class":219}," =>",[86,67058,67059],{"class":235}," import",[86,67061,243],{"class":219},[86,67063,10971],{"class":575},[86,67065,67066],{"class":579},"..\u002Fviews\u002FAboutView.vue",[86,67068,10971],{"class":575},[86,67070,1412],{"class":219},[86,67072,67073],{"class":174,"line":13385},[86,67074,67006],{"class":219},[86,67076,67077],{"class":174,"line":13390},[86,67078,67079],{"class":219},"  ],\n",[86,67081,67082],{"class":174,"line":13396},[86,67083,67084],{"class":219},"});\n",[86,67086,67087],{"class":174,"line":3615},[86,67088,209],{"emptyLinePlaceholder":208},[86,67090,67091,67094,67097,67099],{"class":174,"line":2254},[86,67092,67093],{"class":178},"export",[86,67095,67096],{"class":178}," default",[86,67098,66047],{"class":304},[86,67100,65967],{"class":219},[12,67102,67103,67104,67107,67108,67111,67112,67114,67115,67117,67118,67120,67121,67123,67124,789],{},"Aquí estamos importando las funciones necesarias de Vue Router y definiendo una ruta básica para la vista ",[145,67105,67106],{},"HomeView"," y otra para ",[145,67109,67110],{},"AboutView",". La ruta ",[145,67113,16555],{}," renderiza ",[145,67116,67106],{},", y la ruta ",[145,67119,66744],{}," carga ",[145,67122,67110],{}," utilizando carga diferida (",[22,67125,67128],{"href":67126,"target":27,"rel":67127},"https:\u002F\u002Fmedium.com\u002F@drewcauchi\u002Flazy-loading-in-vue-js-bb32018d2c2d",[7760,7761],"lazy loading",[12,67130,67131],{},"Repasemos el flujo completo:",[117,67133,67134,67142,67151],{},[33,67135,67136,67137,67139,67140,61],{},"El archivo ",[145,67138,66213],{}," es lo que el navegador nos muestra, y lo primero que hace es cargar ",[145,67141,64982],{},[33,67143,67144,67145,67147,67148,67150],{},"En ",[145,67146,64982],{},", se crea la aplicación Vue con ",[145,67149,64976],{}," como componente raíz (a parte de importar estilos, configurar Pinia, Vue Router y otras configuraciones).",[33,67152,67153,67155,67156,67158],{},[145,67154,64976],{}," define la estructura principal de la aplicación (como un layout principal) y utiliza ",[145,67157,66844],{}," para renderizar las vistas según la ruta actual.",[12,67160,67161,67165],{},[1945,67162],{"alt":67163,"src":67164},"Flujo de una app Vue","\u002Fblog\u002Fgetting-started-vue-vite\u002Fes\u002Fexplaining-vue-app.webp",[901,67166,67163],{},[12,67168,67169,67170,67172,67173,67175],{},"Esto quiere decir que todo lo que veas dentro de ",[145,67171,64976],{}," estará siempre presente (como el header y el menú de navegación), mientras que el contenido principal se mostrará dentro de ",[145,67174,66844],{}," y cambiará dependiendo de la ruta actual, gracias a nuestro router.",[12,67177,67178,67179,67181,67182,61],{},"Normalmente, en aplicaciones más complejas, ",[145,67180,64976],{}," también contendrá otros elementos comunes como un footer, barras laterales, modales globales, etc.\nY cuando se necesita, se crean layouts específicos para diferentes módulos de la aplicación, por ejemplo, un layout para las vistas de administración y otro para las vistas públicas como el inicio de sesión. Puedes explorar más en ",[22,67183,67186],{"href":67184,"target":27,"rel":67185},"https:\u002F\u002Fvueschool.io\u002Farticles\u002Fvuejs-tutorials\u002Fcomposing-layouts-with-vue-router\u002F",[7760,7761],"este recurso de Vue School",[43,67188],{},[12,67190,67191],{},"A este punto ya tenemos una idea clara de cómo se estructura y monta una aplicación Vue 3 con Vite. Puedes comenzar a explorar y modificar los componentes, vistas y rutas para familiarizarte más con el framework. Ahora seguiremos explorando otros conceptos y herramientas importantes del ecosistema.",[43,67193],{},[46,67195,67197],{"id":67196},"pinia-para-manejo-de-estado-global","Pinia para manejo de estado global",[12,67199,67200],{},"Pinia nos sirve para manejar el estado global de nuestra aplicación: datos que deben ser accesibles desde cualquier parte de la aplicación, datos que necesitamos compartir entre múltiples componentes o vistas.",[12,67202,67203],{},"Por ejemplo, cuando necesitamos tener acceso a la información del usuario autenticado en diferentes partes de la app, o si queremos manejar un carrito de compras que pueda ser consultado desde distintos componentes.",[12,67205,67206,67207,162],{},"Veamos un ejemplo básico. Crea el archivo ",[145,67208,67209],{},"src\u002Fstore\u002Fauth.store.js",[164,67211,67213],{"className":65949,"code":67212,"language":65951,"meta":169,"style":169},"import { defineStore } from 'pinia';\nexport const useAuthStore = defineStore('auth', {\n  state: () => ({\n    user: null,\n    token: null,\n  }),\n  actions: {\n    login(userData, token) {\n      this.user = userData;\n      this.token = token;\n    },\n    logout() {\n      this.user = null;\n      this.token = null;\n    },\n  },\n});\n",[145,67214,67215,67236,67264,67278,67290,67301,67306,67315,67334,67351,67366,67370,67379,67393,67407,67411,67416],{"__ignoreMap":169},[86,67216,67217,67219,67221,67224,67226,67228,67230,67232,67234],{"class":174,"line":175},[86,67218,179],{"class":178},[86,67220,65978],{"class":219},[86,67222,67223],{"class":304}," defineStore",[86,67225,65984],{"class":219},[86,67227,65987],{"class":178},[86,67229,11970],{"class":575},[86,67231,66014],{"class":579},[86,67233,10971],{"class":575},[86,67235,65967],{"class":219},[86,67237,67238,67240,67243,67246,67248,67250,67252,67254,67257,67259,67261],{"class":174,"line":192},[86,67239,67093],{"class":178},[86,67241,67242],{"class":235}," const",[86,67244,67245],{"class":304}," useAuthStore",[86,67247,220],{"class":219},[86,67249,67223],{"class":239},[86,67251,243],{"class":219},[86,67253,10971],{"class":575},[86,67255,67256],{"class":579},"auth",[86,67258,10971],{"class":575},[86,67260,291],{"class":219},[86,67262,67263],{"class":219}," {\n",[86,67265,67266,67269,67271,67273,67275],{"class":174,"line":205},[86,67267,67268],{"class":239},"  state",[86,67270,162],{"class":219},[86,67272,67053],{"class":219},[86,67274,67056],{"class":219},[86,67276,67277],{"class":219}," ({\n",[86,67279,67280,67283,67285,67288],{"class":174,"line":212},[86,67281,67282],{"class":812},"    user",[86,67284,162],{"class":219},[86,67286,67287],{"class":235}," null",[86,67289,1111],{"class":219},[86,67291,67292,67295,67297,67299],{"class":174,"line":227},[86,67293,67294],{"class":812},"    token",[86,67296,162],{"class":219},[86,67298,67287],{"class":235},[86,67300,1111],{"class":219},[86,67302,67303],{"class":174,"line":232},[86,67304,67305],{"class":219},"  }),\n",[86,67307,67308,67311,67313],{"class":174,"line":252},[86,67309,67310],{"class":812},"  actions",[86,67312,162],{"class":219},[86,67314,67263],{"class":219},[86,67316,67317,67320,67322,67325,67327,67330,67332],{"class":174,"line":276},[86,67318,67319],{"class":239},"    login",[86,67321,243],{"class":219},[86,67323,67324],{"class":304},"userData",[86,67326,291],{"class":219},[86,67328,67329],{"class":304}," token",[86,67331,867],{"class":219},[86,67333,67263],{"class":219},[86,67335,67336,67339,67341,67344,67346,67349],{"class":174,"line":315},[86,67337,67338],{"class":215},"      this",[86,67340,61],{"class":219},[86,67342,67343],{"class":304},"user",[86,67345,220],{"class":219},[86,67347,67348],{"class":304}," userData",[86,67350,65967],{"class":219},[86,67352,67353,67355,67357,67360,67362,67364],{"class":174,"line":3665},[86,67354,67338],{"class":215},[86,67356,61],{"class":219},[86,67358,67359],{"class":304},"token",[86,67361,220],{"class":219},[86,67363,67329],{"class":304},[86,67365,65967],{"class":219},[86,67367,67368],{"class":174,"line":13256},[86,67369,67006],{"class":219},[86,67371,67372,67375,67377],{"class":174,"line":13286},[86,67373,67374],{"class":239},"    logout",[86,67376,13418],{"class":219},[86,67378,67263],{"class":219},[86,67380,67381,67383,67385,67387,67389,67391],{"class":174,"line":13291},[86,67382,67338],{"class":215},[86,67384,61],{"class":219},[86,67386,67343],{"class":304},[86,67388,220],{"class":219},[86,67390,67287],{"class":235},[86,67392,65967],{"class":219},[86,67394,67395,67397,67399,67401,67403,67405],{"class":174,"line":13308},[86,67396,67338],{"class":215},[86,67398,61],{"class":219},[86,67400,67359],{"class":304},[86,67402,220],{"class":219},[86,67404,67287],{"class":235},[86,67406,65967],{"class":219},[86,67408,67409],{"class":174,"line":13334},[86,67410,67006],{"class":219},[86,67412,67413],{"class":174,"line":13359},[86,67414,67415],{"class":219},"  },\n",[86,67417,67418],{"class":174,"line":13385},[86,67419,67084],{"class":219},[12,67421,67422,67423,67425,67426,392,67428,67430,67431,162],{},"Aquí estamos definiendo una store llamada ",[145,67424,67256],{}," que tiene un estado con las propiedades ",[145,67427,67343],{},[145,67429,67359],{},", y dos acciones para iniciar sesión y cerrar sesión.\nAhora, veamos cómo usar esta store en un componente. Crea un componente Vue, por ejemplo ",[145,67432,67433],{},"src\u002Fcomponents\u002FAuth.vue",[164,67435,67437],{"className":66488,"code":67436,"language":65992,"meta":169,"style":169},"\u003Ctemplate>\n  \u003Cdiv>\n    \u003Cdiv v-if=\"authStore.user\">\n      \u003Cp>Welcome, {{ authStore.user.name }}!\u003C\u002Fp>\n      \u003Cbutton @click=\"logout\">Logout\u003C\u002Fbutton>\n    \u003C\u002Fdiv>\n    \u003Cdiv v-else>\n      \u003Cbutton @click=\"login\">Login\u003C\u002Fbutton>\n    \u003C\u002Fdiv>\n  \u003C\u002Fdiv>\n\u003C\u002Ftemplate>\n\u003Cscript setup>\nimport { useAuthStore } from '..\u002Fstore\u002Fauth.store';\nconst authStore = useAuthStore();\nconst login = () => {\n  \u002F\u002F Simulamos un inicio de sesión\n  const userData = { name: 'John Doe', email: 'john.doe@example.com' };\n  const token = 'fake-jwt-token';\n  authStore.login(userData, token);\n};\n\nconst logout = () => {\n  authStore.logout();\n};\n\u003C\u002Fscript>\n",[145,67438,67439,67447,67455,67475,67492,67522,67530,67541,67569,67577,67585,67593,67603,67624,67638,67653,67658,67697,67714,67733,67738,67742,67757,67767,67771],{"__ignoreMap":169},[86,67440,67441,67443,67445],{"class":174,"line":175},[86,67442,41317],{"class":219},[86,67444,66566],{"class":178},[86,67446,41330],{"class":219},[86,67448,67449,67451,67453],{"class":174,"line":192},[86,67450,66255],{"class":219},[86,67452,66391],{"class":178},[86,67454,41330],{"class":219},[86,67456,67457,67459,67461,67464,67466,67468,67471,67473],{"class":174,"line":205},[86,67458,66264],{"class":219},[86,67460,66391],{"class":178},[86,67462,67463],{"class":304}," v-if",[86,67465,258],{"class":219},[86,67467,576],{"class":575},[86,67469,67470],{"class":579},"authStore.user",[86,67472,576],{"class":575},[86,67474,41330],{"class":219},[86,67476,67477,67479,67481,67483,67486,67488,67490],{"class":174,"line":212},[86,67478,66670],{"class":219},[86,67480,12],{"class":178},[86,67482,66356],{"class":219},[86,67484,67485],{"class":182},"Welcome, {{ authStore.user.name }}!",[86,67487,66362],{"class":219},[86,67489,12],{"class":178},[86,67491,41330],{"class":219},[86,67493,67494,67496,67499,67502,67504,67506,67509,67511,67513,67516,67518,67520],{"class":174,"line":227},[86,67495,66670],{"class":219},[86,67497,67498],{"class":178},"button",[86,67500,67501],{"class":304}," @click",[86,67503,258],{"class":219},[86,67505,576],{"class":575},[86,67507,67508],{"class":579},"logout",[86,67510,576],{"class":575},[86,67512,66356],{"class":219},[86,67514,67515],{"class":182},"Logout",[86,67517,66362],{"class":219},[86,67519,67498],{"class":178},[86,67521,41330],{"class":219},[86,67523,67524,67526,67528],{"class":174,"line":232},[86,67525,66771],{"class":219},[86,67527,66391],{"class":178},[86,67529,41330],{"class":219},[86,67531,67532,67534,67536,67539],{"class":174,"line":252},[86,67533,66264],{"class":219},[86,67535,66391],{"class":178},[86,67537,67538],{"class":304}," v-else",[86,67540,41330],{"class":219},[86,67542,67543,67545,67547,67549,67551,67553,67556,67558,67560,67563,67565,67567],{"class":174,"line":276},[86,67544,66670],{"class":219},[86,67546,67498],{"class":178},[86,67548,67501],{"class":304},[86,67550,258],{"class":219},[86,67552,576],{"class":575},[86,67554,67555],{"class":579},"login",[86,67557,576],{"class":575},[86,67559,66356],{"class":219},[86,67561,67562],{"class":182},"Login",[86,67564,66362],{"class":219},[86,67566,67498],{"class":178},[86,67568,41330],{"class":219},[86,67570,67571,67573,67575],{"class":174,"line":315},[86,67572,66771],{"class":219},[86,67574,66391],{"class":178},[86,67576,41330],{"class":219},[86,67578,67579,67581,67583],{"class":174,"line":3665},[86,67580,66371],{"class":219},[86,67582,66391],{"class":178},[86,67584,41330],{"class":219},[86,67586,67587,67589,67591],{"class":174,"line":13256},[86,67588,66362],{"class":219},[86,67590,66566],{"class":178},[86,67592,41330],{"class":219},[86,67594,67595,67597,67599,67601],{"class":174,"line":13286},[86,67596,41317],{"class":219},[86,67598,66416],{"class":178},[86,67600,66500],{"class":304},[86,67602,41330],{"class":219},[86,67604,67605,67607,67609,67611,67613,67615,67617,67620,67622],{"class":174,"line":13291},[86,67606,179],{"class":178},[86,67608,65978],{"class":219},[86,67610,67245],{"class":304},[86,67612,65984],{"class":219},[86,67614,65987],{"class":178},[86,67616,11970],{"class":575},[86,67618,67619],{"class":579},"..\u002Fstore\u002Fauth.store",[86,67621,10971],{"class":575},[86,67623,65967],{"class":219},[86,67625,67626,67628,67631,67633,67635],{"class":174,"line":13308},[86,67627,66067],{"class":235},[86,67629,67630],{"class":304}," authStore",[86,67632,220],{"class":219},[86,67634,67245],{"class":239},[86,67636,67637],{"class":219},"();\n",[86,67639,67640,67642,67645,67647,67649,67651],{"class":174,"line":13334},[86,67641,66067],{"class":235},[86,67643,67644],{"class":239}," login",[86,67646,220],{"class":219},[86,67648,67053],{"class":219},[86,67650,67056],{"class":219},[86,67652,67263],{"class":219},[86,67654,67655],{"class":174,"line":13359},[86,67656,67657],{"class":1360},"  \u002F\u002F Simulamos un inicio de sesión\n",[86,67659,67660,67663,67665,67667,67669,67671,67673,67675,67678,67680,67682,67685,67687,67689,67692,67694],{"class":174,"line":13385},[86,67661,67662],{"class":235},"  const",[86,67664,67348],{"class":304},[86,67666,220],{"class":219},[86,67668,65978],{"class":219},[86,67670,66324],{"class":812},[86,67672,162],{"class":219},[86,67674,11970],{"class":575},[86,67676,67677],{"class":579},"John Doe",[86,67679,10971],{"class":575},[86,67681,291],{"class":219},[86,67683,67684],{"class":812}," email",[86,67686,162],{"class":219},[86,67688,11970],{"class":575},[86,67690,67691],{"class":579},"john.doe@example.com",[86,67693,10971],{"class":575},[86,67695,67696],{"class":219}," };\n",[86,67698,67699,67701,67703,67705,67707,67710,67712],{"class":174,"line":13390},[86,67700,67662],{"class":235},[86,67702,67329],{"class":304},[86,67704,220],{"class":219},[86,67706,11970],{"class":575},[86,67708,67709],{"class":579},"fake-jwt-token",[86,67711,10971],{"class":575},[86,67713,65967],{"class":219},[86,67715,67716,67719,67721,67723,67725,67727,67729,67731],{"class":174,"line":13396},[86,67717,67718],{"class":304},"  authStore",[86,67720,61],{"class":219},[86,67722,67555],{"class":239},[86,67724,243],{"class":219},[86,67726,67324],{"class":304},[86,67728,291],{"class":219},[86,67730,67329],{"class":304},[86,67732,66082],{"class":219},[86,67734,67735],{"class":174,"line":3615},[86,67736,67737],{"class":219},"};\n",[86,67739,67740],{"class":174,"line":2254},[86,67741,209],{"emptyLinePlaceholder":208},[86,67743,67744,67746,67749,67751,67753,67755],{"class":174,"line":13492},[86,67745,66067],{"class":235},[86,67747,67748],{"class":239}," logout",[86,67750,220],{"class":219},[86,67752,67053],{"class":219},[86,67754,67056],{"class":219},[86,67756,67263],{"class":219},[86,67758,67759,67761,67763,67765],{"class":174,"line":13545},[86,67760,67718],{"class":304},[86,67762,61],{"class":219},[86,67764,67508],{"class":239},[86,67766,67637],{"class":219},[86,67768,67769],{"class":174,"line":13550},[86,67770,67737],{"class":219},[86,67772,67773,67775,67777],{"class":174,"line":13566},[86,67774,66362],{"class":219},[86,67776,66416],{"class":178},[86,67778,41330],{"class":219},[12,67780,67781,67782,67785,67786,67788,67789,392,67791,67793],{},"Aquí estamos importando la store ",[145,67783,67784],{},"useAuthStore"," y usándola para acceder al estado ",[145,67787,67343],{}," y las acciones ",[145,67790,67555],{},[145,67792,67508],{},".