class: center middle main-title section-title-8 top-logo .small[ # Regresión múltiple: predictores cualitativos ] .class-info[ <br> **Sesión N° 7**<br> **Estadísitica II** <br> .pull-right.small[ **Profesora** Valentina Andrade de la Horra <br> **Apoyo docente** Nicolás Godoy <br> **Ayudantes** Moira Martinez, Charo Astorga y Alberto Reyes .tiny[Universidad Alberto Hurtado<br> ] ] ] --- class: title title-inv-8 # Contenidos Sesión -- .box-8.medium.sp-after-half[Predictores **dicotómicos**] -- .box-8.medium.sp-after-half[Predictores **politómicos**] --- class: center middle main-title section-title-8 top-logo # Predictores cualitativos --- <div id="htmlwidget-6fe9402b364601a1cb79" style="width:504px;height:504px;" class="grViz html-widget"></div> <script type="application/json" data-for="htmlwidget-6fe9402b364601a1cb79">{"x":{"diagram":"digraph {\n\n\n\n\n \"1\" [label = \"Variable\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Variable\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"2\" [label = \"Cualitativa\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Cualitativa\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"3\" [label = \"Nominal\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Nominal\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"4\" [label = \"Ordinal\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Ordinal\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"5\" [label = \"Cuantitativa\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Cuantitativa\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"6\" [label = \"Discreta\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Discreta\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"7\" [label = \"Continua\", style = \"filled,rounded\", shape = \"box\", fontname = \"helvetica\", tooltip = \"- name: Continua\", fillcolor = \"LightGray\", fontcolor = \"#000000\"] \n \"1\"->\"2\" \n \"1\"->\"5\" \n \"2\"->\"3\" \n \"2\"->\"4\" \n \"5\"->\"6\" \n \"5\"->\"7\" \n}","config":{"engine":"dot","options":null}},"evals":[],"jsHooks":[]}</script> --- class: title title-8 # Predictores cualitativos - También se les llamada predictores **categóricos** pues tienen categorías de respuesta --- class: title title-8 # Predictores cualitativos - Pueden tener 2 a más categorías de respuesta: - **Dicotómico**: 2 categorías de respuesta (Si/No, Ausencia/Presencia, Apruebo/Rechazo, Mujer/Hombre) - **Politómico**: más de 2 categorías de respuesta (Bajo/Medio/Alto, Izquierda/Centro/Derecha, Mujer/Hombre/No binario ) -- - Si no recuerdas mucho este contenido [revisa este material](https://learn-r-uah.netlify.app/resource/r-datatypes-example/) --- class: center middle main-title section-title-8 top-logo # Predictores dicotómicos (*dummy*) --- class: title title-8 # Predictores dicotómicos - Imaginemos que `\(x_3\)` es una variable independiente **dicotómica** - ( `\(x_3 = \lbrace 0, 1 \rbrace\)` ) `$$y = \beta_0 + \beta_3 x_3 + u$$` --- class: title title-8 # Predictores dicotómicos .pull-left[ Si `\(x_3 = 0\)` $$E(y|x_3 = 0) = \beta_0 $$ ] .pull-right[ Si `\(x_3 = 1\)` `$$E(y|x_3 = 1) = \beta_0 + \beta_3$$` ] -- - ¿Cuál es la diferencia entre el grupo con `\(x_3 = 1\)` y el grupo con `\(x_3 = 0\)` --- class: title title-8 # Predictores dicotómicos `$$E(y|x_3 = 1) - E(y|x_3 = 0) \\ \beta_0 + \beta_3 - \beta_0 \\ \beta_3$$` --- class: center middle main-title section-title-8 top-logo # Interpretación `\(\beta_3\)` ## Diferencia **promedio** del grupo 1 respecto del grupo 0, **manteniendo el resto constante** -- ### Efecto parcial de `\(x_3 = 1\)` sobre y --- class: title title-8 # Categoría de referencia - Al grupo cuando `\(x_3 = 0\)` se le llama **categoría de referencia** -- - Sobre esta categoría de referencia siempre de comparan los otros grupos. En este caso como son dos grupos, el grupo que `\(x_3 = 1\)` se compara con `\(x_3 = 0\)`. --- class: title title-8 # Ejemplo promedio universidad - Muestra de 141 estudiantes de una universidad. - `colGPA`: (col:college, GPA:notas) promedio general de calificaciones de la universidad, en escala de 0 a 4 puntos - `hsGPA`: (hs: high school) promedio general de calificaciones en la enseñanza media, en escala de 0 a 4 puntos - `ACT`: puntaje en el examen de admisión a la universidad, que va de 16 a 33 puntos - `sex`: sexo del estudiante, donde `sex = 1` (Hombre) y `sex = 0` (Mujer) --- class: title title-8 # 1. Hipótesis: promedio universidad - `\(H_1\)`: A mayor puntaje en la prueba de admisión, mayores son las notas de la universidad - `\(H_2\)`: A mayor notas en enseñanza media, mayores son las notas en la universidad - `\(H_3\)`: Existen diferencias significativas **por sexo** en el promedio de notas en la universidad --- class: title title-8 # 2. Describir variables: univariado ``` ## ## ## Basic descriptive statistics ## ## var n NA.prc mean sd range ## colGPA 141 0 3.06 0.37 1.8 (2.2-4) ## hsGPA 141 0 3.40 0.32 1.6 (2.4-4) ## ACT 141 0 24.16 2.84 17 (16-33) ``` --- class: title title-8 # 2. Describir variables: univariado ``` ## x <categorical> ## # total N=141 valid N=141 mean=1.52 sd=0.50 ## ## Value | N | Raw % | Valid % | Cum. % ## -------------------------------------- ## Mujer | 67 | 47.52 | 47.52 | 47.52 ## Hombre | 74 | 52.48 | 52.48 | 100.00 ## <NA> | 0 | 0.00 | <NA> | <NA> ``` --- class: title title-8 # 2. Describir variables: bivariado <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-4-1.png" width="100%" style="display: block; margin: auto;" /> --- class: title title-8 # 2. Describir variables: bivariado <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-5-1.png" width="100%" style="display: block; margin: auto;" /> --- class: title title-8 # 2. Describir variables: bivariado <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-6-1.png" width="100%" style="display: block; margin: auto;" /> -- - **Usted no lo haga** --- class: title title-8 # 2. Describir variables: bivariado <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-7-1.png" width="100%" style="display: block; margin: auto;" /> --- class: title title-8 # 3. Modelos ```r model1 <- lm(colGPA ~ ACT, data = gpa) model2 <- lm(colGPA ~ ACT + hsGPA, data = gpa) model3 <- lm(colGPA ~ ACT + hsGPA + sex, data = gpa) ``` --- class: title title-8 # 3. Modelos <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 1</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 2</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 3</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictors</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">2.40 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.29 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.29 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">ACT</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.03 ^*</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">hsGPA</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">sex [Hombre]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.01 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.043 / 0.036</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.176 / 0.164</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.177 / 0.158</td> </tr> <tr> <td colspan="4" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> --- class: center middle main-title section-title-8 top-logo ## Los hombres tienen en promedio 0.01 puntos menos de nota que las mujeres, manteniendo el resto de las variables constantes -- ### ¡Ojo! La escala de notas va de 0 a 4 puntos. --- # Diferencias de intercepto <center> <img src="data:image/png;base64,#https://raw.githubusercontent.com/statistics-R/slides/main/img/07/22.png" alt="drawing" style="width:1000px;"/> </center> --- # Diferencias de intercepto ```r plot_model(model3, type = "pred", terms = c("hsGPA","sex"), title = "") ``` <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-10-1.png" width="100%" style="display: block; margin: auto;" /> --- class: center middle main-title section-title-8 top-logo # Predictores politómicos --- class: title title-8 # Predictores politómicos - Variables cualitativas con **más de 2 categorías de respuesta** - La forma de interpretar es similar a la de variables *dicotómicas* -- - Es decir, los coeficientes se interpretan como **la diferencia promedio respecto a la categoría de referencia** - La **única diferencia** es que tendremos tantos coeficientes como categorías de respuesta de la variable menos la de referencia --- class: title title-8 # Predictores politómicos - Sea `\(x_4 = \lbrace 0, 1, 2 \rbrace\)`, donde `\(0= Bajo, 1= Medio, 2 = Alto\)` `$$y = \beta_0 + \beta_4 * x_{4,medio} + \beta_5 * x_{4,alto}$$` - `\(x_4\)` tiene 3 categorías de respuesta, y en la regresión hay 2 coeficientes asociados a `\(x_4\)` --- class: title title-8 ## `\(\beta_4\)`: Corresponde a la diferencia promedio entre el grupo "Medio" y "Bajo", manteniendo el resto constante ## `\(\beta_5\)`: Corresponde a la diferencia promedio entre el grupo "Alto" y "Bajo", manteniendo el resto constante --- class: title title-8 # Categorías de referencia - Definir el grupo "base" o "referencia" es **arbitrario** - Los software entienden por lo general que la categoría con valor 0 es la de referencia. - Pero si queremos cambiar la categoría de referencia a una que haga sentido, *solo debemos recodificar*. [Link](https://learn-r-uah.netlify.app/example/06-practico/) --- class: title title-8 # Ejemplo promedio universidad - Muestra de 141 estudiantes de una universidad: - `colGPA`: (col:college, GPA:notas) promedio general de calificaciones de la universidad, en escala de 0 a 4 puntos - `hsGPA`: (hs: high school) promedio general de calificaciones en la enseñanza media, en escala de 0 a 4 puntos - `ACT`: puntaje en el examen de admisión a la universidad, que va de 16 a 33 puntos - `sex`: sexo del estudiante, donde `sex = 1` (Hombre) y `sex = 0` (Mujer) -- - **`job`: si el estudiante trabaja, donde `job = 0` (No trabaja), `job = 1` (Trabaja <= de 19 horas semanales), `job = 2` (Trabaja > 19 horas semanales)** --- class: title title-8 # 1. Hipótesis: promedio universidad - `\(H_1\)`: A mayor puntaje en la prueba de admisión, mayores son las notas de la universidad - `\(H_2\)`: A mayor notas en enseñanza media, mayores son las notas en la universidad - `\(H_3\)`: Existen diferencias significativas por sexo en el promedio de notas en la universidad -- - `\(H_4\)`: Existen diferencias significativas en el promedio de notas en la universidad **entre estudiantes que trabajan y aquellos que no**. Entre más horas trabajadas, las notas promedio serán más bajas. --- class: title title-8 # 2. Describir variables: univariado ``` ## x <categorical> ## # total N=141 valid N=141 mean=1.75 sd=0.73 ## ## Value | N | Raw % | Valid % | Cum. % ## ------------------------------------------------- ## No trabaja | 59 | 41.84 | 41.84 | 41.84 ## Trabaja <= 19 hrs | 58 | 41.13 | 41.13 | 82.98 ## Trabaja > 19 hrs | 24 | 17.02 | 17.02 | 100.00 ## <NA> | 0 | 0.00 | <NA> | <NA> ``` --- class: title title-8 # 2. Describir variables: bivariado <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-12-1.png" width="100%" style="display: block; margin: auto;" /> --- class: title title-8 # 3. Modelos ```r model4 <- lm(colGPA ~ ACT + hsGPA + job, data = gpa) ``` --- class: title title-8 # 3. Modelos <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 1</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 2</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 3</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 4</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictors</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">2.40 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.29 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.29 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.30 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">ACT</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.03 ^*</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">hsGPA</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">sex [Hombre]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">job [Trabaja <= 19 hrs]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.03 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">job [Trabaja > 19 hrs]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.07 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.043 / 0.036</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.176 / 0.164</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.177 / 0.158</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.181 / 0.156</td> </tr> <tr> <td colspan="5" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> --- class: center middle main-title section-title-8 top-logo ## Las personas que trabajan menos de 19 horas tienen en promedio 0.03 puntos menos de nota que los que no trabajan, manteniendo el resto de las variables constantes ## Las personas que trabajan más de 19 horas tienen en promedio 0.07 puntos menos de nota que los que no trabajan, manteniendo el resto de las variables constantes --- # Diferencias de intercepto <center> <img src="data:image/png;base64,#https://raw.githubusercontent.com/statistics-R/slides/main/img/07/23.png" alt="drawing" style="width:1000px;"/> </center> --- # Diferencias de intercepto <img src="data:image/png;base64,#07-slide_files/figure-html/unnamed-chunk-15-1.png" width="100%" style="display: block; margin: auto;" /> --- class: title title-8 # Tarea ```r model5 <- lm(colGPA ~ ACT + hsGPA + sex + job, data = gpa) ``` <table style="border-collapse:collapse; border:none;"> <tr> <th style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; text-align:left; ">&nbsp;</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 3</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 4</th> <th colspan="1" style="border-top: double; text-align:center; font-style:normal; font-weight:bold; padding:0.2cm; ">Modelo 5</th> </tr> <tr> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; text-align:left; ">Predictors</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> <td style=" text-align:center; border-bottom:1px solid; font-style:italic; font-weight:normal; ">Estimates</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">(Intercept)</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.29 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.30 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">1.31 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">ACT</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.01 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">hsGPA</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">0.45 ^***</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">sex [Hombre]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.01 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.01 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">job [Trabaja <= 19 hrs]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.03 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.03 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; ">job [Trabaja > 19 hrs]</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; "></td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.07 </td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:center; ">&#45;0.07 </td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm; border-top:1px solid;">Observations</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left; border-top:1px solid;" colspan="1">141</td> </tr> <tr> <td style=" padding:0.2cm; text-align:left; vertical-align:top; text-align:left; padding-top:0.1cm; padding-bottom:0.1cm;">R² / R² adjusted</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.177 / 0.158</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.181 / 0.156</td> <td style=" padding:0.2cm; text-align:left; vertical-align:top; padding-top:0.1cm; padding-bottom:0.1cm; text-align:left;" colspan="1">0.181 / 0.150</td> </tr> <tr> <td colspan="4" style="font-style:italic; border-top:double black; text-align:right;">* p&lt;0.05&nbsp;&nbsp;&nbsp;** p&lt;0.01&nbsp;&nbsp;&nbsp;*** p&lt;0.001</td> </tr> </table> - Interpretar cada uno de los coeficientes de la regresión - Analizar cómo cambian los resultados entre el modelo 3, modelo 4 y modelo 5 --- layout: false class: center middle main-title section-title-8 top-logo .small[ # Regresión **múltiple**: predictores categóricos ] .class-info[ <br> **Sesión N° 7**<br> **Estadísitica II** <br> .pull-right.small[ **Profesora** Valentina Andrade de la Horra <br> **Apoyo docente** Nicolás Godoy <br> **Ayudantes** Moira Martinez, Charo Astorga y Alberto Reyes .tiny[Universidad Alberto Hurtado<br> ] ] ]