\nGracias a Pinia, el estado del usuario se mantiene consistente en todas partes, y cualquier cambio (como iniciar o cerrar sesión) se refleja automáticamente en todos los componentes que usan esta store.",[12,67795,67796],{},"Algunos casos reales de uso:",[30,67798,67799,67805,67811],{},[33,67800,67801,67804],{},[122,67802,67803],{},"Autenticación de usuarios",": Creas una store para manejar el estado del usuario autenticado, con datos como el token, nombre, roles, etc. Puedes crear acciones para iniciar sesión, cerrar sesión y actualizar la información del usuario.",[33,67806,67807,67810],{},[122,67808,67809],{},"Carrito de compras",": Creas una store para manejar los productos en el carrito, con acciones para agregar, eliminar y actualizar productos. Este estado puede ser accedido desde cualquier parte de la aplicación, como la página de productos y la página del carrito.",[33,67812,67813,67816],{},[122,67814,67815],{},"Preferencias de usuario",": Creas una store para manejar las preferencias del usuario, como el tema (claro\u002Foscuro), idioma, etc. Puedes crear acciones para actualizar estas preferencias y reflejarlas en toda la aplicación.",[12,67818,67819,67820,61],{},"Puedes explorar más sobre Pinia en la ",[22,67821,64614],{"href":64953,"target":27,"rel":67822},[7760,7761],[43,67824],{},[46,67826,67828],{"id":67827},"composables","Composables",[12,67830,67831],{},"Los composables son funciones reutilizables que encapsulan lógica específica, con estado, y pueden ser usados entre diferentes componentes.",[12,67833,67834,67835,67838],{},"Nos permiten organizar mejor nuestro código, promoviendo la reutilización y la separación de responsabilidades. Normalmente toda lógica con estado la pondríamos dentro de un ",[145,67836,67837],{},"\u003Cscript setup>"," en un componente Vue, pero si esa lógica es algo que podría ser útil en varios componentes, podemos extraerla a un composable.",[12,67840,67841,67842,162],{},"Veamos un ejemplo bastante básico. Crea un archivo llamado ",[145,67843,67844],{},"src\u002Fcomposables\u002FuseClipboard.js",[164,67846,67848],{"className":65949,"code":67847,"language":65951,"meta":169,"style":169},"import { ref } from 'vue';\n\nexport function useClipboard() {\n  const copied = ref(false);\n\n  const copyToClipboard = async (text) => {\n    try {\n      await navigator.clipboard.writeText(text);\n      copied.value = true;\n      setTimeout(() => {\n        copied.value = false;\n      }, 2000);\n    } catch (error) {\n      console.error('Failed to copy: ', error);\n    }\n  };\n\n  return {\n    copied,\n    copyToClipboard,\n  };\n}\n",[145,67849,67850,67871,67875,67889,67906,67910,67932,67939,67963,67980,67992,68008,68018,68035,68060,68065,68070,68074,68081,68088,68095,68099],{"__ignoreMap":169},[86,67851,67852,67854,67856,67859,67861,67863,67865,67867,67869],{"class":174,"line":175},[86,67853,179],{"class":178},[86,67855,65978],{"class":219},[86,67857,67858],{"class":304}," ref",[86,67860,65984],{"class":219},[86,67862,65987],{"class":178},[86,67864,11970],{"class":575},[86,67866,65992],{"class":579},[86,67868,10971],{"class":575},[86,67870,65967],{"class":219},[86,67872,67873],{"class":174,"line":192},[86,67874,209],{"emptyLinePlaceholder":208},[86,67876,67877,67879,67882,67885,67887],{"class":174,"line":205},[86,67878,67093],{"class":178},[86,67880,67881],{"class":235}," function",[86,67883,67884],{"class":239}," useClipboard",[86,67886,13418],{"class":219},[86,67888,67263],{"class":219},[86,67890,67891,67893,67896,67898,67900,67902,67904],{"class":174,"line":212},[86,67892,67662],{"class":235},[86,67894,67895],{"class":304}," copied",[86,67897,220],{"class":219},[86,67899,67858],{"class":239},[86,67901,243],{"class":219},[86,67903,3295],{"class":178},[86,67905,66082],{"class":219},[86,67907,67908],{"class":174,"line":227},[86,67909,209],{"emptyLinePlaceholder":208},[86,67911,67912,67914,67917,67919,67922,67924,67926,67928,67930],{"class":174,"line":232},[86,67913,67662],{"class":235},[86,67915,67916],{"class":239}," copyToClipboard",[86,67918,220],{"class":219},[86,67920,67921],{"class":235}," async",[86,67923,606],{"class":219},[86,67925,3141],{"class":304},[86,67927,867],{"class":219},[86,67929,67056],{"class":219},[86,67931,67263],{"class":219},[86,67933,67934,67937],{"class":174,"line":252},[86,67935,67936],{"class":178},"    try",[86,67938,67263],{"class":219},[86,67940,67941,67944,67947,67949,67952,67954,67957,67959,67961],{"class":174,"line":276},[86,67942,67943],{"class":178},"      await",[86,67945,67946],{"class":304}," navigator",[86,67948,61],{"class":219},[86,67950,67951],{"class":304},"clipboard",[86,67953,61],{"class":219},[86,67955,67956],{"class":239},"writeText",[86,67958,243],{"class":219},[86,67960,3141],{"class":304},[86,67962,66082],{"class":219},[86,67964,67965,67968,67970,67973,67975,67978],{"class":174,"line":315},[86,67966,67967],{"class":304},"      copied",[86,67969,61],{"class":219},[86,67971,67972],{"class":304},"value",[86,67974,220],{"class":219},[86,67976,67977],{"class":178}," true",[86,67979,65967],{"class":219},[86,67981,67982,67985,67988,67990],{"class":174,"line":3665},[86,67983,67984],{"class":239},"      setTimeout",[86,67986,67987],{"class":219},"(()",[86,67989,67056],{"class":219},[86,67991,67263],{"class":219},[86,67993,67994,67997,67999,68001,68003,68006],{"class":174,"line":13256},[86,67995,67996],{"class":304},"        copied",[86,67998,61],{"class":219},[86,68000,67972],{"class":304},[86,68002,220],{"class":219},[86,68004,68005],{"class":178}," false",[86,68007,65967],{"class":219},[86,68009,68010,68013,68016],{"class":174,"line":13286},[86,68011,68012],{"class":219},"      },",[86,68014,68015],{"class":223}," 2000",[86,68017,66082],{"class":219},[86,68019,68020,68023,68026,68028,68031,68033],{"class":174,"line":13291},[86,68021,68022],{"class":219},"    }",[86,68024,68025],{"class":178}," catch",[86,68027,606],{"class":219},[86,68029,68030],{"class":304},"error",[86,68032,867],{"class":219},[86,68034,67263],{"class":219},[86,68036,68037,68040,68042,68044,68046,68048,68051,68053,68055,68058],{"class":174,"line":13308},[86,68038,68039],{"class":304},"      console",[86,68041,61],{"class":219},[86,68043,68030],{"class":239},[86,68045,243],{"class":219},[86,68047,10971],{"class":575},[86,68049,68050],{"class":579},"Failed to copy: ",[86,68052,10971],{"class":575},[86,68054,291],{"class":219},[86,68056,68057],{"class":304}," error",[86,68059,66082],{"class":219},[86,68061,68062],{"class":174,"line":13334},[86,68063,68064],{"class":219},"    }\n",[86,68066,68067],{"class":174,"line":13359},[86,68068,68069],{"class":219},"  };\n",[86,68071,68072],{"class":174,"line":13385},[86,68073,209],{"emptyLinePlaceholder":208},[86,68075,68076,68079],{"class":174,"line":13390},[86,68077,68078],{"class":178},"  return",[86,68080,67263],{"class":219},[86,68082,68083,68086],{"class":174,"line":13396},[86,68084,68085],{"class":304},"    copied",[86,68087,1111],{"class":219},[86,68089,68090,68093],{"class":174,"line":3615},[86,68091,68092],{"class":304},"    copyToClipboard",[86,68094,1111],{"class":219},[86,68096,68097],{"class":174,"line":2254},[86,68098,68069],{"class":219},[86,68100,68101],{"class":174,"line":13492},[86,68102,68103],{"class":219},"}\n",[12,68105,68106,68107,68110,68111,68114,68115,68118],{},"Aquí estamos definiendo un composable llamado ",[145,68108,68109],{},"useClipboard"," que proporciona una función para copiar texto al portapapeles y un estado ",[122,68112,68113],{},"reactivo"," ",[145,68116,68117],{},"copied"," que indica si el texto fue copiado exitosamente.",[12,68120,68121,68122,162],{},"Al implementarlo podríamos tener algo como esto. Crea un componente llamado ",[145,68123,68124],{},"src\u002Fcomponents\u002FClipboardExample.vue",[164,68126,68128],{"className":66488,"code":68127,"language":65992,"meta":169,"style":169},"\u003Ctemplate>\n  \u003Cdiv>\n    \u003Cinput v-model=\"textToCopy\" placeholder=\"Type something to copy\" \u002F>\n    \u003Cbutton @click=\"copyToClipboard(textToCopy)\">Copy to Clipboard\u003C\u002Fbutton>\n    \u003Cp v-if=\"copied\">Text copied!\u003C\u002Fp>\n  \u003C\u002Fdiv>\n\u003C\u002Ftemplate>\n\u003Cscript setup>\nimport { ref } from 'vue';\nimport { useClipboard } from '..\u002Fcomposables\u002FuseClipboard';\nconst { copied, copyToClipboard } = useClipboard();\nconst textToCopy = ref('');\n\u003C\u002Fscript>\n",[145,68129,68130,68138,68146,68179,68207,68234,68242,68250,68260,68280,68301,68321,68339],{"__ignoreMap":169},[86,68131,68132,68134,68136],{"class":174,"line":175},[86,68133,41317],{"class":219},[86,68135,66566],{"class":178},[86,68137,41330],{"class":219},[86,68139,68140,68142,68144],{"class":174,"line":192},[86,68141,66255],{"class":219},[86,68143,66391],{"class":178},[86,68145,41330],{"class":219},[86,68147,68148,68150,68153,68156,68158,68160,68163,68165,68168,68170,68172,68175,68177],{"class":174,"line":205},[86,68149,66264],{"class":219},[86,68151,68152],{"class":178},"input",[86,68154,68155],{"class":304}," v-model",[86,68157,258],{"class":219},[86,68159,576],{"class":575},[86,68161,68162],{"class":579},"textToCopy",[86,68164,576],{"class":575},[86,68166,68167],{"class":304}," placeholder",[86,68169,258],{"class":219},[86,68171,576],{"class":575},[86,68173,68174],{"class":579},"Type something to copy",[86,68176,576],{"class":575},[86,68178,66282],{"class":219},[86,68180,68181,68183,68185,68187,68189,68191,68194,68196,68198,68201,68203,68205],{"class":174,"line":212},[86,68182,66264],{"class":219},[86,68184,67498],{"class":178},[86,68186,67501],{"class":304},[86,68188,258],{"class":219},[86,68190,576],{"class":575},[86,68192,68193],{"class":579},"copyToClipboard(textToCopy)",[86,68195,576],{"class":575},[86,68197,66356],{"class":219},[86,68199,68200],{"class":182},"Copy to Clipboard",[86,68202,66362],{"class":219},[86,68204,67498],{"class":178},[86,68206,41330],{"class":219},[86,68208,68209,68211,68213,68215,68217,68219,68221,68223,68225,68228,68230,68232],{"class":174,"line":227},[86,68210,66264],{"class":219},[86,68212,12],{"class":178},[86,68214,67463],{"class":304},[86,68216,258],{"class":219},[86,68218,576],{"class":575},[86,68220,68117],{"class":579},[86,68222,576],{"class":575},[86,68224,66356],{"class":219},[86,68226,68227],{"class":182},"Text copied!",[86,68229,66362],{"class":219},[86,68231,12],{"class":178},[86,68233,41330],{"class":219},[86,68235,68236,68238,68240],{"class":174,"line":232},[86,68237,66371],{"class":219},[86,68239,66391],{"class":178},[86,68241,41330],{"class":219},[86,68243,68244,68246,68248],{"class":174,"line":252},[86,68245,66362],{"class":219},[86,68247,66566],{"class":178},[86,68249,41330],{"class":219},[86,68251,68252,68254,68256,68258],{"class":174,"line":276},[86,68253,41317],{"class":219},[86,68255,66416],{"class":178},[86,68257,66500],{"class":304},[86,68259,41330],{"class":219},[86,68261,68262,68264,68266,68268,68270,68272,68274,68276,68278],{"class":174,"line":315},[86,68263,179],{"class":178},[86,68265,65978],{"class":219},[86,68267,67858],{"class":304},[86,68269,65984],{"class":219},[86,68271,65987],{"class":178},[86,68273,11970],{"class":575},[86,68275,65992],{"class":579},[86,68277,10971],{"class":575},[86,68279,65967],{"class":219},[86,68281,68282,68284,68286,68288,68290,68292,68294,68297,68299],{"class":174,"line":3665},[86,68283,179],{"class":178},[86,68285,65978],{"class":219},[86,68287,67884],{"class":304},[86,68289,65984],{"class":219},[86,68291,65987],{"class":178},[86,68293,11970],{"class":575},[86,68295,68296],{"class":579},"..\u002Fcomposables\u002FuseClipboard",[86,68298,10971],{"class":575},[86,68300,65967],{"class":219},[86,68302,68303,68305,68307,68309,68311,68313,68315,68317,68319],{"class":174,"line":13256},[86,68304,66067],{"class":235},[86,68306,65978],{"class":219},[86,68308,67895],{"class":304},[86,68310,291],{"class":219},[86,68312,67916],{"class":304},[86,68314,65984],{"class":219},[86,68316,220],{"class":219},[86,68318,67884],{"class":239},[86,68320,67637],{"class":219},[86,68322,68323,68325,68328,68330,68332,68334,68337],{"class":174,"line":13286},[86,68324,66067],{"class":235},[86,68326,68327],{"class":304}," textToCopy",[86,68329,220],{"class":219},[86,68331,67858],{"class":239},[86,68333,243],{"class":219},[86,68335,68336],{"class":575},"''",[86,68338,66082],{"class":219},[86,68340,68341,68343,68345],{"class":174,"line":13291},[86,68342,66362],{"class":219},[86,68344,66416],{"class":178},[86,68346,41330],{"class":219},[12,68348,68349,68350,68352,68353,68355],{},"Y luego importa este componente en ",[145,68351,64976],{}," y añádelo debajo del componente ",[145,68354,66673],{}," para probarlo:",[164,68357,68359],{"className":66488,"code":68358,"language":65992,"meta":169,"style":169},"\u003Cscript setup>\nimport { RouterLink, RouterView } from 'vue-router';\nimport HelloWorld from '.\u002Fcomponents\u002FHelloWorld.vue';\nimport ClipboardExample from '.\u002Fcomponents\u002FClipboardExample.vue';\n\u003C\u002Fscript>\n\n\u003Ctemplate>\n  \u003Cheader>\n    \u003Cimg alt=\"Vue logo\" class=\"logo\" src=\"@\u002Fassets\u002Flogo.svg\" width=\"125\" height=\"125\" \u002F>\n\n    \u003Cdiv class=\"wrapper\">\n      \u003CHelloWorld msg=\"You did it!\" \u002F>\n      \u003CClipboardExample \u002F>\n      \u003C!-- Aquí -->\n      \u003Cnav>\n        \u003CRouterLink to=\"\u002F\">Home\u003C\u002FRouterLink>\n        \u003CRouterLink to=\"\u002Fabout\">About\u003C\u002FRouterLink>\n      \u003C\u002Fnav>\n    \u003C\u002Fdiv>\n  \u003C\u002Fheader>\n\n  \u003CRouterView \u002F>\n\u003C\u002Ftemplate>\n",[145,68360,68361,68371,68395,68411,68429,68437,68441,68449,68457,68515,68519,68537,68555,68564,68569,68577,68603,68629,68637,68645,68653,68657,68665],{"__ignoreMap":169},[86,68362,68363,68365,68367,68369],{"class":174,"line":175},[86,68364,41317],{"class":219},[86,68366,66416],{"class":178},[86,68368,66500],{"class":304},[86,68370,41330],{"class":219},[86,68372,68373,68375,68377,68379,68381,68383,68385,68387,68389,68391,68393],{"class":174,"line":192},[86,68374,179],{"class":178},[86,68376,65978],{"class":219},[86,68378,66511],{"class":304},[86,68380,291],{"class":219},[86,68382,66516],{"class":304},[86,68384,65984],{"class":219},[86,68386,65987],{"class":178},[86,68388,11970],{"class":575},[86,68390,66525],{"class":579},[86,68392,10971],{"class":575},[86,68394,65967],{"class":219},[86,68396,68397,68399,68401,68403,68405,68407,68409],{"class":174,"line":205},[86,68398,179],{"class":178},[86,68400,66536],{"class":304},[86,68402,65987],{"class":178},[86,68404,11970],{"class":575},[86,68406,66543],{"class":579},[86,68408,10971],{"class":575},[86,68410,65967],{"class":219},[86,68412,68413,68415,68418,68420,68422,68425,68427],{"class":174,"line":212},[86,68414,179],{"class":178},[86,68416,68417],{"class":304}," ClipboardExample",[86,68419,65987],{"class":178},[86,68421,11970],{"class":575},[86,68423,68424],{"class":579},".\u002Fcomponents\u002FClipboardExample.vue",[86,68426,10971],{"class":575},[86,68428,65967],{"class":219},[86,68430,68431,68433,68435],{"class":174,"line":227},[86,68432,66362],{"class":219},[86,68434,66416],{"class":178},[86,68436,41330],{"class":219},[86,68438,68439],{"class":174,"line":232},[86,68440,209],{"emptyLinePlaceholder":208},[86,68442,68443,68445,68447],{"class":174,"line":252},[86,68444,41317],{"class":219},[86,68446,66566],{"class":178},[86,68448,41330],{"class":219},[86,68450,68451,68453,68455],{"class":174,"line":276},[86,68452,66255],{"class":219},[86,68454,66575],{"class":178},[86,68456,41330],{"class":219},[86,68458,68459,68461,68463,68465,68467,68469,68471,68473,68475,68477,68479,68481,68483,68485,68487,68489,68491,68493,68495,68497,68499,68501,68503,68505,68507,68509,68511,68513],{"class":174,"line":315},[86,68460,66264],{"class":219},[86,68462,1945],{"class":178},[86,68464,66586],{"class":304},[86,68466,258],{"class":219},[86,68468,576],{"class":575},[86,68470,66593],{"class":579},[86,68472,576],{"class":575},[86,68474,66598],{"class":304},[86,68476,258],{"class":219},[86,68478,576],{"class":575},[86,68480,66605],{"class":579},[86,68482,576],{"class":575},[86,68484,66431],{"class":304},[86,68486,258],{"class":219},[86,68488,576],{"class":575},[86,68490,66616],{"class":579},[86,68492,576],{"class":575},[86,68494,66621],{"class":304},[86,68496,258],{"class":219},[86,68498,576],{"class":575},[86,68500,66628],{"class":579},[86,68502,576],{"class":575},[86,68504,34993],{"class":304},[86,68506,258],{"class":219},[86,68508,576],{"class":575},[86,68510,66628],{"class":579},[86,68512,576],{"class":575},[86,68514,66282],{"class":219},[86,68516,68517],{"class":174,"line":3665},[86,68518,209],{"emptyLinePlaceholder":208},[86,68520,68521,68523,68525,68527,68529,68531,68533,68535],{"class":174,"line":13256},[86,68522,66264],{"class":219},[86,68524,66391],{"class":178},[86,68526,66598],{"class":304},[86,68528,258],{"class":219},[86,68530,576],{"class":575},[86,68532,66661],{"class":579},[86,68534,576],{"class":575},[86,68536,41330],{"class":219},[86,68538,68539,68541,68543,68545,68547,68549,68551,68553],{"class":174,"line":13286},[86,68540,66670],{"class":219},[86,68542,66673],{"class":178},[86,68544,66676],{"class":304},[86,68546,258],{"class":219},[86,68548,576],{"class":575},[86,68550,66683],{"class":579},[86,68552,576],{"class":575},[86,68554,66282],{"class":219},[86,68556,68557,68559,68562],{"class":174,"line":13291},[86,68558,66670],{"class":219},[86,68560,68561],{"class":178},"ClipboardExample",[86,68563,66282],{"class":219},[86,68565,68566],{"class":174,"line":13308},[86,68567,68568],{"class":1360},"      \u003C!-- Aquí -->\n",[86,68570,68571,68573,68575],{"class":174,"line":13334},[86,68572,66670],{"class":219},[86,68574,66698],{"class":178},[86,68576,41330],{"class":219},[86,68578,68579,68581,68583,68585,68587,68589,68591,68593,68595,68597,68599,68601],{"class":174,"line":13359},[86,68580,66705],{"class":219},[86,68582,66708],{"class":178},[86,68584,41346],{"class":304},[86,68586,258],{"class":219},[86,68588,576],{"class":575},[86,68590,16555],{"class":579},[86,68592,576],{"class":575},[86,68594,66356],{"class":219},[86,68596,66723],{"class":182},[86,68598,66362],{"class":219},[86,68600,66708],{"class":178},[86,68602,41330],{"class":219},[86,68604,68605,68607,68609,68611,68613,68615,68617,68619,68621,68623,68625,68627],{"class":174,"line":13385},[86,68606,66705],{"class":219},[86,68608,66708],{"class":178},[86,68610,41346],{"class":304},[86,68612,258],{"class":219},[86,68614,576],{"class":575},[86,68616,66744],{"class":579},[86,68618,576],{"class":575},[86,68620,66356],{"class":219},[86,68622,66751],{"class":182},[86,68624,66362],{"class":219},[86,68626,66708],{"class":178},[86,68628,41330],{"class":219},[86,68630,68631,68633,68635],{"class":174,"line":13390},[86,68632,66762],{"class":219},[86,68634,66698],{"class":178},[86,68636,41330],{"class":219},[86,68638,68639,68641,68643],{"class":174,"line":13396},[86,68640,66771],{"class":219},[86,68642,66391],{"class":178},[86,68644,41330],{"class":219},[86,68646,68647,68649,68651],{"class":174,"line":3615},[86,68648,66371],{"class":219},[86,68650,66575],{"class":178},[86,68652,41330],{"class":219},[86,68654,68655],{"class":174,"line":2254},[86,68656,209],{"emptyLinePlaceholder":208},[86,68658,68659,68661,68663],{"class":174,"line":13492},[86,68660,66255],{"class":219},[86,68662,66794],{"class":178},[86,68664,66282],{"class":219},[86,68666,68667,68669,68671],{"class":174,"line":13545},[86,68668,66362],{"class":219},[86,68670,66566],{"class":178},[86,68672,41330],{"class":219},[12,68674,68675,68676,68678],{},"El estado ",[145,68677,68117],{}," nos permite mostrar un mensaje cuando el texto ha sido copiado exitosamente.",[12,68680,68681],{},"¿Que logramos con esto?",[30,68683,68684,68693,68699],{},[33,68685,68686,68689,68690,68692],{},[122,68687,68688],{},"Reutilización",": Podemos usar ",[145,68691,68109],{}," en cualquier componente que necesite funcionalidad de copiar al portapapeles, sin duplicar código.",[33,68694,68695,68698],{},[122,68696,68697],{},"Organización",": La lógica relacionada con el portapapeles está encapsulada en un solo lugar.",[33,68700,68701,68704],{},[122,68702,68703],{},"Mantenimiento",": Si necesitamos cambiar la forma en que copiamos al portapapeles, solo tenemos que modificar el composable, no todos los componentes que lo usan.",[323,68706,68708],{"id":68707},"cuál-es-la-diferencia-entre-un-composable-y-una-store-de-pinia","¿Cuál es la diferencia entre un composable y una store de Pinia?",[12,68710,68711,68714,68715,68718],{},[122,68712,68713],{},"Estado global vs estado local",": Las stores de Pinia están diseñadas para manejar un estado global en la aplicación, datos que deben ser ",[122,68716,68717],{},"accesibles y compartidos"," desde cualquier parte.",[12,68720,68721,68722,68725,68726,68728],{},"Los composables, por otro lado, manejan lógica y estado que puede ser reutilizado en múltiples componentes, pero que ",[122,68723,68724],{},"nada de eso es compartido",". Por ejemplo, si tengo varios componentes que necesitan funcionalidad para copiar al portapapeles (y que necesitan algún control de estado), usaría un composable, y el estado ",[145,68727,68117],{}," sería local en cada instancia del composable. En cambio, si necesito saber en varios lugares si actualmente se ha realizado una copia al portapapeles a nivel de aplicación, usaría una store de Pinia, porque aquí si se darían cuenta todos los componentes y todos podrían reaccionar a ese cambio.",[12,68730,68731,68732,68734,68735,68737],{},"Pongámoslo como un ejemplo: gracias a la variable ",[145,68733,68117],{}," puedo mostrar algo dentro del mismo componente, como el mensaje de \"Texto copiado\", ahora, si quisiera que por ejemplo el layout de mi aplicación muestre un ícono en la barra de navegación cada vez que se copie algo al portapapeles, entonces sería mejor que utilizara una store de Pinia para manejar ese estado globalmente, así al copiar desde mi componente ",[145,68736,68561],{},", el layout también se daría cuenta del cambio y podría mostrar el ícono.",[323,68739,68741],{"id":68740},"cuál-es-la-diferencia-entre-un-composable-y-un-archivo-de-utilidades-utils","¿Cuál es la diferencia entre un composable y un archivo de utilidades (utils)?",[12,68743,68744,68745,68747],{},"Las funciones de utilidades son generalmente más simples y no tienen estado, reciben entradas (algunas) y devuelven salidas sin efectos secundarios. Por ejemplo, si no necesitáramos el estado ",[145,68746,68117],{}," y solo quisiéramos una función para copiar texto, podríamos crear una simple función de utilidad en lugar de un composable:",[164,68749,68751],{"className":65949,"code":68750,"language":65951,"meta":169,"style":169},"export function copyToClipboard(text) {\n  return navigator.clipboard.writeText(text);\n}\n",[145,68752,68753,68769,68789],{"__ignoreMap":169},[86,68754,68755,68757,68759,68761,68763,68765,68767],{"class":174,"line":175},[86,68756,67093],{"class":178},[86,68758,67881],{"class":235},[86,68760,67916],{"class":239},[86,68762,243],{"class":219},[86,68764,3141],{"class":304},[86,68766,867],{"class":219},[86,68768,67263],{"class":219},[86,68770,68771,68773,68775,68777,68779,68781,68783,68785,68787],{"class":174,"line":192},[86,68772,68078],{"class":178},[86,68774,67946],{"class":304},[86,68776,61],{"class":219},[86,68778,67951],{"class":304},[86,68780,61],{"class":219},[86,68782,67956],{"class":239},[86,68784,243],{"class":219},[86,68786,3141],{"class":304},[86,68788,66082],{"class":219},[86,68790,68791],{"class":174,"line":205},[86,68792,68103],{"class":219},[12,68794,68795],{},"Lecturas recomendadas:",[30,68797,68798,68805,68812],{},[33,68799,68800],{},[22,68801,68804],{"href":68802,"target":27,"rel":68803},"https:\u002F\u002Fvuejs.org\u002Fguide\u002Freusability\u002Fcomposables.html",[7760,7761],"Composables - Vue.js Documentation",[33,68806,68807],{},[22,68808,68811],{"href":68809,"target":27,"rel":68810},"https:\u002F\u002Fdev.to\u002Fjacobandrewsky\u002Fgood-practices-and-design-patterns-for-vue-composables-24lk",[7760,7761],"Good Practices and Design Patterns for Vue Composables",[33,68813,68814],{},[22,68815,68818],{"href":68816,"target":27,"rel":68817},"https:\u002F\u002Frobconery.com\u002Ffrontend\u002Fwhat-should-be-a-plugin-vs-a-composable-vs-a-store-in-nuxt\u002F",[7760,7761],"What should be a Plugin vs a Composable vs a Store in Nuxt",[323,68820,68822],{"id":68821},"vueuse","VueUse",[12,68824,68825,68829],{},[22,68826,68822],{"href":68827,"target":27,"rel":68828},"https:\u002F\u002Fvueuse.org\u002F",[7760,7761]," es una colección de composables para Vue 3. Proporciona una amplia gama de funcionalidades listas para usar, desde manejo de estado hasta interacciones con el DOM y APIs del navegador. Puedes explorar la documentación oficial para ver todos los composables disponibles y cómo usarlos en tus proyectos.",[12,68831,68832,68835],{},[1945,68833],{"alt":68822,"src":68834},"\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fvue-use.webp",[901,68836,68822],{},[12,68838,68839],{},"Algunos ejemplos populares de composables en VueUse incluyen:",[30,68841,68842,68848,68854,68860,68866],{},[33,68843,68844,68847],{},[145,68845,68846],{},"useBreakpoints",": para poder manejar breakpoints en tu aplicación y ayudar con el diseño responsivo.",[33,68849,68850,68853],{},[145,68851,68852],{},"useFetch",": para realizar solicitudes HTTP de manera sencilla.",[33,68855,68856,68859],{},[145,68857,68858],{},"useLocalStorage",": para sincronizar datos con el almacenamiento local del navegador.",[33,68861,68862,68865],{},[145,68863,68864],{},"useDark",": para manejar temas oscuros y claros en la aplicación.",[33,68867,68868,68870],{},[145,68869,68109],{},": para copiar texto al portapapeles (similar al que creamos antes).",[12,68872,68873],{},"Es una colección muy útil que puede ahorrarte tiempo si necesitas alguna de estas funcionalidades.\nSolo ten cuidado de no sobrecargar tu proyecto con dependencias innecesarias, instala solo lo que realmente vayas a usar y solo si realmente necesitas una librería para ella.",[43,68875],{},[46,68877,68879],{"id":68878},"eslint-y-prettier","ESLint y Prettier",[12,68881,68882,68883,68886],{},"Acostúmbrate a usar ",[122,68884,68885],{},"ESLint",", es demasiado útil para mantener la calidad del código y evitar errores comunes.\nLa configuración generada por Vite es un buen punto de partida, pero siempre recomiendo personalizarla.",[12,68888,68889,68890,68894,68895,61],{},"Puedes explorar las reglas disponibles en la documentación oficial ",[22,68891,68885],{"href":68892,"target":27,"rel":68893},"https:\u002F\u002Feslint.org\u002Fdocs\u002Frules\u002F",[7760,7761]," y de ",[22,68896,68899],{"href":68897,"target":27,"rel":68898},"https:\u002F\u002Feslint.vuejs.org\u002Frules\u002F",[7760,7761],"eslint-plugin-vue",[12,68901,68902],{},"Todas las reglas pueden ser configuradas como \"off\", \"warn\" o \"error\", dependiendo de la severidad que quieras asignarles:",[164,68904,68908],{"className":68905,"code":68906,"language":68907,"meta":169,"style":169},"language-js shiki shiki-themes vitesse-light vitesse-dark","\"no-console\": \"warn\", \u002F\u002F Muestra una advertencia si se usa console.log\n\"eqeqeq\": \"error\", \u002F\u002F Fuerza el uso de === y !== en lugar de == y !=\n\"vue\u002Fmulti-word-component-names\": \"off\", \u002F\u002F Desactiva la regla que obliga a usar nombres de componentes con múltiples palabras\n","js",[145,68909,68910,68933,68955],{"__ignoreMap":169},[86,68911,68912,68914,68917,68919,68921,68923,68926,68928,68930],{"class":174,"line":175},[86,68913,576],{"class":575},[86,68915,68916],{"class":579},"no-console",[86,68918,576],{"class":575},[86,68920,45122],{"class":182},[86,68922,576],{"class":575},[86,68924,68925],{"class":579},"warn",[86,68927,576],{"class":575},[86,68929,291],{"class":219},[86,68931,68932],{"class":1360}," \u002F\u002F Muestra una advertencia si se usa console.log\n",[86,68934,68935,68937,68940,68942,68944,68946,68948,68950,68952],{"class":174,"line":192},[86,68936,576],{"class":575},[86,68938,68939],{"class":579},"eqeqeq",[86,68941,576],{"class":575},[86,68943,45122],{"class":182},[86,68945,576],{"class":575},[86,68947,68030],{"class":579},[86,68949,576],{"class":575},[86,68951,291],{"class":219},[86,68953,68954],{"class":1360}," \u002F\u002F Fuerza el uso de === y !== en lugar de == y !=\n",[86,68956,68957,68959,68962,68964,68966,68968,68971,68973,68975],{"class":174,"line":205},[86,68958,576],{"class":575},[86,68960,68961],{"class":579},"vue\u002Fmulti-word-component-names",[86,68963,576],{"class":575},[86,68965,45122],{"class":182},[86,68967,576],{"class":575},[86,68969,68970],{"class":579},"off",[86,68972,576],{"class":575},[86,68974,291],{"class":219},[86,68976,68977],{"class":1360}," \u002F\u002F Desactiva la regla que obliga a usar nombres de componentes con múltiples palabras\n",[12,68979,68980,68981,68984,68985,61],{},"En el proyecto que creamos, puedes usar el comando ",[145,68982,68983],{},"npm run lint"," para revisar todo tu código según la configuración del archivo ",[145,68986,68987],{},"eslint.config.js",[12,68989,68990,68993],{},[122,68991,68992],{},"Sobre Prettier",", existe cierto debate sobre su uso, a mucha gente no le gusta porque puede imponer un estilo que no les agrada, así que pruébalo, explóralo y úsalo solo si te sientes cómodo con él.\nEn lugar de Prettier, para intentar siempre mantener un estilo consistente, puedes usar alternativas como EditorConfig, las propias reglas de ESLint o la configuración del editor de código que estés usando.",[12,68995,68996],{},"Si usas algunas de estas herramientas puedes explorar sus extensiones:",[30,68998,68999,69006,69013],{},[33,69000,69001],{},[22,69002,69005],{"href":69003,"target":27,"rel":69004},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=dbaeumer.vscode-eslint",[7760,7761],"ESLint extension for VS Code",[33,69007,69008],{},[22,69009,69012],{"href":69010,"target":27,"rel":69011},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=esbenp.prettier-vscode",[7760,7761],"Prettier - Code formatter",[33,69014,69015],{},[22,69016,69019],{"href":69017,"target":27,"rel":69018},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=EditorConfig.EditorConfig",[7760,7761],"EditorConfig for VS Code",[43,69021],{},[46,69023,69025],{"id":69024},"extra-instalando-tailwind-css-v4","EXTRA: Instalando Tailwind CSS v4",[12,69027,69028,69029,69034],{},"CSS puro está más que bien, puede lograr resultados increíbles (a veces incluso ",[22,69030,69033],{"href":69031,"target":27,"rel":69032},"https:\u002F\u002Fgithub.com\u002Fyou-dont-need\u002FYou-Dont-Need-JavaScript",[7760,7761],"sin necesitar JavaScript","), pero un opción que tienes para acelerar tu desarrollo y mantener un estilo consistente es Tailwind CSS.",[12,69036,69037,69038,69043],{},"Siguiendo los pasos oficiales de la ",[22,69039,69042],{"href":69040,"target":27,"rel":69041},"https:\u002F\u002Ftailwindcss.com\u002Fdocs\u002Finstallation\u002Fusing-vite",[7760,7761],"documentación de Tailwind CSS",", instalemos Tailwind CSS v4 en nuestro proyecto Vue con Vite.",[12,69045,69046],{},"Primero (estando dentro de la carpeta del proyecto), instala Tailwind CSS y su plugin para Vite:",[164,69048,69050],{"className":64293,"code":69049,"language":64295,"meta":169,"style":169},"npm install tailwindcss @tailwindcss\u002Fvite\n",[145,69051,69052],{"__ignoreMap":169},[86,69053,69054,69056,69059,69062],{"class":174,"line":175},[86,69055,64231],{"class":239},[86,69057,69058],{"class":579}," install",[86,69060,69061],{"class":579}," tailwindcss",[86,69063,69064],{"class":579}," @tailwindcss\u002Fvite\n",[12,69066,69067,69068,162],{},"Luego, agregamos el plugin a nuestro archivo ",[145,69069,69070],{},"vite.config.js",[164,69072,69074],{"className":65949,"code":69073,"language":65951,"meta":169,"style":169},"import { fileURLToPath, URL } from 'node:url';\n\nimport { defineConfig } from 'vite';\nimport vue from '@vitejs\u002Fplugin-vue';\nimport vueDevTools from 'vite-plugin-vue-devtools';\nimport tailwindcss from '@tailwindcss\u002Fvite'; \u002F\u002F Importamos el plugin\n\n\u002F\u002F https:\u002F\u002Fvite.dev\u002Fconfig\u002F\nexport default defineConfig({\n  plugins: [\n    vue(),\n    vueDevTools(),\n    tailwindcss(), \u002F\u002F Agregamos a la configuración de Vite\n  ],\n  resolve: {\n    alias: {\n      '@': fileURLToPath(new URL('.\u002Fsrc', import.meta.url)),\n    },\n  },\n});\n",[145,69075,69076,69103,69107,69129,69147,69165,69186,69190,69195,69205,69214,69222,69229,69239,69243,69252,69261,69307,69311,69315],{"__ignoreMap":169},[86,69077,69078,69080,69082,69085,69087,69090,69092,69094,69096,69099,69101],{"class":174,"line":175},[86,69079,179],{"class":178},[86,69081,65978],{"class":219},[86,69083,69084],{"class":304}," fileURLToPath",[86,69086,291],{"class":219},[86,69088,69089],{"class":304}," URL",[86,69091,65984],{"class":219},[86,69093,65987],{"class":178},[86,69095,11970],{"class":575},[86,69097,69098],{"class":579},"node:url",[86,69100,10971],{"class":575},[86,69102,65967],{"class":219},[86,69104,69105],{"class":174,"line":192},[86,69106,209],{"emptyLinePlaceholder":208},[86,69108,69109,69111,69113,69116,69118,69120,69122,69125,69127],{"class":174,"line":205},[86,69110,179],{"class":178},[86,69112,65978],{"class":219},[86,69114,69115],{"class":304}," defineConfig",[86,69117,65984],{"class":219},[86,69119,65987],{"class":178},[86,69121,11970],{"class":575},[86,69123,69124],{"class":579},"vite",[86,69126,10971],{"class":575},[86,69128,65967],{"class":219},[86,69130,69131,69133,69136,69138,69140,69143,69145],{"class":174,"line":212},[86,69132,179],{"class":178},[86,69134,69135],{"class":304}," vue",[86,69137,65987],{"class":178},[86,69139,11970],{"class":575},[86,69141,69142],{"class":579},"@vitejs\u002Fplugin-vue",[86,69144,10971],{"class":575},[86,69146,65967],{"class":219},[86,69148,69149,69151,69154,69156,69158,69161,69163],{"class":174,"line":227},[86,69150,179],{"class":178},[86,69152,69153],{"class":304}," vueDevTools",[86,69155,65987],{"class":178},[86,69157,11970],{"class":575},[86,69159,69160],{"class":579},"vite-plugin-vue-devtools",[86,69162,10971],{"class":575},[86,69164,65967],{"class":219},[86,69166,69167,69169,69171,69173,69175,69178,69180,69183],{"class":174,"line":232},[86,69168,179],{"class":178},[86,69170,69061],{"class":304},[86,69172,65987],{"class":178},[86,69174,11970],{"class":575},[86,69176,69177],{"class":579},"@tailwindcss\u002Fvite",[86,69179,10971],{"class":575},[86,69181,69182],{"class":219},";",[86,69184,69185],{"class":1360}," \u002F\u002F Importamos el plugin\n",[86,69187,69188],{"class":174,"line":252},[86,69189,209],{"emptyLinePlaceholder":208},[86,69191,69192],{"class":174,"line":276},[86,69193,69194],{"class":1360},"\u002F\u002F https:\u002F\u002Fvite.dev\u002Fconfig\u002F\n",[86,69196,69197,69199,69201,69203],{"class":174,"line":315},[86,69198,67093],{"class":178},[86,69200,67096],{"class":178},[86,69202,69115],{"class":239},[86,69204,44326],{"class":219},[86,69206,69207,69210,69212],{"class":174,"line":3665},[86,69208,69209],{"class":812},"  plugins",[86,69211,162],{"class":219},[86,69213,66954],{"class":219},[86,69215,69216,69219],{"class":174,"line":13256},[86,69217,69218],{"class":239},"    vue",[86,69220,69221],{"class":219},"(),\n",[86,69223,69224,69227],{"class":174,"line":13286},[86,69225,69226],{"class":239},"    vueDevTools",[86,69228,69221],{"class":219},[86,69230,69231,69234,69236],{"class":174,"line":13291},[86,69232,69233],{"class":239},"    tailwindcss",[86,69235,44184],{"class":219},[86,69237,69238],{"class":1360}," \u002F\u002F Agregamos a la configuración de Vite\n",[86,69240,69241],{"class":174,"line":13308},[86,69242,67079],{"class":219},[86,69244,69245,69248,69250],{"class":174,"line":13334},[86,69246,69247],{"class":812},"  resolve",[86,69249,162],{"class":219},[86,69251,67263],{"class":219},[86,69253,69254,69257,69259],{"class":174,"line":13359},[86,69255,69256],{"class":812},"    alias",[86,69258,162],{"class":219},[86,69260,67263],{"class":219},[86,69262,69263,69266,69269,69271,69273,69275,69277,69280,69282,69284,69286,69289,69291,69293,69295,69297,69299,69301,69304],{"class":174,"line":13385},[86,69264,69265],{"class":575},"      '",[86,69267,69268],{"class":579},"@",[86,69270,10971],{"class":575},[86,69272,162],{"class":219},[86,69274,69084],{"class":239},[86,69276,243],{"class":219},[86,69278,69279],{"class":235},"new",[86,69281,69089],{"class":239},[86,69283,243],{"class":219},[86,69285,10971],{"class":575},[86,69287,69288],{"class":579},".\u002Fsrc",[86,69290,10971],{"class":575},[86,69292,291],{"class":219},[86,69294,67059],{"class":178},[86,69296,61],{"class":219},[86,69298,66267],{"class":812},[86,69300,61],{"class":219},[86,69302,69303],{"class":304},"url",[86,69305,69306],{"class":219},")),\n",[86,69308,69309],{"class":174,"line":13390},[86,69310,67006],{"class":219},[86,69312,69313],{"class":174,"line":13396},[86,69314,67415],{"class":219},[86,69316,69317],{"class":174,"line":3615},[86,69318,67084],{"class":219},[12,69320,69321,69322,69325],{},"Luego en el archivo ",[145,69323,69324],{},"src\u002Fassets\u002Fmain.css",", reemplaza todo el contenido por lo siguiente:",[164,69327,69331],{"className":69328,"code":69329,"language":69330,"meta":169,"style":169},"language-css shiki shiki-themes vitesse-light vitesse-dark","@import '.\u002Fbase.css';\n\n@import 'tailwindcss';\n","css",[145,69332,69333,69348,69352],{"__ignoreMap":169},[86,69334,69335,69337,69339,69341,69344,69346],{"class":174,"line":175},[86,69336,69268],{"class":219},[86,69338,179],{"class":178},[86,69340,11970],{"class":575},[86,69342,69343],{"class":579},".\u002Fbase.css",[86,69345,10971],{"class":575},[86,69347,65967],{"class":219},[86,69349,69350],{"class":174,"line":192},[86,69351,209],{"emptyLinePlaceholder":208},[86,69353,69354,69356,69358,69360,69363,69365],{"class":174,"line":205},[86,69355,69268],{"class":219},[86,69357,179],{"class":178},[86,69359,11970],{"class":575},[86,69361,69362],{"class":579},"tailwindcss",[86,69364,10971],{"class":575},[86,69366,65967],{"class":219},[12,69368,69369,69370,69373],{},"Aprovechamos a limpiar el archivo ",[145,69371,69372],{},"src\u002Fassets\u002Fbase.css"," y dejar solo lo necesario:",[164,69375,69377],{"className":69328,"code":69376,"language":69330,"meta":169,"style":169},"*,\n*::before,\n*::after {\n  box-sizing: border-box;\n  margin: 0;\n  font-weight: normal;\n}\n\nbody {\n  min-height: 100vh;\n  color: #333;\n  background: #fff;\n  transition:\n    color 0.5s,\n    background-color 0.5s;\n  line-height: 1.6;\n  font-family: Inter, sans-serif;\n  font-size: 15px;\n  text-rendering: optimizeLegibility;\n  -webkit-font-smoothing: antialiased;\n  -moz-osx-font-smoothing: grayscale;\n}\n",[145,69378,69379,69385,69397,69408,69420,69431,69443,69447,69451,69457,69472,69487,69501,69508,69520,69531,69543,69560,69574,69586,69598,69610],{"__ignoreMap":169},[86,69380,69381,69383],{"class":174,"line":175},[86,69382,34946],{"class":178},[86,69384,1111],{"class":219},[86,69386,69387,69389,69392,69395],{"class":174,"line":192},[86,69388,34946],{"class":178},[86,69390,69391],{"class":219},"::",[86,69393,69394],{"class":304},"before",[86,69396,1111],{"class":219},[86,69398,69399,69401,69403,69406],{"class":174,"line":205},[86,69400,34946],{"class":178},[86,69402,69391],{"class":219},[86,69404,69405],{"class":304},"after",[86,69407,67263],{"class":219},[86,69409,69410,69413,69415,69418],{"class":174,"line":212},[86,69411,69412],{"class":812},"  box-sizing",[86,69414,162],{"class":219},[86,69416,69417],{"class":215}," border-box",[86,69419,65967],{"class":219},[86,69421,69422,69425,69427,69429],{"class":174,"line":227},[86,69423,69424],{"class":812},"  margin",[86,69426,162],{"class":219},[86,69428,33979],{"class":223},[86,69430,65967],{"class":219},[86,69432,69433,69436,69438,69441],{"class":174,"line":232},[86,69434,69435],{"class":812},"  font-weight",[86,69437,162],{"class":219},[86,69439,69440],{"class":215}," normal",[86,69442,65967],{"class":219},[86,69444,69445],{"class":174,"line":252},[86,69446,68103],{"class":219},[86,69448,69449],{"class":174,"line":276},[86,69450,209],{"emptyLinePlaceholder":208},[86,69452,69453,69455],{"class":174,"line":315},[86,69454,66382],{"class":178},[86,69456,67263],{"class":219},[86,69458,69459,69462,69464,69467,69470],{"class":174,"line":3665},[86,69460,69461],{"class":812},"  min-height",[86,69463,162],{"class":219},[86,69465,69466],{"class":223}," 100",[86,69468,69469],{"class":235},"vh",[86,69471,65967],{"class":219},[86,69473,69474,69477,69479,69482,69485],{"class":174,"line":13256},[86,69475,69476],{"class":812},"  color",[86,69478,162],{"class":219},[86,69480,69481],{"class":219}," #",[86,69483,69484],{"class":215},"333",[86,69486,65967],{"class":219},[86,69488,69489,69492,69494,69496,69499],{"class":174,"line":13286},[86,69490,69491],{"class":812},"  background",[86,69493,162],{"class":219},[86,69495,69481],{"class":219},[86,69497,69498],{"class":215},"fff",[86,69500,65967],{"class":219},[86,69502,69503,69506],{"class":174,"line":13291},[86,69504,69505],{"class":812},"  transition",[86,69507,34896],{"class":219},[86,69509,69510,69513,69516,69518],{"class":174,"line":13308},[86,69511,69512],{"class":215},"    color",[86,69514,69515],{"class":223}," 0.5",[86,69517,7892],{"class":235},[86,69519,1111],{"class":219},[86,69521,69522,69525,69527,69529],{"class":174,"line":13334},[86,69523,69524],{"class":182},"    background-color ",[86,69526,31150],{"class":223},[86,69528,7892],{"class":235},[86,69530,65967],{"class":219},[86,69532,69533,69536,69538,69541],{"class":174,"line":13359},[86,69534,69535],{"class":812},"  line-height",[86,69537,162],{"class":219},[86,69539,69540],{"class":223}," 1.6",[86,69542,65967],{"class":219},[86,69544,69545,69548,69550,69553,69555,69558],{"class":174,"line":13385},[86,69546,69547],{"class":812},"  font-family",[86,69549,162],{"class":219},[86,69551,69552],{"class":182}," Inter",[86,69554,291],{"class":219},[86,69556,69557],{"class":215}," sans-serif",[86,69559,65967],{"class":219},[86,69561,69562,69565,69567,69569,69572],{"class":174,"line":13390},[86,69563,69564],{"class":812},"  font-size",[86,69566,162],{"class":219},[86,69568,40857],{"class":223},[86,69570,69571],{"class":235},"px",[86,69573,65967],{"class":219},[86,69575,69576,69579,69581,69584],{"class":174,"line":13396},[86,69577,69578],{"class":812},"  text-rendering",[86,69580,162],{"class":219},[86,69582,69583],{"class":215}," optimizeLegibility",[86,69585,65967],{"class":219},[86,69587,69588,69591,69593,69596],{"class":174,"line":3615},[86,69589,69590],{"class":812},"  -webkit-font-smoothing",[86,69592,162],{"class":219},[86,69594,69595],{"class":215}," antialiased",[86,69597,65967],{"class":219},[86,69599,69600,69603,69605,69608],{"class":174,"line":2254},[86,69601,69602],{"class":812},"  -moz-osx-font-smoothing",[86,69604,162],{"class":219},[86,69606,69607],{"class":215}," grayscale",[86,69609,65967],{"class":219},[86,69611,69612],{"class":174,"line":13492},[86,69613,68103],{"class":219},[12,69615,69616,69617,69620],{},"Ahora probemos que todo funciona correctamente. Primero, detén el servidor de desarrollo si está corriendo (",[145,69618,69619],{},"Ctrl + C"," en la terminal) y luego vuelve a iniciarlo:",[164,69622,69623],{"className":64293,"code":64541,"language":64295,"meta":169,"style":169},[145,69624,69625],{"__ignoreMap":169},[86,69626,69627,69629,69631],{"class":174,"line":175},[86,69628,64231],{"class":239},[86,69630,64530],{"class":579},[86,69632,64552],{"class":579},[12,69634,66482,69635,69637],{},[145,69636,66485],{}," y reemplaza todo el contenido por lo siguiente:",[164,69639,69641],{"className":66488,"code":69640,"language":65992,"meta":169,"style":169},"\u003Cscript setup>\nimport { RouterLink, RouterView } from 'vue-router';\n\u003C\u002Fscript>\n\n\u003Ctemplate>\n  \u003Cdiv class=\"flex h-screen flex-col bg-gray-50\">\n    \u003C!-- App Bar -->\n    \u003Cheader class=\"flex h-16 items-center justify-between bg-white px-6 shadow-sm\">\n      \u003Cdiv class=\"text-xl font-bold text-gray-800\">My Project\u003C\u002Fdiv>\n      \u003Cnav class=\"flex gap-4\" aria-label=\"Main Navigation\">\n        \u003Ca href=\"#\" class=\"text-gray-600 hover:text-gray-900\">Home\u003C\u002Fa>\n        \u003Ca href=\"#\" class=\"text-gray-600 hover:text-gray-900\">Profile\u003C\u002Fa>\n      \u003C\u002Fnav>\n    \u003C\u002Fheader>\n\n    \u003Cdiv class=\"flex flex-1 overflow-hidden\">\n      \u003C!-- Sidebar -->\n      \u003Caside class=\"w-64 overflow-y-auto bg-white border-r border-gray-200\">\n        \u003Cnav class=\"p-4 space-y-2\" aria-label=\"Sidebar Navigation\">\n          \u003CRouterLink\n            to=\"\u002F\"\n            class=\"block rounded-md px-4 py-2 text-gray-700 hover:bg-gray-100\"\n            exact-active-class=\"text-indigo-700 font-bold\"\n          >\n            Home\n          \u003C\u002FRouterLink>\n          \u003CRouterLink\n            to=\"\u002Fabout\"\n            class=\"block rounded-md px-4 py-2 text-gray-700 hover:bg-gray-100\"\n            exact-active-class=\"text-indigo-700 font-bold\"\n          >\n            About\n          \u003C\u002FRouterLink>\n        \u003C\u002Fnav>\n      \u003C\u002Faside>\n\n      \u003C!-- Main Content -->\n      \u003Cmain class=\"flex-1 overflow-y-auto p-6\">\n        \u003CRouterView \u002F>\n      \u003C\u002Fmain>\n    \u003C\u002Fdiv>\n\n    \u003C!-- Footer -->\n    \u003Cfooter\n      class=\"flex h-12 items-center justify-center bg-white border-t border-gray-200 text-sm text-gray-500\"\n    >\n      © 2025 My Project. All rights reserved.\n    \u003C\u002Ffooter>\n  \u003C\u002Fdiv>\n\u003C\u002Ftemplate>\n",[145,69642,69643,69653,69677,69685,69689,69697,69716,69721,69740,69768,69799,69837,69874,69882,69890,69894,69913,69918,69938,69968,69976,69990,70004,70018,70023,70028,70037,70043,70055,70067,70079,70083,70088,70096,70105,70113,70117,70122,70142,70150,70158,70166,70170,70175,70182,70196,70201,70213,70222,70230],{"__ignoreMap":169},[86,69644,69645,69647,69649,69651],{"class":174,"line":175},[86,69646,41317],{"class":219},[86,69648,66416],{"class":178},[86,69650,66500],{"class":304},[86,69652,41330],{"class":219},[86,69654,69655,69657,69659,69661,69663,69665,69667,69669,69671,69673,69675],{"class":174,"line":192},[86,69656,179],{"class":178},[86,69658,65978],{"class":219},[86,69660,66511],{"class":304},[86,69662,291],{"class":219},[86,69664,66516],{"class":304},[86,69666,65984],{"class":219},[86,69668,65987],{"class":178},[86,69670,11970],{"class":575},[86,69672,66525],{"class":579},[86,69674,10971],{"class":575},[86,69676,65967],{"class":219},[86,69678,69679,69681,69683],{"class":174,"line":205},[86,69680,66362],{"class":219},[86,69682,66416],{"class":178},[86,69684,41330],{"class":219},[86,69686,69687],{"class":174,"line":212},[86,69688,209],{"emptyLinePlaceholder":208},[86,69690,69691,69693,69695],{"class":174,"line":227},[86,69692,41317],{"class":219},[86,69694,66566],{"class":178},[86,69696,41330],{"class":219},[86,69698,69699,69701,69703,69705,69707,69709,69712,69714],{"class":174,"line":232},[86,69700,66255],{"class":219},[86,69702,66391],{"class":178},[86,69704,66598],{"class":304},[86,69706,258],{"class":219},[86,69708,576],{"class":575},[86,69710,69711],{"class":579},"flex h-screen flex-col bg-gray-50",[86,69713,576],{"class":575},[86,69715,41330],{"class":219},[86,69717,69718],{"class":174,"line":252},[86,69719,69720],{"class":1360},"    \u003C!-- App Bar -->\n",[86,69722,69723,69725,69727,69729,69731,69733,69736,69738],{"class":174,"line":276},[86,69724,66264],{"class":219},[86,69726,66575],{"class":178},[86,69728,66598],{"class":304},[86,69730,258],{"class":219},[86,69732,576],{"class":575},[86,69734,69735],{"class":579},"flex h-16 items-center justify-between bg-white px-6 shadow-sm",[86,69737,576],{"class":575},[86,69739,41330],{"class":219},[86,69741,69742,69744,69746,69748,69750,69752,69755,69757,69759,69762,69764,69766],{"class":174,"line":315},[86,69743,66670],{"class":219},[86,69745,66391],{"class":178},[86,69747,66598],{"class":304},[86,69749,258],{"class":219},[86,69751,576],{"class":575},[86,69753,69754],{"class":579},"text-xl font-bold text-gray-800",[86,69756,576],{"class":575},[86,69758,66356],{"class":219},[86,69760,69761],{"class":182},"My Project",[86,69763,66362],{"class":219},[86,69765,66391],{"class":178},[86,69767,41330],{"class":219},[86,69769,69770,69772,69774,69776,69778,69780,69783,69785,69788,69790,69792,69795,69797],{"class":174,"line":3665},[86,69771,66670],{"class":219},[86,69773,66698],{"class":178},[86,69775,66598],{"class":304},[86,69777,258],{"class":219},[86,69779,576],{"class":575},[86,69781,69782],{"class":579},"flex gap-4",[86,69784,576],{"class":575},[86,69786,69787],{"class":304}," aria-label",[86,69789,258],{"class":219},[86,69791,576],{"class":575},[86,69793,69794],{"class":579},"Main Navigation",[86,69796,576],{"class":575},[86,69798,41330],{"class":219},[86,69800,69801,69803,69805,69807,69809,69811,69814,69816,69818,69820,69822,69825,69827,69829,69831,69833,69835],{"class":174,"line":13256},[86,69802,66705],{"class":219},[86,69804,22],{"class":178},[86,69806,66304],{"class":304},[86,69808,258],{"class":219},[86,69810,576],{"class":575},[86,69812,69813],{"class":579},"#",[86,69815,576],{"class":575},[86,69817,66598],{"class":304},[86,69819,258],{"class":219},[86,69821,576],{"class":575},[86,69823,69824],{"class":579},"text-gray-600 hover:text-gray-900",[86,69826,576],{"class":575},[86,69828,66356],{"class":219},[86,69830,66723],{"class":182},[86,69832,66362],{"class":219},[86,69834,22],{"class":178},[86,69836,41330],{"class":219},[86,69838,69839,69841,69843,69845,69847,69849,69851,69853,69855,69857,69859,69861,69863,69865,69868,69870,69872],{"class":174,"line":13286},[86,69840,66705],{"class":219},[86,69842,22],{"class":178},[86,69844,66304],{"class":304},[86,69846,258],{"class":219},[86,69848,576],{"class":575},[86,69850,69813],{"class":579},[86,69852,576],{"class":575},[86,69854,66598],{"class":304},[86,69856,258],{"class":219},[86,69858,576],{"class":575},[86,69860,69824],{"class":579},[86,69862,576],{"class":575},[86,69864,66356],{"class":219},[86,69866,69867],{"class":182},"Profile",[86,69869,66362],{"class":219},[86,69871,22],{"class":178},[86,69873,41330],{"class":219},[86,69875,69876,69878,69880],{"class":174,"line":13291},[86,69877,66762],{"class":219},[86,69879,66698],{"class":178},[86,69881,41330],{"class":219},[86,69883,69884,69886,69888],{"class":174,"line":13308},[86,69885,66771],{"class":219},[86,69887,66575],{"class":178},[86,69889,41330],{"class":219},[86,69891,69892],{"class":174,"line":13334},[86,69893,209],{"emptyLinePlaceholder":208},[86,69895,69896,69898,69900,69902,69904,69906,69909,69911],{"class":174,"line":13359},[86,69897,66264],{"class":219},[86,69899,66391],{"class":178},[86,69901,66598],{"class":304},[86,69903,258],{"class":219},[86,69905,576],{"class":575},[86,69907,69908],{"class":579},"flex flex-1 overflow-hidden",[86,69910,576],{"class":575},[86,69912,41330],{"class":219},[86,69914,69915],{"class":174,"line":13385},[86,69916,69917],{"class":1360},"      \u003C!-- Sidebar -->\n",[86,69919,69920,69922,69925,69927,69929,69931,69934,69936],{"class":174,"line":13390},[86,69921,66670],{"class":219},[86,69923,69924],{"class":178},"aside",[86,69926,66598],{"class":304},[86,69928,258],{"class":219},[86,69930,576],{"class":575},[86,69932,69933],{"class":579},"w-64 overflow-y-auto bg-white border-r border-gray-200",[86,69935,576],{"class":575},[86,69937,41330],{"class":219},[86,69939,69940,69942,69944,69946,69948,69950,69953,69955,69957,69959,69961,69964,69966],{"class":174,"line":13396},[86,69941,66705],{"class":219},[86,69943,66698],{"class":178},[86,69945,66598],{"class":304},[86,69947,258],{"class":219},[86,69949,576],{"class":575},[86,69951,69952],{"class":579},"p-4 space-y-2",[86,69954,576],{"class":575},[86,69956,69787],{"class":304},[86,69958,258],{"class":219},[86,69960,576],{"class":575},[86,69962,69963],{"class":579},"Sidebar Navigation",[86,69965,576],{"class":575},[86,69967,41330],{"class":219},[86,69969,69970,69973],{"class":174,"line":3615},[86,69971,69972],{"class":219},"          \u003C",[86,69974,69975],{"class":178},"RouterLink\n",[86,69977,69978,69981,69983,69985,69987],{"class":174,"line":2254},[86,69979,69980],{"class":304},"            to",[86,69982,258],{"class":219},[86,69984,576],{"class":575},[86,69986,16555],{"class":579},[86,69988,69989],{"class":575},"\"\n",[86,69991,69992,69995,69997,69999,70002],{"class":174,"line":13492},[86,69993,69994],{"class":304},"            class",[86,69996,258],{"class":219},[86,69998,576],{"class":575},[86,70000,70001],{"class":579},"block rounded-md px-4 py-2 text-gray-700 hover:bg-gray-100",[86,70003,69989],{"class":575},[86,70005,70006,70009,70011,70013,70016],{"class":174,"line":13545},[86,70007,70008],{"class":304},"            exact-active-class",[86,70010,258],{"class":219},[86,70012,576],{"class":575},[86,70014,70015],{"class":579},"text-indigo-700 font-bold",[86,70017,69989],{"class":575},[86,70019,70020],{"class":174,"line":13550},[86,70021,70022],{"class":219},"          >\n",[86,70024,70025],{"class":174,"line":13566},[86,70026,70027],{"class":182},"            Home\n",[86,70029,70030,70033,70035],{"class":174,"line":13591},[86,70031,70032],{"class":219},"          \u003C\u002F",[86,70034,66708],{"class":178},[86,70036,41330],{"class":219},[86,70038,70039,70041],{"class":174,"line":13616},[86,70040,69972],{"class":219},[86,70042,69975],{"class":178},[86,70044,70045,70047,70049,70051,70053],{"class":174,"line":13641},[86,70046,69980],{"class":304},[86,70048,258],{"class":219},[86,70050,576],{"class":575},[86,70052,66744],{"class":579},[86,70054,69989],{"class":575},[86,70056,70057,70059,70061,70063,70065],{"class":174,"line":37784},[86,70058,69994],{"class":304},[86,70060,258],{"class":219},[86,70062,576],{"class":575},[86,70064,70001],{"class":579},[86,70066,69989],{"class":575},[86,70068,70069,70071,70073,70075,70077],{"class":174,"line":37795},[86,70070,70008],{"class":304},[86,70072,258],{"class":219},[86,70074,576],{"class":575},[86,70076,70015],{"class":579},[86,70078,69989],{"class":575},[86,70080,70081],{"class":174,"line":37807},[86,70082,70022],{"class":219},[86,70084,70085],{"class":174,"line":37822},[86,70086,70087],{"class":182},"            About\n",[86,70089,70090,70092,70094],{"class":174,"line":37837},[86,70091,70032],{"class":219},[86,70093,66708],{"class":178},[86,70095,41330],{"class":219},[86,70097,70098,70101,70103],{"class":174,"line":37852},[86,70099,70100],{"class":219},"        \u003C\u002F",[86,70102,66698],{"class":178},[86,70104,41330],{"class":219},[86,70106,70107,70109,70111],{"class":174,"line":37867},[86,70108,66762],{"class":219},[86,70110,69924],{"class":178},[86,70112,41330],{"class":219},[86,70114,70115],{"class":174,"line":37882},[86,70116,209],{"emptyLinePlaceholder":208},[86,70118,70119],{"class":174,"line":37887},[86,70120,70121],{"class":1360},"      \u003C!-- Main Content -->\n",[86,70123,70124,70126,70129,70131,70133,70135,70138,70140],{"class":174,"line":37911},[86,70125,66670],{"class":219},[86,70127,70128],{"class":178},"main",[86,70130,66598],{"class":304},[86,70132,258],{"class":219},[86,70134,576],{"class":575},[86,70136,70137],{"class":579},"flex-1 overflow-y-auto p-6",[86,70139,576],{"class":575},[86,70141,41330],{"class":219},[86,70143,70144,70146,70148],{"class":174,"line":37934},[86,70145,66705],{"class":219},[86,70147,66794],{"class":178},[86,70149,66282],{"class":219},[86,70151,70152,70154,70156],{"class":174,"line":37957},[86,70153,66762],{"class":219},[86,70155,70128],{"class":178},[86,70157,41330],{"class":219},[86,70159,70160,70162,70164],{"class":174,"line":37980},[86,70161,66771],{"class":219},[86,70163,66391],{"class":178},[86,70165,41330],{"class":219},[86,70167,70168],{"class":174,"line":38008},[86,70169,209],{"emptyLinePlaceholder":208},[86,70171,70172],{"class":174,"line":38013},[86,70173,70174],{"class":1360},"    \u003C!-- Footer -->\n",[86,70176,70177,70179],{"class":174,"line":38019},[86,70178,66264],{"class":219},[86,70180,70181],{"class":178},"footer\n",[86,70183,70184,70187,70189,70191,70194],{"class":174,"line":38067},[86,70185,70186],{"class":304},"      class",[86,70188,258],{"class":219},[86,70190,576],{"class":575},[86,70192,70193],{"class":579},"flex h-12 items-center justify-center bg-white border-t border-gray-200 text-sm text-gray-500",[86,70195,69989],{"class":575},[86,70197,70198],{"class":174,"line":38156},[86,70199,70200],{"class":219},"    >\n",[86,70202,70203,70206,70208,70210],{"class":174,"line":38180},[86,70204,70205],{"class":219},"      &",[86,70207,33250],{"class":215},[86,70209,69182],{"class":219},[86,70211,70212],{"class":182}," 2025 My Project. All rights reserved.\n",[86,70214,70215,70217,70220],{"class":174,"line":38204},[86,70216,66771],{"class":219},[86,70218,70219],{"class":178},"footer",[86,70221,41330],{"class":219},[86,70223,70224,70226,70228],{"class":174,"line":38227},[86,70225,66371],{"class":219},[86,70227,66391],{"class":178},[86,70229,41330],{"class":219},[86,70231,70232,70234,70236],{"class":174,"line":38250},[86,70233,66362],{"class":219},[86,70235,66566],{"class":178},[86,70237,41330],{"class":219},[12,70239,70240,70241,70243],{},"Con esto hemos creado una estructura básica con un app bar, un sidebar, un área principal de contenido y un footer, todo estilizado con clases de Tailwind CSS.\nIdealmente cada bloque (AppBar, Sidebar, Footer) debería ser un componente separado para promover la reutilización y el mantenimiento, pero para este ejemplo lo dejamos todo en ",[145,70242,64976],{}," para simplificar.",[12,70245,70246,70247,70250],{},"Verifica que todo funcione correctamente abriendo ",[145,70248,70249],{},"http:\u002F\u002Flocalhost:5173"," en tu navegador. Deberías ver la estructura básica con estilos aplicados.",[12,70252,70253,70254,70258,70259,61],{},"Con esto ya tienes Tailwind CSS v4 funcionando en tu proyecto. Explora su ",[22,70255,64614],{"href":70256,"target":27,"rel":70257},"https:\u002F\u002Ftailwindcss.com",[7760,7761]," e instala su extensión para un mejor autocompletado en VS Code: ",[22,70260,70263],{"href":70261,"target":27,"rel":70262},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=bradlc.vscode-tailwindcss",[7760,7761],"Tailwind CSS IntelliSense",[43,70265],{},[46,70267,70269],{"id":70268},"extra-subiendo-el-proyecto-a-github","EXTRA: Subiendo el proyecto a GitHub",[12,70271,70272],{},"Para esto tenemos muchas opciones. Antes de comenzar asumo que ya tienes una cuenta en GitHub y que tienes Git instalado en tu máquina.",[117,70274,70275],{},[33,70276,70277],{},"Primero inicializamos un repositorio Git en la carpeta del proyecto:",[164,70279,70281],{"className":64293,"code":70280,"language":64295,"meta":169,"style":169},"git init\n",[145,70282,70283],{"__ignoreMap":169},[86,70284,70285,70288],{"class":174,"line":175},[86,70286,70287],{"class":239},"git",[86,70289,70290],{"class":579}," init\n",[117,70292,70293],{"start":192},[33,70294,70295,70296,70299],{},"Luego creamos un archivo ",[145,70297,70298],{},".gitignore"," en la raíz del proyecto (es probable que ya lo tengas) y nos aseguraremos de tener las siguientes líneas para ignorar archivos y carpetas innecesarias:",[164,70301,70304],{"className":70302,"code":70303,"language":3141},[3139],"# Logs\nlogs\n*.log\nnpm-debug.log*\nyarn-debug.log*\nyarn-error.log*\npnpm-debug.log*\nlerna-debug.log*\n\nnode_modules\n.DS_Store\ndist\ndist-ssr\ncoverage\n*.local\n\n# Editor directories and files\n.vscode\u002F*\n!.vscode\u002Fextensions.json\n.idea\n*.suo\n*.ntvs*\n*.njsproj\n*.sln\n*.sw?\n\n*.tsbuildinfo\n\n.eslintcache\n\n# Cypress\n\u002Fcypress\u002Fvideos\u002F\n\u002Fcypress\u002Fscreenshots\u002F\n\n# Vitest\n__screenshots__\u002F\n\n",[145,70305,70303],{"__ignoreMap":169},[117,70307,70308],{"start":205},[33,70309,70310],{},"Ahora agregamos todos los archivos y hacemos el commit inicial:",[164,70312,70314],{"className":64293,"code":70313,"language":64295,"meta":169,"style":169},"git add .\n",[145,70315,70316],{"__ignoreMap":169},[86,70317,70318,70320,70323],{"class":174,"line":175},[86,70319,70287],{"class":239},[86,70321,70322],{"class":579}," add",[86,70324,70325],{"class":579}," .\n",[164,70327,70329],{"className":64293,"code":70328,"language":64295,"meta":169,"style":169},"git commit -m \"Initial commit\"\n",[145,70330,70331],{"__ignoreMap":169},[86,70332,70333,70335,70338,70341,70343,70346],{"class":174,"line":175},[86,70334,70287],{"class":239},[86,70336,70337],{"class":579}," commit",[86,70339,70340],{"class":215}," -m",[86,70342,737],{"class":575},[86,70344,70345],{"class":579},"Initial commit",[86,70347,69989],{"class":575},[117,70349,70350,70357],{"start":212},[33,70351,70352,70353,70356],{},"Ahora vamos a GitHub y creamos un nuevo repositorio. Puedes hacer esto haciendo clic en el botón \"+\" en la esquina superior derecha y seleccionando \"New repository\". Ponle un nombre a tu repositorio (por ejemplo, ",[145,70354,70355],{},"my-vue-app","), agrega una descripción si quieres, y déjalo como público o privado según prefieras. No agregues ningún archivo adicional (como README, .gitignore o licencia), ya los tenemos localmente.",[33,70358,70359],{},"Luego, seguimos las instrucciones que GitHub nos da para conectar nuestro repositorio local con el remoto. Normalmente son algo así:",[164,70361,70363],{"className":64293,"code":70362,"language":64295,"meta":169,"style":169},"git remote add origin https:\u002F\u002Fexample-url.git\n",[145,70364,70365],{"__ignoreMap":169},[86,70366,70367,70369,70372,70374,70377],{"class":174,"line":175},[86,70368,70287],{"class":239},[86,70370,70371],{"class":579}," remote",[86,70373,70322],{"class":579},[86,70375,70376],{"class":579}," origin",[86,70378,70379],{"class":579}," https:\u002F\u002Fexample-url.git\n",[164,70381,70383],{"className":64293,"code":70382,"language":64295,"meta":169,"style":169},"git branch -M main\n",[145,70384,70385],{"__ignoreMap":169},[86,70386,70387,70389,70392,70395],{"class":174,"line":175},[86,70388,70287],{"class":239},[86,70390,70391],{"class":579}," branch",[86,70393,70394],{"class":215}," -M",[86,70396,70397],{"class":579}," main\n",[164,70399,70401],{"className":64293,"code":70400,"language":64295,"meta":169,"style":169},"git push -u origin main\n",[145,70402,70403],{"__ignoreMap":169},[86,70404,70405,70407,70410,70413,70415],{"class":174,"line":175},[86,70406,70287],{"class":239},[86,70408,70409],{"class":579}," push",[86,70411,70412],{"class":215}," -u",[86,70414,70376],{"class":579},[86,70416,70397],{"class":579},[117,70418,70419],{"start":232},[33,70420,70421],{},"Verificamos status",[164,70423,70425],{"className":64293,"code":70424,"language":64295,"meta":169,"style":169},"git status\n",[145,70426,70427],{"__ignoreMap":169},[86,70428,70429,70431],{"class":174,"line":175},[86,70430,70287],{"class":239},[86,70432,70433],{"class":579}," status\n",[12,70435,70436,70437,70439,70440,70443],{},"Debe decir que estamos en la rama ",[145,70438,70128],{},", estamos sincronizados con el repositorio remoto ",[145,70441,70442],{},"origin\u002Fmain"," y que no hay nada para hacer commit.",[117,70445,70446],{"start":252},[33,70447,70448],{},"Finalmente, cada vez que hagamos cambios y queramos subirlos a GitHub, hacemos:",[164,70450,70452],{"className":64293,"code":70451,"language":64295,"meta":169,"style":169},"git add .\ngit commit -m \"Descripción de los cambios\"\ngit push\n",[145,70453,70454,70462,70477],{"__ignoreMap":169},[86,70455,70456,70458,70460],{"class":174,"line":175},[86,70457,70287],{"class":239},[86,70459,70322],{"class":579},[86,70461,70325],{"class":579},[86,70463,70464,70466,70468,70470,70472,70475],{"class":174,"line":192},[86,70465,70287],{"class":239},[86,70467,70337],{"class":579},[86,70469,70340],{"class":215},[86,70471,737],{"class":575},[86,70473,70474],{"class":579},"Descripción de los cambios",[86,70476,69989],{"class":575},[86,70478,70479,70481],{"class":174,"line":205},[86,70480,70287],{"class":239},[86,70482,70483],{"class":579}," push\n",[12,70485,70486],{},"¡Y eso es todo! Ahora tienes tu proyecto Vue 3 con Vite subido a GitHub.",[12,70488,70489],{},"Lo normal es que siempre uses un controlador de versiones como Git para manejar tu código, incluso en proyectos personales. Te ayudará a mantener un historial de cambios, colaborar con otros y proteger tu trabajo.",[12,70491,70492,70493,70498],{},"Te recomiendo explorar también sobre ",[22,70494,70497],{"href":70495,"target":27,"rel":70496},"https:\u002F\u002Fwww.conventionalcommits.org\u002Fen\u002Fv1.0.0\u002F",[7760,7761],"Conventional Commits"," para mantener mensajes de commit consistentes y significativos. Es algo que usan muchas empresas, equipos y proyectos open source.",[12,70500,70501],{},"Algunos recursos para aprender más sobre Git y GitHub:",[30,70503,70504,70511,70518],{},[33,70505,70506],{},[22,70507,70510],{"href":70508,"target":27,"rel":70509},"https:\u002F\u002Fgithub.com\u002Fdjayepro3\u002FGuide-Git-GitHub-VSCode",[7760,7761],"Git & GitHub with VS Code: A Beginner's Guide",[33,70512,70513],{},[22,70514,70517],{"href":70515,"target":27,"rel":70516},"https:\u002F\u002Fdocs.github.com\u002Fen\u002Fget-started\u002Fstart-your-journey",[7760,7761],"GitHub Quickstart Guide",[33,70519,70520],{},[22,70521,70524],{"href":70522,"target":27,"rel":70523},"https:\u002F\u002Fgit-scm.com\u002Fdoc",[7760,7761],"Git Documentation",[12,70526,70527],{},"Extensiones para VS Code:",[30,70529,70530,70537],{},[33,70531,70532],{},[22,70533,70536],{"href":70534,"target":27,"rel":70535},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=eamodio.gitlens",[7760,7761],"Gitlens",[33,70538,70539],{},[22,70540,70543],{"href":70541,"target":27,"rel":70542},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=mhutchie.git-graph",[7760,7761],"Git Graph",[43,70545],{},[46,70547,70549],{"id":70548},"extra-otras-extensiones-útiles-para-vs-code","EXTRA: Otras extensiones útiles para VS Code",[12,70551,70552],{},"Algunas extensiones que siempre recomiendo para VS Code (sin importar el tipo de proyecto):",[30,70554,70555,70563,70571,70579],{},[33,70556,70557,70562],{},[22,70558,70561],{"href":70559,"target":27,"rel":70560},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=usernamehw.errorlens",[7760,7761],"Error Lens",": Resalta errores y advertencias directamente en el código, facilitando su identificación y corrección.",[33,70564,70565,70570],{},[22,70566,70569],{"href":70567,"target":27,"rel":70568},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=naumovs.color-highlight",[7760,7761],"Color Highlight",": Resalta los colores definidos en tu código CSS, facilitando la visualización de los mismos.",[33,70572,70573,70578],{},[22,70574,70577],{"href":70575,"target":27,"rel":70576},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=aaron-bond.better-comments",[7760,7761],"Better Comments",": Mejora la legibilidad de los comentarios en el código mediante colores y estilos.",[33,70580,70581,70586,70587,70592],{},[22,70582,70585],{"href":70583,"target":27,"rel":70584},"https:\u002F\u002Fmarketplace.visualstudio.com\u002Fitems?itemName=antfu.iconify",[7760,7761],"Iconify Intellisense",": Si quieres trabajar con iconos, esta extensión te permite buscar e insertar iconos de múltiples bibliotecas directamente en tu código. A parte de ello recomiendo explorar su librería ",[22,70588,70591],{"href":70589,"target":27,"rel":70590},"https:\u002F\u002Ficon-sets.iconify.design\u002F",[7760,7761],"Iconify"," dónde puedes encontrar una gran variedad de icon sets gratuitos.",[43,70594],{},[12,70596,70597],{},"Bueno, eso sería todo para esta guía introductoria sobre Vue 3 con Vite. Espero que te haya sido útil para comenzar tu viaje con este framework y su ecosistema.",[43,70599],{},[2218,70601,70602],{},"html pre.shiki code .s_xSY, html code.shiki .s_xSY{--shiki-default:#59873A;--shiki-dark:#80A665}html pre.shiki code .spP0B, html code.shiki .spP0B{--shiki-default:#B56959;--shiki-dark:#C98A7D}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sHLBJ, html code.shiki .sHLBJ{--shiki-default:#998418;--shiki-dark:#B8A965}html pre.shiki code .snYqZ, html code.shiki .snYqZ{--shiki-default:#A0ADA0;--shiki-dark:#758575DD}html pre.shiki code .sTPum, html code.shiki .sTPum{--shiki-default:#1E754F;--shiki-dark:#4D9375}html pre.shiki code .scnC2, html code.shiki .scnC2{--shiki-default:#B5695977;--shiki-dark:#C98A7D77}html pre.shiki code .si6no, html code.shiki .si6no{--shiki-default:#999999;--shiki-dark:#666666}html pre.shiki code .s9nN2, html code.shiki .s9nN2{--shiki-default:#B07D48;--shiki-dark:#BD976A}html pre.shiki code .s5TCs, html code.shiki .s5TCs{--shiki-default:#AB5959;--shiki-dark:#CB7676}html pre.shiki code .s8w-G, html code.shiki .s8w-G{--shiki-default:#393A34;--shiki-dark:#DBD7CAEE}html pre.shiki code .sfsYZ, html code.shiki .sfsYZ{--shiki-default:#A65E2B;--shiki-dark:#C99076}html pre.shiki code .sqbOQ, html code.shiki .sqbOQ{--shiki-default:#2F798A;--shiki-dark:#4C9A91}",{"title":169,"searchDepth":205,"depth":205,"links":70604},[70605,70606,70607,70608,70612,70613,70614,70619,70620,70621,70622],{"id":64206,"depth":192,"text":64207},{"id":64266,"depth":192,"text":64267},{"id":64286,"depth":192,"text":64287},{"id":64620,"depth":192,"text":64621,"children":70609},[70610,70611],{"id":64904,"depth":205,"text":64905},{"id":64986,"depth":205,"text":64987},{"id":65936,"depth":192,"text":65937},{"id":67196,"depth":192,"text":67197},{"id":67827,"depth":192,"text":67828,"children":70615},[70616,70617,70618],{"id":68707,"depth":205,"text":68708},{"id":68740,"depth":205,"text":68741},{"id":68821,"depth":205,"text":68822},{"id":68878,"depth":192,"text":68879},{"id":69024,"depth":192,"text":69025},{"id":70268,"depth":192,"text":70269},{"id":70548,"depth":192,"text":70549},"2025-12-04","\u002Fblog\u002Fgetting-started-vue-vite\u002Fshared\u002Fvite+vue.webp","2025-12-22",{},"\u002Fblog\u002Fblog\u002Fgetting-started-vue-vite",{"title":64194,"description":64199},{"loc":70630,"priority":2259,"lastmod":70625},"\u002Fes\u002Fblog\u002Fgetting-started-vue-vite","getting-started-vue-vite","blog\u002Fblog\u002Fgetting-started-vue-vite","Una guía completa para configurar tu primer proyecto Vue 3 con Vite, incluyendo mejores prácticas y herramientas modernas.",[70635,69124,70636,65951,70637,70638,66014],"vue.js","tailwind css","frontend development","vue router","jGinDOms2x9idyYzmIghKvfougXhDuNbM5hgrqHBLMU",{"id":2274,"title":2275,"author":7,"body":70641,"date":3610,"description":3611,"extension":2250,"image":3612,"lastmod":3613,"meta":71762,"navigation":208,"order":3615,"path":3616,"seo":71763,"sitemap":71764,"slug":3620,"stem":3621,"summary":3622,"tags":71765,"__hash__":3628},{"type":9,"value":70642,"toc":71755},[70643,70648,70650,70652,70654,70660,70666,70668,70670,70680,70682,70686,70694,70696,70714,70718,70720,70722,70754,70756,70760,70766,70768,70770,70772,70782,70786,71272,71274,71280,71284,71286,71292,71294,71300,71302,71308,71310,71316,71320,71322,71326,71328,71332,71334,71340,71344,71350,71352,71354,71360,71362,71366,71370,71372,71377,71379,71389,71393,71395,71481,71483,71560,71562,71564,71569,71571,71589,71594,71600,71602,71606,71608,71616,71618,71626,71628,71632,71634,71700,71702,71738,71740,71742,71747,71749,71751],[12,70644,2280,70645,2286],{},[22,70646,2285],{"href":2283,"rel":70647},[26],[40,70649],{},[43,70651],{},[46,70653,2294],{"id":2293},[12,70655,2297,70656,2301,70658,2305],{},[122,70657,2300],{},[122,70659,2304],{},[16,70661,70662],{},[12,70663,2310,70664,2314],{},[122,70665,2313],{},[323,70667,2318],{"id":2317},[12,70669,2321],{},[30,70671,70672],{},[33,70673,2326,70674,2330,70676,2334,70678,2338],{},[122,70675,2329],{},[122,70677,2333],{},[122,70679,2337],{},[12,70681,2341],{},[16,70683,70684],{},[12,70685,2346],{},[30,70687,70688],{},[33,70689,2351,70690,2355,70692,2359],{},[122,70691,2354],{},[122,70693,2358],{},[12,70695,2362],{},[30,70697,70698,70702,70706,70710],{},[33,70699,70700,2370],{},[122,70701,2369],{},[33,70703,70704,2376],{},[122,70705,2375],{},[33,70707,70708,2382],{},[122,70709,2381],{},[33,70711,70712,2388],{},[122,70713,2387],{},[16,70715,70716],{},[12,70717,2393],{},[323,70719,2397],{"id":2396},[12,70721,2400],{},[30,70723,70724,70740],{},[33,70725,70726,2408,70728],{},[122,70727,2407],{},[30,70729,70730,70732,70734,70736,70738],{},[33,70731,2413],{},[33,70733,2416],{},[33,70735,2419],{},[33,70737,2422],{},[33,70739,2425],{},[33,70741,70742,2431,70744],{},[122,70743,2430],{},[30,70745,70746,70748,70750,70752],{},[33,70747,2436],{},[33,70749,2439],{},[33,70751,2442],{},[33,70753,2445],{},[12,70755,2448],{},[16,70757,70758],{},[12,70759,2453],{},[12,70761,2456,70762,2460,70764,2464],{},[122,70763,2459],{},[122,70765,2463],{},[323,70767,2468],{"id":2467},[12,70769,2471],{},[12,70771,2474],{},[30,70773,70774,70776,70778,70780],{},[33,70775,2479],{},[33,70777,2482],{},[33,70779,2485],{},[33,70781,2488],{},[12,70783,2491,70784,61],{},[122,70785,2494],{},[461,70787,70788,70822],{},[464,70789,70790],{},[467,70791,70792,70794,70796,70798,70800,70802,70804,70806,70808,70810,70812,70814,70816,70818,70820],{},[470,70793,2503],{},[470,70795,2506],{},[470,70797,2509],{},[470,70799,2512],{},[470,70801,2515],{},[470,70803,168],{},[470,70805,2520],{},[470,70807,2523],{},[470,70809,2526],{},[470,70811,2529],{},[470,70813,2532],{},[470,70815,2535],{},[470,70817,2538],{},[470,70819,2541],{},[470,70821,2544],{},[480,70823,70824,70856,70888,70920,70952,70984,71016,71048,71080,71112,71144,71176,71208,71240],{},[467,70825,70826,70828,70830,70832,70834,70836,70838,70840,70842,70844,70846,70848,70850,70852,70854],{},[485,70827,2506],{},[485,70829,2553],{},[485,70831,980],{},[485,70833,2553],{},[485,70835,2553],{},[485,70837,2553],{},[485,70839,2553],{},[485,70841,2553],{},[485,70843,2553],{},[485,70845,2553],{},[485,70847,2553],{},[485,70849,2553],{},[485,70851,2553],{},[485,70853,2553],{},[485,70855,2553],{},[467,70857,70858,70860,70862,70864,70866,70868,70870,70872,70874,70876,70878,70880,70882,70884,70886],{},[485,70859,2509],{},[485,70861,2553],{},[485,70863,2553],{},[485,70865,802],{},[485,70867,2553],{},[485,70869,2553],{},[485,70871,802],{},[485,70873,2553],{},[485,70875,2553],{},[485,70877,2553],{},[485,70879,2553],{},[485,70881,2553],{},[485,70883,2553],{},[485,70885,2553],{},[485,70887,2553],{},[467,70889,70890,70892,70894,70896,70898,70900,70902,70904,70906,70908,70910,70912,70914,70916,70918],{},[485,70891,2512],{},[485,70893,2553],{},[485,70895,2553],{},[485,70897,2553],{},[485,70899,980],{},[485,70901,2553],{},[485,70903,2553],{},[485,70905,2553],{},[485,70907,2553],{},[485,70909,2553],{},[485,70911,2553],{},[485,70913,2553],{},[485,70915,2553],{},[485,70917,2553],{},[485,70919,2553],{},[467,70921,70922,70924,70926,70928,70930,70932,70934,70936,70938,70940,70942,70944,70946,70948,70950],{},[485,70923,2515],{},[485,70925,2553],{},[485,70927,2553],{},[485,70929,2553],{},[485,70931,2553],{},[485,70933,802],{},[485,70935,2553],{},[485,70937,2553],{},[485,70939,2553],{},[485,70941,802],{},[485,70943,2553],{},[485,70945,2553],{},[485,70947,2553],{},[485,70949,2553],{},[485,70951,2553],{},[467,70953,70954,70956,70958,70960,70962,70964,70966,70968,70970,70972,70974,70976,70978,70980,70982],{},[485,70955,168],{},[485,70957,2553],{},[485,70959,2553],{},[485,70961,2553],{},[485,70963,2553],{},[485,70965,2553],{},[485,70967,2553],{},[485,70969,2553],{},[485,70971,2553],{},[485,70973,2553],{},[485,70975,2553],{},[485,70977,2553],{},[485,70979,2553],{},[485,70981,2553],{},[485,70983,2553],{},[467,70985,70986,70988,70990,70992,70994,70996,70998,71000,71002,71004,71006,71008,71010,71012,71014],{},[485,70987,2520],{},[485,70989,2553],{},[485,70991,2553],{},[485,70993,2553],{},[485,70995,2553],{},[485,70997,2553],{},[485,70999,2553],{},[485,71001,802],{},[485,71003,2553],{},[485,71005,2553],{},[485,71007,2553],{},[485,71009,2553],{},[485,71011,802],{},[485,71013,2553],{},[485,71015,2553],{},[467,71017,71018,71020,71022,71024,71026,71028,71030,71032,71034,71036,71038,71040,71042,71044,71046],{},[485,71019,2523],{},[485,71021,2553],{},[485,71023,2553],{},[485,71025,2553],{},[485,71027,2553],{},[485,71029,2553],{},[485,71031,2553],{},[485,71033,2553],{},[485,71035,802],{},[485,71037,2553],{},[485,71039,2553],{},[485,71041,2553],{},[485,71043,2553],{},[485,71045,2553],{},[485,71047,2553],{},[467,71049,71050,71052,71054,71056,71058,71060,71062,71064,71066,71068,71070,71072,71074,71076,71078],{},[485,71051,2526],{},[485,71053,2553],{},[485,71055,2553],{},[485,71057,2553],{},[485,71059,2553],{},[485,71061,2553],{},[485,71063,2553],{},[485,71065,2553],{},[485,71067,2553],{},[485,71069,2553],{},[485,71071,2553],{},[485,71073,2553],{},[485,71075,2553],{},[485,71077,2553],{},[485,71079,2553],{},[467,71081,71082,71084,71086,71088,71090,71092,71094,71096,71098,71100,71102,71104,71106,71108,71110],{},[485,71083,2529],{},[485,71085,2553],{},[485,71087,2553],{},[485,71089,2553],{},[485,71091,2553],{},[485,71093,2553],{},[485,71095,2553],{},[485,71097,2553],{},[485,71099,2553],{},[485,71101,2553],{},[485,71103,802],{},[485,71105,2553],{},[485,71107,2553],{},[485,71109,2553],{},[485,71111,2553],{},[467,71113,71114,71116,71118,71120,71122,71124,71126,71128,71130,71132,71134,71136,71138,71140,71142],{},[485,71115,2532],{},[485,71117,2553],{},[485,71119,2553],{},[485,71121,2553],{},[485,71123,2553],{},[485,71125,2553],{},[485,71127,2553],{},[485,71129,2553],{},[485,71131,2553],{},[485,71133,2553],{},[485,71135,2553],{},[485,71137,802],{},[485,71139,2553],{},[485,71141,2553],{},[485,71143,802],{},[467,71145,71146,71148,71150,71152,71154,71156,71158,71160,71162,71164,71166,71168,71170,71172,71174],{},[485,71147,2535],{},[485,71149,2553],{},[485,71151,2553],{},[485,71153,2553],{},[485,71155,2553],{},[485,71157,2553],{},[485,71159,2553],{},[485,71161,2553],{},[485,71163,2553],{},[485,71165,2553],{},[485,71167,2553],{},[485,71169,2553],{},[485,71171,2553],{},[485,71173,2553],{},[485,71175,2553],{},[467,71177,71178,71180,71182,71184,71186,71188,71190,71192,71194,71196,71198,71200,71202,71204,71206],{},[485,71179,2538],{},[485,71181,2553],{},[485,71183,2553],{},[485,71185,2553],{},[485,71187,2553],{},[485,71189,2553],{},[485,71191,2553],{},[485,71193,2553],{},[485,71195,2553],{},[485,71197,2553],{},[485,71199,2553],{},[485,71201,2553],{},[485,71203,2553],{},[485,71205,802],{},[485,71207,2553],{},[467,71209,71210,71212,71214,71216,71218,71220,71222,71224,71226,71228,71230,71232,71234,71236,71238],{},[485,71211,2541],{},[485,71213,2553],{},[485,71215,2553],{},[485,71217,2553],{},[485,71219,2553],{},[485,71221,2553],{},[485,71223,2553],{},[485,71225,2553],{},[485,71227,2553],{},[485,71229,2553],{},[485,71231,802],{},[485,71233,2553],{},[485,71235,2553],{},[485,71237,2553],{},[485,71239,2553],{},[467,71241,71242,71244,71246,71248,71250,71252,71254,71256,71258,71260,71262,71264,71266,71268,71270],{},[485,71243,2544],{},[485,71245,2553],{},[485,71247,2553],{},[485,71249,2553],{},[485,71251,2553],{},[485,71253,2553],{},[485,71255,2553],{},[485,71257,2553],{},[485,71259,2553],{},[485,71261,2553],{},[485,71263,2553],{},[485,71265,2553],{},[485,71267,2553],{},[485,71269,2553],{},[485,71271,2553],{},[12,71273,2998],{},[16,71275,71276],{},[12,71277,3003,71278,576],{},[122,71279,3006],{},[12,71281,3009,71282,61],{},[122,71283,3012],{},[12,71285,3015],{},[30,71287,71288,71290],{},[33,71289,3020],{},[33,71291,3023],{},[12,71293,3026],{},[30,71295,71296,71298],{},[33,71297,3031],{},[33,71299,3034],{},[12,71301,3037],{},[30,71303,71304,71306],{},[33,71305,3042],{},[33,71307,3045],{},[12,71309,3048],{},[16,71311,71312],{},[12,71313,3053,71314,576],{},[122,71315,3006],{},[12,71317,3058,71318,61],{},[122,71319,3061],{},[12,71321,3064],{},[30,71323,71324],{},[33,71325,3069],{},[12,71327,3072],{},[30,71329,71330],{},[33,71331,3077],{},[12,71333,3080],{},[16,71335,71336],{},[12,71337,3085,71338,576],{},[122,71339,3006],{},[12,71341,3090,71342,3094],{},[122,71343,3093],{},[30,71345,71346,71348],{},[33,71347,3099],{},[33,71349,3102],{},[12,71351,3105],{},[12,71353,3108],{},[30,71355,71356,71358],{},[33,71357,2479],{},[33,71359,3115],{},[12,71361,3118],{},[12,71363,3121,71364,3125],{},[122,71365,3124],{},[12,71367,3128,71368,3132],{},[122,71369,3131],{},[12,71371,3135],{},[164,71373,71375],{"className":71374,"code":3140,"language":3141},[3139],[145,71376,3140],{"__ignoreMap":169},[12,71378,3146],{},[30,71380,71381,71383,71385,71387],{},[33,71382,3151],{},[33,71384,3154],{},[33,71386,3157],{},[33,71388,3160],{},[12,71390,3163,71391,3166],{},[122,71392,3154],{},[12,71394,3169],{},[86,71396,71398],{"className":71397},[3173],[86,71399,71401,71422],{"className":71400},[955],[86,71402,71404],{"className":71403},[959],[961,71405,71406],{"xmlns":963,"display":3182},[965,71407,71408,71420],{},[968,71409,71410,71412,71414],{},[974,71411,3189],{},[3191,71413,3193],{},[971,71415,71416,71418],{},[974,71417,976],{"mathvariant":3198},[978,71419,3201],{},[982,71421,3204],{"encoding":984},[86,71423,71425,71443],{"className":71424,"ariaHidden":990},[989],[86,71426,71428,71431,71434,71437,71440],{"className":71427},[994],[86,71429],{"className":71430,"style":3214},[998],[86,71432,3189],{"className":71433},[1003,1007],[86,71435],{"className":71436,"style":3222},[3221],[86,71438,3193],{"className":71439},[3226],[86,71441],{"className":71442,"style":3222},[3221],[86,71444,71446,71449],{"className":71445},[994],[86,71447],{"className":71448,"style":3236},[998],[86,71450,71452,71455],{"className":71451},[1003],[86,71453,976],{"className":71454},[1003,3243],[86,71456,71458],{"className":71457},[1012],[86,71459,71461],{"className":71460},[1016],[86,71462,71464],{"className":71463},[1020],[86,71465,71467],{"className":71466,"style":3236},[1024],[86,71468,71469,71472],{"style":3258},[86,71470],{"className":71471,"style":1032},[1031],[86,71473,71475],{"className":71474},[1036,1037,1038,1039],[86,71476,71478],{"className":71477},[1003,1039],[86,71479,3201],{"className":71480},[1003,1039],[12,71482,3273],{},[30,71484,71485,71487],{},[33,71486,3278],{},[33,71488,71489,3357],{},[86,71490,71492,71513],{"className":71491},[955],[86,71493,71495],{"className":71494},[959],[961,71496,71497],{"xmlns":963},[965,71498,71499,71511],{},[968,71500,71501,71503,71509],{},[3191,71502,243],{"stretchy":3295},[971,71504,71505,71507],{},[974,71506,976],{"mathvariant":3198},[978,71508,3201],{},[3191,71510,867],{"stretchy":3295},[982,71512,3306],{"encoding":984},[86,71514,71516],{"className":71515,"ariaHidden":990},[989],[86,71517,71519,71522,71525,71557],{"className":71518},[994],[86,71520],{"className":71521,"style":3316},[998],[86,71523,243],{"className":71524},[3320],[86,71526,71528,71531],{"className":71527},[1003],[86,71529,976],{"className":71530},[1003,3243],[86,71532,71534],{"className":71533},[1012],[86,71535,71537],{"className":71536},[1016],[86,71538,71540],{"className":71539},[1020],[86,71541,71543],{"className":71542,"style":999},[1024],[86,71544,71545,71548],{"style":1027},[86,71546],{"className":71547,"style":1032},[1031],[86,71549,71551],{"className":71550},[1036,1037,1038,1039],[86,71552,71554],{"className":71553},[1003,1039],[86,71555,3201],{"className":71556},[1003,1039],[86,71558,867],{"className":71559},[3356],[12,71561,3360],{},[12,71563,3363],{},[164,71565,71567],{"className":71566,"code":3367,"language":3141},[3139],[145,71568,3367],{"__ignoreMap":169},[12,71570,3372],{},[30,71572,71573,71575,71577,71579,71581,71583,71585,71587],{},[33,71574,3377],{},[33,71576,3380],{},[33,71578,3383],{},[33,71580,3386],{},[33,71582,3389],{},[33,71584,3392],{},[33,71586,3395],{},[33,71588,3398],{},[164,71590,71592],{"className":71591,"code":3402,"language":3141},[3139],[145,71593,3402],{"__ignoreMap":169},[16,71595,71596],{},[12,71597,3409,71598,3413],{},[145,71599,3412],{},[12,71601,3416],{},[12,71603,3419,71604,3423],{},[122,71605,3422],{},[12,71607,3426],{},[30,71609,71610,71612,71614],{},[33,71611,3431],{},[33,71613,3434],{},[33,71615,3437],{},[12,71617,3440],{},[30,71619,71620,71622,71624],{},[33,71621,3445],{},[33,71623,3448],{},[33,71625,3451],{},[12,71627,3454],{},[12,71629,3457,71630,3461],{},[145,71631,3460],{},[12,71633,3464],{},[86,71635,71637],{"className":71636},[3173],[86,71638,71640,71659],{"className":71639},[955],[86,71641,71643],{"className":71642},[959],[961,71644,71645],{"xmlns":963,"display":3182},[965,71646,71647,71657],{},[968,71648,71649,71651],{},[974,71650,419],{},[971,71652,71653,71655],{},[974,71654,3486],{},[974,71656,3489],{},[982,71658,3492],{"encoding":984},[86,71660,71662],{"className":71661,"ariaHidden":990},[989],[86,71663,71665,71668,71671],{"className":71664},[994],[86,71666],{"className":71667,"style":3502},[998],[86,71669,419],{"className":71670},[1003,1007],[86,71672,71674,71677],{"className":71673},[1003],[86,71675,3486],{"className":71676,"style":3512},[1003,1007],[86,71678,71680],{"className":71679},[1012],[86,71681,71683],{"className":71682},[1016],[86,71684,71686],{"className":71685},[1020],[86,71687,71689],{"className":71688,"style":3525},[1024],[86,71690,71691,71694],{"style":3258},[86,71692],{"className":71693,"style":1032},[1031],[86,71695,71697],{"className":71696},[1036,1037,1038,1039],[86,71698,3489],{"className":71699,"style":3537},[1003,1007,1039],[12,71701,3273],{},[30,71703,71704,71706,71708],{},[33,71705,3544],{},[33,71707,3547],{},[33,71709,71710,3579],{},[86,71711,71713,71726],{"className":71712},[955],[86,71714,71716],{"className":71715},[959],[961,71717,71718],{"xmlns":963},[965,71719,71720,71724],{},[968,71721,71722],{},[974,71723,3489],{},[982,71725,3489],{"encoding":984},[86,71727,71729],{"className":71728,"ariaHidden":990},[989],[86,71730,71732,71735],{"className":71731},[994],[86,71733],{"className":71734,"style":3575},[998],[86,71736,3489],{"className":71737,"style":3537},[1003,1007],[12,71739,3582],{},[12,71741,3585],{},[164,71743,71745],{"className":71744,"code":3589,"language":3141},[3139],[145,71746,3589],{"__ignoreMap":169},[12,71748,3594],{},[12,71750,3597],{},[16,71752,71753],{},[12,71754,3602],{},{"title":169,"searchDepth":205,"depth":205,"links":71756},[71757],{"id":2293,"depth":192,"text":2294,"children":71758},[71759,71760,71761],{"id":2317,"depth":205,"text":2318},{"id":2396,"depth":205,"text":2397},{"id":2467,"depth":205,"text":2468},{},{"title":2275,"description":3611},{"loc":3619,"priority":2259,"lastmod":3613},[3624,3625,3626,3627,2264],{"prev":71767,"next":71793},{"id":3630,"title":3631,"author":7,"body":71768,"date":3661,"description":3662,"extension":2250,"image":3663,"lastmod":3661,"meta":71789,"navigation":208,"order":3665,"path":3666,"seo":71790,"sitemap":71791,"slug":3670,"stem":3671,"summary":3672,"tags":71792,"__hash__":3677},{"type":9,"value":71769,"toc":71786},[71770,71775,71780,71782,71784],[12,71771,3636,71772],{},[22,71773,3641],{"href":3639,"rel":71774},[26],[12,71776,3644,71777],{},[22,71778,3649],{"href":3647,"rel":71779},[26],[40,71781],{},[43,71783],{},[46,71785,3657],{"id":3656},{"title":169,"searchDepth":205,"depth":205,"links":71787},[71788],{"id":3656,"depth":192,"text":3657},{},{"title":3631,"description":3662},{"loc":3669,"priority":2259,"lastmod":3661},[3625,3674,3675,2264,3676],{"id":5,"title":6,"author":7,"body":71794,"date":2249,"description":14,"extension":2250,"image":2251,"lastmod":2252,"meta":73478,"navigation":208,"order":2254,"path":2255,"seo":73479,"sitemap":73480,"slug":2260,"stem":2261,"summary":2262,"tags":73481,"__hash__":2272},{"type":9,"value":71795,"toc":73450},[71796,71798,71805,71811,71813,71815,71817,71819,71824,71826,71830,71834,71836,71838,71848,71850,71852,71854,71856,71858,71872,71874,71882,71886,71992,71994,71996,72006,72012,72040,72044,72046,72058,72068,72076,72078,72120,72130,72132,72134,72136,72142,72196,72198,72206,72208,72212,72214,72216,72218,72254,72258,72346,72348,72352,72354,72360,72404,72410,72414,72416,72420,72430,72498,72586,72648,72650,72654,72656,72660,72670,72672,72680,72686,72796,72806,72812,72814,72816,72820,72886,72888,72950,72952,72954,73048,73172,73174,73178,73180,73182,73230,73236,73240,73246,73252,73258,73260,73262,73266,73270,73354,73360,73362,73364,73432,73434,73448],[12,71797,14],{},[16,71799,71800],{},[12,71801,20,71802],{},[22,71803,28],{"href":24,"rel":71804,"target":27},[26],[30,71806,71807,71809],{},[33,71808,35],{},[33,71810,38],{},[40,71812],{},[43,71814],{},[46,71816,49],{"id":48},[12,71818,52],{},[12,71820,55,71821,61],{},[22,71822,60],{"href":58,"rel":71823},[26],[12,71825,64],{},[16,71827,71828],{},[12,71829,69],{},[16,71831,71832],{},[12,71833,74],{},[46,71835,78],{"id":77},[12,71837,81],{},[12,71839,84,71840,89,71842,93,71844,93,71846,61],{},[86,71841,88],{},[86,71843,92],{},[86,71845,96],{},[86,71847,99],{},[12,71849,102],{},[12,71851,105],{},[12,71853,108],{},[46,71855,112],{"id":111},[12,71857,115],{},[117,71859,71860,71864,71868],{},[33,71861,71862,125],{},[122,71863,124],{},[33,71865,71866,131],{},[122,71867,130],{},[33,71869,71870,137],{},[122,71871,136],{},[46,71873,124],{"id":140},[12,71875,143,71876,148,71878,155],{},[145,71877,147],{},[122,71879,151,71880],{},[145,71881,154],{},[12,71883,158,71884,162],{},[145,71885,161],{},[164,71887,71888],{"className":166,"code":167,"language":168,"meta":169,"style":169},[145,71889,71890,71900,71910,71914,71922,71926,71938,71956,71986],{"__ignoreMap":169},[86,71891,71892,71894,71896,71898],{"class":174,"line":175},[86,71893,179],{"class":178},[86,71895,183],{"class":182},[86,71897,186],{"class":178},[86,71899,189],{"class":182},[86,71901,71902,71904,71906,71908],{"class":174,"line":192},[86,71903,179],{"class":178},[86,71905,197],{"class":182},[86,71907,186],{"class":178},[86,71909,202],{"class":182},[86,71911,71912],{"class":174,"line":205},[86,71913,209],{"emptyLinePlaceholder":208},[86,71915,71916,71918,71920],{"class":174,"line":212},[86,71917,216],{"class":215},[86,71919,220],{"class":219},[86,71921,224],{"class":223},[86,71923,71924],{"class":174,"line":227},[86,71925,209],{"emptyLinePlaceholder":208},[86,71927,71928,71930,71932,71934,71936],{"class":174,"line":232},[86,71929,236],{"class":235},[86,71931,240],{"class":239},[86,71933,243],{"class":219},[86,71935,246],{"class":182},[86,71937,249],{"class":219},[86,71939,71940,71942,71944,71946,71948,71950,71952,71954],{"class":174,"line":252},[86,71941,255],{"class":182},[86,71943,258],{"class":219},[86,71945,261],{"class":182},[86,71947,61],{"class":219},[86,71949,266],{"class":182},[86,71951,243],{"class":219},[86,71953,246],{"class":182},[86,71955,273],{"class":219},[86,71957,71958,71960,71962,71964,71966,71968,71970,71972,71974,71976,71978,71980,71982,71984],{"class":174,"line":276},[86,71959,279],{"class":182},[86,71961,61],{"class":219},[86,71963,284],{"class":182},[86,71965,243],{"class":219},[86,71967,216],{"class":215},[86,71969,291],{"class":219},[86,71971,294],{"class":182},[86,71973,61],{"class":219},[86,71975,299],{"class":182},[86,71977,291],{"class":219},[86,71979,305],{"class":304},[86,71981,258],{"class":219},[86,71983,310],{"class":178},[86,71985,273],{"class":219},[86,71987,71988,71990],{"class":174,"line":315},[86,71989,318],{"class":178},[86,71991,321],{"class":182},[323,71993,326],{"id":325},[12,71995,329],{},[117,71997,71998,72002],{},[33,71999,72000,337],{},[122,72001,336],{},[33,72003,72004,343],{},[122,72005,342],{},[12,72007,346,72008,350,72010,354],{},[122,72009,349],{},[145,72011,353],{},[16,72013,72014],{},[12,72015,72016,93,72018,93,72020,93,72022,93,72024,93,72026,93,72028,93,72030,93,72032,93,72034,93,72036,392,72038,61],{},[145,72017,361],{},[145,72019,364],{},[145,72021,367],{},[145,72023,370],{},[145,72025,373],{},[145,72027,376],{},[145,72029,379],{},[145,72031,382],{},[145,72033,385],{},[145,72035,388],{},[145,72037,391],{},[145,72039,395],{},[12,72041,398,72042,402],{},[122,72043,401],{},[323,72045,406],{"id":405},[12,72047,409,72048,412,72050,416,72052,420,72054,424,72056,428],{},[145,72049,353],{},[122,72051,415],{},[145,72053,419],{},[145,72055,423],{},[145,72057,427],{},[12,72059,431,72060,392,72062,437,72064,441,72066,445],{},[145,72061,434],{},[145,72063,423],{},[122,72065,440],{},[122,72067,444],{},[12,72069,448,72070,61],{},[122,72071,451,72072,392,72074,456],{},[145,72073,419],{},[145,72075,353],{},[12,72077,459],{},[461,72079,72080,72090],{},[464,72081,72082],{},[467,72083,72084,72086,72088],{},[470,72085,472],{},[470,72087,475],{},[470,72089,478],{},[480,72091,72092,72104],{},[467,72093,72094,72098,72102],{},[485,72095,72096],{},[122,72097,489],{},[485,72099,72100,494],{},[145,72101,419],{},[485,72103,497],{},[467,72105,72106,72110,72114],{},[485,72107,72108],{},[122,72109,504],{},[485,72111,72112,509],{},[145,72113,353],{},[485,72115,512,72116,515,72118,519],{},[145,72117,353],{},[122,72119,518],{},[12,72121,522,72122,526,72124,530,72126,534,72128,537],{},[145,72123,525],{},[145,72125,529],{},[145,72127,533],{},[145,72129,353],{},[46,72131,541],{"id":540},[12,72133,544],{},[323,72135,548],{"id":547},[12,72137,551,72138,555,72140,559],{},[145,72139,554],{},[145,72141,558],{},[164,72143,72144],{"className":166,"code":562,"language":168,"meta":169,"style":169},[145,72145,72146],{"__ignoreMap":169},[86,72147,72148,72150,72152,72154,72156,72158,72160,72162,72164,72166,72168,72170,72172,72174,72176,72178,72180,72182,72184,72186,72188,72190,72192,72194],{"class":174,"line":175},[86,72149,569],{"class":182},[86,72151,572],{"class":219},[86,72153,576],{"class":575},[86,72155,580],{"class":579},[86,72157,576],{"class":575},[86,72159,585],{"class":219},[86,72161,220],{"class":219},[86,72163,590],{"class":182},[86,72165,572],{"class":219},[86,72167,576],{"class":575},[86,72169,554],{"class":579},[86,72171,576],{"class":575},[86,72173,585],{"class":219},[86,72175,603],{"class":235},[86,72177,606],{"class":219},[86,72179,569],{"class":182},[86,72181,572],{"class":219},[86,72183,576],{"class":575},[86,72185,558],{"class":579},[86,72187,576],{"class":575},[86,72189,585],{"class":219},[86,72191,621],{"class":235},[86,72193,624],{"class":223},[86,72195,273],{"class":219},[12,72197,629],{},[12,72199,632,72200,61],{},[122,72201,635,72202,392,72204,640],{},[145,72203,558],{},[145,72205,554],{},[12,72207,643],{},[12,72209,646,72210,650],{},[122,72211,649],{},[323,72213,654],{"id":653},[12,72215,657],{},[12,72217,660],{},[461,72219,72220,72228],{},[464,72221,72222],{},[467,72223,72224,72226],{},[470,72225,669],{},[470,72227,672],{},[480,72229,72230,72238,72246],{},[467,72231,72232,72236],{},[485,72233,72234],{},[145,72235,681],{},[485,72237,684],{},[467,72239,72240,72244],{},[485,72241,72242],{},[145,72243,691],{},[485,72245,694],{},[467,72247,72248,72252],{},[485,72249,72250],{},[145,72251,701],{},[485,72253,704],{},[12,72255,707,72256,711],{},[122,72257,710],{},[164,72259,72260],{"className":166,"code":714,"language":168,"meta":169,"style":169},[145,72261,72262,72294],{"__ignoreMap":169},[86,72263,72264,72266,72268,72270,72272,72274,72276,72278,72280,72282,72284,72286,72288,72290,72292],{"class":174,"line":175},[86,72265,721],{"class":182},[86,72267,258],{"class":219},[86,72269,726],{"class":219},[86,72271,576],{"class":575},[86,72273,681],{"class":579},[86,72275,576],{"class":575},[86,72277,291],{"class":219},[86,72279,737],{"class":575},[86,72281,691],{"class":579},[86,72283,576],{"class":575},[86,72285,291],{"class":219},[86,72287,737],{"class":575},[86,72289,701],{"class":579},[86,72291,576],{"class":575},[86,72293,752],{"class":219},[86,72295,72296,72298,72300,72302,72304,72306,72308,72310,72312,72314,72316,72318,72320,72322,72324,72326,72328,72330,72332,72334,72336,72338,72340,72342,72344],{"class":174,"line":192},[86,72297,569],{"class":182},[86,72299,572],{"class":219},[86,72301,576],{"class":575},[86,72303,763],{"class":579},[86,72305,576],{"class":575},[86,72307,585],{"class":219},[86,72309,220],{"class":219},[86,72311,606],{"class":219},[86,72313,569],{"class":182},[86,72315,572],{"class":219},[86,72317,778],{"class":182},[86,72319,585],{"class":219},[86,72321,783],{"class":235},[86,72323,786],{"class":223},[86,72325,789],{"class":219},[86,72327,792],{"class":182},[86,72329,243],{"class":219},[86,72331,797],{"class":304},[86,72333,258],{"class":219},[86,72335,802],{"class":223},[86,72337,789],{"class":219},[86,72339,807],{"class":182},[86,72341,243],{"class":219},[86,72343,813],{"class":812},[86,72345,273],{"class":219},[12,72347,818],{},[16,72349,72350],{},[12,72351,823],{},[46,72353,827],{"id":826},[12,72355,830,72356,838],{},[122,72357,833,72358,837],{},[145,72359,836],{},[461,72361,72362,72372],{},[464,72363,72364],{},[467,72365,72366,72368,72370],{},[470,72367,847],{},[470,72369,850],{},[470,72371,853],{},[480,72373,72374,72390],{},[467,72375,72376,72384,72386],{},[485,72377,860,72378,93,72380,93,72382,867],{},[145,72379,525],{},[145,72381,529],{},[145,72383,533],{},[485,72385,870],{},[485,72387,873,72388,867],{},[145,72389,876],{},[467,72391,72392,72398,72400],{},[485,72393,881,72394,392,72396,867],{},[145,72395,419],{},[145,72397,353],{},[485,72399,888],{},[485,72401,72402],{},[145,72403,893],{},[12,72405,896,72406,606,72408,904],{},[122,72407,899],{},[901,72409,903],{},[12,72411,907,72412,910],{},[145,72413,876],{},[46,72415,914],{"id":913},[12,72417,917,72418,162],{},[122,72419,920],{},[30,72421,72422,72426],{},[33,72423,72424,928],{},[122,72425,927],{},[33,72427,72428,934],{},[122,72429,933],{},[12,72431,937,72432,941,72434,945,72436,949,72438,1043],{},[122,72433,940],{},[122,72435,944],{},[122,72437,948],{},[122,72439,72440],{},[86,72441,72443,72460],{"className":72442},[955],[86,72444,72446],{"className":72445},[959],[961,72447,72448],{"xmlns":963},[965,72449,72450,72458],{},[968,72451,72452],{},[971,72453,72454,72456],{},[974,72455,976],{},[978,72457,980],{},[982,72459,985],{"encoding":984},[86,72461,72463],{"className":72462,"ariaHidden":990},[989],[86,72464,72466,72469],{"className":72465},[994],[86,72467],{"className":72468,"style":999},[998],[86,72470,72472,72475],{"className":72471},[1003],[86,72473,976],{"className":72474,"style":1008},[1003,1007],[86,72476,72478],{"className":72477},[1012],[86,72479,72481],{"className":72480},[1016],[86,72482,72484],{"className":72483},[1020],[86,72485,72487],{"className":72486,"style":999},[1024],[86,72488,72489,72492],{"style":1027},[86,72490],{"className":72491,"style":1032},[1031],[86,72493,72495],{"className":72494},[1036,1037,1038,1039],[86,72496,980],{"className":72497},[1003,1039],[164,72499,72500],{"className":166,"code":1046,"language":168,"meta":169,"style":169},[145,72501,72502,72516,72520,72530,72552,72582],{"__ignoreMap":169},[86,72503,72504,72506,72508,72510,72512,72514],{"class":174,"line":175},[86,72505,1053],{"class":178},[86,72507,1056],{"class":182},[86,72509,61],{"class":219},[86,72511,1061],{"class":182},[86,72513,179],{"class":178},[86,72515,1066],{"class":182},[86,72517,72518],{"class":174,"line":192},[86,72519,209],{"emptyLinePlaceholder":208},[86,72521,72522,72524,72526,72528],{"class":174,"line":205},[86,72523,1075],{"class":182},[86,72525,258],{"class":219},[86,72527,1080],{"class":182},[86,72529,1083],{"class":219},[86,72531,72532,72534,72536,72538,72540,72542,72544,72546,72548,72550],{"class":174,"line":212},[86,72533,1088],{"class":182},[86,72535,291],{"class":219},[86,72537,1093],{"class":182},[86,72539,291],{"class":219},[86,72541,1098],{"class":182},[86,72543,291],{"class":219},[86,72545,1103],{"class":304},[86,72547,258],{"class":219},[86,72549,1108],{"class":223},[86,72551,1111],{"class":219},[86,72553,72554,72556,72558,72560,72562,72564,72566,72568,72570,72572,72574,72576,72578,72580],{"class":174,"line":227},[86,72555,1116],{"class":304},[86,72557,1119],{"class":219},[86,72559,576],{"class":575},[86,72561,1124],{"class":579},[86,72563,576],{"class":575},[86,72565,291],{"class":219},[86,72567,737],{"class":575},[86,72569,1133],{"class":579},[86,72571,576],{"class":575},[86,72573,291],{"class":219},[86,72575,737],{"class":575},[86,72577,1142],{"class":579},[86,72579,576],{"class":575},[86,72581,1147],{"class":219},[86,72583,72584],{"class":174,"line":232},[86,72585,273],{"class":219},[12,72587,1154,72588,1213,72646,1217],{},[86,72589,72591,72608],{"className":72590},[955],[86,72592,72594],{"className":72593},[959],[961,72595,72596],{"xmlns":963},[965,72597,72598,72606],{},[968,72599,72600],{},[971,72601,72602,72604],{},[974,72603,976],{},[978,72605,980],{},[982,72607,985],{"encoding":984},[86,72609,72611],{"className":72610,"ariaHidden":990},[989],[86,72612,72614,72617],{"className":72613},[994],[86,72615],{"className":72616,"style":999},[998],[86,72618,72620,72623],{"className":72619},[1003],[86,72621,976],{"className":72622,"style":1008},[1003,1007],[86,72624,72626],{"className":72625},[1012],[86,72627,72629],{"className":72628},[1016],[86,72630,72632],{"className":72631},[1020],[86,72633,72635],{"className":72634,"style":999},[1024],[86,72636,72637,72640],{"style":1027},[86,72638],{"className":72639,"style":1032},[1031],[86,72641,72643],{"className":72642},[1036,1037,1038,1039],[86,72644,980],{"className":72645},[1003,1039],[122,72647,1216],{},[46,72649,136],{"id":1220},[12,72651,1223,72652,1227],{},[122,72653,1226],{},[323,72655,1231],{"id":1230},[12,72657,1234,72658,1238],{},[122,72659,1237],{},[30,72661,72662,72666],{},[33,72663,1243,72664,1247],{},[122,72665,1246],{},[33,72667,1243,72668,1253],{},[122,72669,1252],{},[323,72671,1257],{"id":1256},[12,72673,1260,72674,1264,72676,606,72678,1271],{},[145,72675,1263],{},[122,72677,1267],{},[901,72679,1270],{},[12,72681,1274,72682,1278,72684,1282],{},[122,72683,1277],{},[145,72685,1281],{},[164,72687,72688],{"className":166,"code":1285,"language":168,"meta":169,"style":169},[145,72689,72690,72708,72722,72726,72732,72750,72776,72792],{"__ignoreMap":169},[86,72691,72692,72694,72696,72698,72700,72702,72704,72706],{"class":174,"line":175},[86,72693,1053],{"class":178},[86,72695,1294],{"class":182},[86,72697,61],{"class":219},[86,72699,1299],{"class":182},[86,72701,179],{"class":178},[86,72703,1304],{"class":182},[86,72705,186],{"class":178},[86,72707,1309],{"class":182},[86,72709,72710,72712,72714,72716,72718,72720],{"class":174,"line":192},[86,72711,1053],{"class":178},[86,72713,1294],{"class":182},[86,72715,61],{"class":219},[86,72717,1320],{"class":182},[86,72719,179],{"class":178},[86,72721,1325],{"class":215},[86,72723,72724],{"class":174,"line":205},[86,72725,209],{"emptyLinePlaceholder":208},[86,72727,72728,72730],{"class":174,"line":212},[86,72729,1334],{"class":182},[86,72731,1337],{"class":219},[86,72733,72734,72736,72738,72740,72742,72744,72746,72748],{"class":174,"line":227},[86,72735,1342],{"class":219},[86,72737,576],{"class":575},[86,72739,1347],{"class":579},[86,72741,576],{"class":575},[86,72743,291],{"class":219},[86,72745,1354],{"class":182},[86,72747,1357],{"class":219},[86,72749,1361],{"class":1360},[86,72751,72752,72754,72756,72758,72760,72762,72764,72766,72768,72770,72772,72774],{"class":174,"line":232},[86,72753,1342],{"class":219},[86,72755,576],{"class":575},[86,72757,1370],{"class":579},[86,72759,576],{"class":575},[86,72761,291],{"class":219},[86,72763,1377],{"class":182},[86,72765,243],{"class":219},[86,72767,1382],{"class":304},[86,72769,258],{"class":219},[86,72771,1387],{"class":223},[86,72773,1390],{"class":219},[86,72775,1393],{"class":1360},[86,72777,72778,72780,72782,72784,72786,72788,72790],{"class":174,"line":252},[86,72779,1342],{"class":219},[86,72781,576],{"class":575},[86,72783,1402],{"class":579},[86,72785,576],{"class":575},[86,72787,291],{"class":219},[86,72789,1409],{"class":182},[86,72791,1412],{"class":219},[86,72793,72794],{"class":174,"line":276},[86,72795,1417],{"class":219},[12,72797,1420,72798,1423,72800,1426,72802,1429,72804,1433],{},[145,72799,836],{},[145,72801,1281],{},[145,72803,1281],{},[122,72805,1432],{},[12,72807,1436,72808,1440,72810,1444],{},[122,72809,1439],{},[122,72811,1443],{},[46,72813,1448],{"id":1447},[323,72815,1452],{"id":1451},[12,72817,1455,72818,1459],{},[122,72819,1458],{},[461,72821,72822,72832],{},[464,72823,72824],{},[467,72825,72826,72828,72830],{},[470,72827,472],{},[470,72829,1470],{},[470,72831,1473],{},[480,72833,72834,72854,72868],{},[467,72835,72836,72840,72852],{},[485,72837,72838],{},[145,72839,1482],{},[485,72841,72842,93,72844,93,72846,93,72848,93,72850],{},[145,72843,1487],{},[145,72845,1490],{},[145,72847,1493],{},[145,72849,1496],{},[145,72851,1499],{},[485,72853,1502],{},[467,72855,72856,72860,72866],{},[485,72857,72858],{},[145,72859,1509],{},[485,72861,72862,93,72864],{},[145,72863,1514],{},[145,72865,1517],{},[485,72867,1520],{},[467,72869,72870,72874,72884],{},[485,72871,72872],{},[145,72873,1527],{},[485,72875,72876,93,72878,93,72880,93,72882],{},[145,72877,1487],{},[145,72879,1490],{},[145,72881,1496],{},[145,72883,1499],{},[485,72885,1540],{},[323,72887,1544],{"id":1543},[12,72889,1547,72890,1606,72948,1610],{},[86,72891,72893,72910],{"className":72892},[955],[86,72894,72896],{"className":72895},[959],[961,72897,72898],{"xmlns":963},[965,72899,72900,72908],{},[968,72901,72902],{},[971,72903,72904,72906],{},[974,72905,976],{},[978,72907,980],{},[982,72909,985],{"encoding":984},[86,72911,72913],{"className":72912,"ariaHidden":990},[989],[86,72914,72916,72919],{"className":72915},[994],[86,72917],{"className":72918,"style":999},[998],[86,72920,72922,72925],{"className":72921},[1003],[86,72923,976],{"className":72924,"style":1008},[1003,1007],[86,72926,72928],{"className":72927},[1012],[86,72929,72931],{"className":72930},[1016],[86,72932,72934],{"className":72933},[1020],[86,72935,72937],{"className":72936,"style":999},[1024],[86,72938,72939,72942],{"style":1027},[86,72940],{"className":72941,"style":1032},[1031],[86,72943,72945],{"className":72944},[1036,1037,1038,1039],[86,72946,980],{"className":72947},[1003,1039],[122,72949,1609],{},[1612,72951,1615],{"id":1614},[12,72953,1618],{},[461,72955,72956,73026],{},[464,72957,72958],{},[467,72959,72960,72962,72964,72966],{},[470,72961,472],{},[470,72963,948],{},[470,72965,944],{},[470,72967,72968],{},[86,72969,72971,72988],{"className":72970},[955],[86,72972,72974],{"className":72973},[959],[961,72975,72976],{"xmlns":963},[965,72977,72978,72986],{},[968,72979,72980],{},[971,72981,72982,72984],{},[974,72983,976],{},[978,72985,980],{},[982,72987,985],{"encoding":984},[86,72989,72991],{"className":72990,"ariaHidden":990},[989],[86,72992,72994,72997],{"className":72993},[994],[86,72995],{"className":72996,"style":999},[998],[86,72998,73000,73003],{"className":72999},[1003],[86,73001,976],{"className":73002,"style":1008},[1003,1007],[86,73004,73006],{"className":73005},[1012],[86,73007,73009],{"className":73008},[1016],[86,73010,73012],{"className":73011},[1020],[86,73013,73015],{"className":73014,"style":999},[1024],[86,73016,73017,73020],{"style":1027},[86,73018],{"className":73019,"style":1032},[1031],[86,73021,73023],{"className":73022},[1036,1037,1038,1039],[86,73024,980],{"className":73025},[1003,1039],[480,73027,73028,73038],{},[467,73029,73030,73032,73034,73036],{},[485,73031,927],{},[485,73033,1699],{},[485,73035,1702],{},[485,73037,1705],{},[467,73039,73040,73042,73044,73046],{},[485,73041,1710],{},[485,73043,1713],{},[485,73045,1716],{},[485,73047,1719],{},[12,73049,1243,73050,1783,73110,1842,73168,1846,73170,61],{},[122,73051,73052,1782],{},[86,73053,73055,73072],{"className":73054},[955],[86,73056,73058],{"className":73057},[959],[961,73059,73060],{"xmlns":963},[965,73061,73062,73070],{},[968,73063,73064],{},[971,73065,73066,73068],{},[974,73067,976],{},[978,73069,980],{},[982,73071,985],{"encoding":984},[86,73073,73075],{"className":73074,"ariaHidden":990},[989],[86,73076,73078,73081],{"className":73077},[994],[86,73079],{"className":73080,"style":999},[998],[86,73082,73084,73087],{"className":73083},[1003],[86,73085,976],{"className":73086,"style":1008},[1003,1007],[86,73088,73090],{"className":73089},[1012],[86,73091,73093],{"className":73092},[1016],[86,73094,73096],{"className":73095},[1020],[86,73097,73099],{"className":73098,"style":999},[1024],[86,73100,73101,73104],{"style":1027},[86,73102],{"className":73103,"style":1032},[1031],[86,73105,73107],{"className":73106},[1036,1037,1038,1039],[86,73108,980],{"className":73109},[1003,1039],[86,73111,73113,73130],{"className":73112},[955],[86,73114,73116],{"className":73115},[959],[961,73117,73118],{"xmlns":963},[965,73119,73120,73128],{},[968,73121,73122],{},[971,73123,73124,73126],{},[974,73125,976],{},[978,73127,980],{},[982,73129,985],{"encoding":984},[86,73131,73133],{"className":73132,"ariaHidden":990},[989],[86,73134,73136,73139],{"className":73135},[994],[86,73137],{"className":73138,"style":999},[998],[86,73140,73142,73145],{"className":73141},[1003],[86,73143,976],{"className":73144,"style":1008},[1003,1007],[86,73146,73148],{"className":73147},[1012],[86,73149,73151],{"className":73150},[1016],[86,73152,73154],{"className":73153},[1020],[86,73155,73157],{"className":73156,"style":999},[1024],[86,73158,73159,73162],{"style":1027},[86,73160],{"className":73161,"style":1032},[1031],[86,73163,73165],{"className":73164},[1036,1037,1038,1039],[86,73166,980],{"className":73167},[1003,1039],[901,73169,1845],{},[122,73171,1849],{},[12,73173,1852],{},[12,73175,1855,73176,61],{},[122,73177,1858],{},[1612,73179,1862],{"id":1861},[12,73181,1865],{},[461,73183,73184,73198],{},[464,73185,73186],{},[467,73187,73188,73190,73192,73194,73196],{},[470,73189,472],{},[470,73191,1876],{},[470,73193,1879],{},[470,73195,1882],{},[470,73197,1252],{},[480,73199,73200,73218],{},[467,73201,73202,73204,73206,73210,73214],{},[485,73203,1891],{},[485,73205,1894],{},[485,73207,73208],{},[122,73209,1899],{},[485,73211,73212],{},[122,73213,1904],{},[485,73215,73216],{},[122,73217,1909],{},[467,73219,73220,73222,73224,73226,73228],{},[485,73221,1710],{},[485,73223,1916],{},[485,73225,1919],{},[485,73227,1922],{},[485,73229,1909],{},[12,73231,1927,73232,1931,73234,1935],{},[901,73233,1930],{},[122,73235,1934],{},[12,73237,1938,73238,1941],{},[122,73239,1609],{},[12,73241,73242,73244],{},[1945,73243],{"alt":1947,"src":1948},[901,73245,1951],{},[12,73247,1954,73248,1958,73250,1962],{},[122,73249,1957],{},[145,73251,1961],{},[12,73253,73254,73256],{},[1945,73255],{"alt":1967,"src":1968},[901,73257,1971],{},[12,73259,1974],{},[323,73261,1978],{"id":1977},[12,73263,1981,73264,1985],{},[122,73265,1984],{},[12,73267,1988,73268,1992],{},[122,73269,1991],{},[461,73271,73272,73282],{},[464,73273,73274],{},[467,73275,73276,73278,73280],{},[470,73277,2001],{},[470,73279,2004],{},[470,73281,2007],{},[480,73283,73284,73294,73306,73314,73322,73330,73338,73346],{},[467,73285,73286,73290,73292],{},[485,73287,73288],{},[901,73289,2016],{},[485,73291,1991],{},[485,73293,2021],{},[467,73295,73296,73300,73302],{},[485,73297,73298,2029],{},[122,73299,2028],{},[485,73301,2032],{},[485,73303,73304],{},[122,73305,2037],{},[467,73307,73308,73310,73312],{},[485,73309,2042],{},[485,73311,2045],{},[485,73313,2048],{},[467,73315,73316,73318,73320],{},[485,73317,2053],{},[485,73319,2056],{},[485,73321,2059],{},[467,73323,73324,73326,73328],{},[485,73325,2064],{},[485,73327,2067],{},[485,73329,2070],{},[467,73331,73332,73334,73336],{},[485,73333,2075],{},[485,73335,1991],{},[485,73337,2080],{},[467,73339,73340,73342,73344],{},[485,73341,2085],{},[485,73343,2088],{},[485,73345,2091],{},[467,73347,73348,73350,73352],{},[485,73349,2096],{},[485,73351,2099],{},[485,73353,2102],{},[12,73355,2105,73356,2109,73358,2113],{},[122,73357,2108],{},[901,73359,2112],{},[46,73361,2117],{"id":2116},[12,73363,2120],{},[30,73365,73366,73428],{},[33,73367,1243,73368,606,73370,2186],{},[122,73369,2127],{},[86,73371,73373,73390],{"className":73372},[955],[86,73374,73376],{"className":73375},[959],[961,73377,73378],{"xmlns":963},[965,73379,73380,73388],{},[968,73381,73382],{},[971,73383,73384,73386],{},[974,73385,976],{},[978,73387,980],{},[982,73389,985],{"encoding":984},[86,73391,73393],{"className":73392,"ariaHidden":990},[989],[86,73394,73396,73399],{"className":73395},[994],[86,73397],{"className":73398,"style":999},[998],[86,73400,73402,73405],{"className":73401},[1003],[86,73403,976],{"className":73404,"style":1008},[1003,1007],[86,73406,73408],{"className":73407},[1012],[86,73409,73411],{"className":73410},[1016],[86,73412,73414],{"className":73413},[1020],[86,73415,73417],{"className":73416,"style":999},[1024],[86,73418,73419,73422],{"style":1027},[86,73420],{"className":73421,"style":1032},[1031],[86,73423,73425],{"className":73424},[1036,1037,1038,1039],[86,73426,980],{"className":73427},[1003,1039],[33,73429,1243,73430,2192],{},[122,73431,2191],{},[12,73433,2195],{},[30,73435,73436,73438,73440,73444],{},[33,73437,2200],{},[33,73439,2203],{},[33,73441,2206,73442,2210],{},[122,73443,2209],{},[33,73445,2213,73446,2216],{},[901,73447,1930],{},[2218,73449,2220],{},{"title":169,"searchDepth":205,"depth":205,"links":73451},[73452,73453,73454,73455,73459,73463,73464,73465,73469,73477],{"id":48,"depth":192,"text":49},{"id":77,"depth":192,"text":78},{"id":111,"depth":192,"text":112},{"id":140,"depth":192,"text":124,"children":73456},[73457,73458],{"id":325,"depth":205,"text":326},{"id":405,"depth":205,"text":406},{"id":540,"depth":192,"text":541,"children":73460},[73461,73462],{"id":547,"depth":205,"text":548},{"id":653,"depth":205,"text":654},{"id":826,"depth":192,"text":827},{"id":913,"depth":192,"text":914},{"id":1220,"depth":192,"text":136,"children":73466},[73467,73468],{"id":1230,"depth":205,"text":1231},{"id":1256,"depth":205,"text":1257},{"id":1447,"depth":192,"text":1448,"children":73470},[73471,73472,73476],{"id":1451,"depth":205,"text":1452},{"id":1543,"depth":205,"text":1544,"children":73473},[73474,73475],{"id":1614,"depth":212,"text":1615},{"id":1861,"depth":212,"text":1862},{"id":1977,"depth":205,"text":1978},{"id":2116,"depth":192,"text":2117},{},{"title":6,"description":14},{"loc":2258,"priority":2259,"lastmod":2252},[2264,2265,2266,2267,2268,2269,2270,2271],1783532542765]