Modelo de regresión lineal múltiple
Módulo 5- Unidad 5.2
dgonzalez
En construcción
Guía de aprendizaje 5.2
1. Introducción
2. Objetivos de la unidad
3. Duración
4. Cronograma de trabajo
| Actividad | Descripción |
|---|
5. Criterios de evaluación
6. Entregables
7. Presentaciones
Recursos
Ejemplo 1
Modelo
Se requiere modelar el numero de días que un trabajador se ausenta de su puesto de trabajo durante un año, para lo cual se tienen en cuenta las siguientes variables :
| Taller | si la persona trabaja en el taller (1) o no (0) |
| sexo | hombre (1) , mujer (0 |
| edad | edad del trabajador en año |
| antigüedad | años de trabajo en la empresa |
| salario | cuanto devenga el trabajador (U$) |
\[y_{i} = \beta_{0} + \beta_{1} Taller_{i} + \beta_{2} sexo_{i} + \beta_{3} edad_{i} + \beta_{4} antiguedad_{i} + \beta_{5} salario_{i} + u\]
para \(i=1,.....n\)
library(readr)
data=read_delim("data/ausentismo.csv", delim = ";", escape_double = FALSE, trim_ws = TRUE)Rows: 48 Columns: 7── Column specification ────────────────────────────────────────────────────────
Delimiter: ";"
dbl (7): id, ausen, taller, sexo, edad, antg, sala
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.round(cov(data), 2) # matriz de varianzas-covarianzas id ausen taller sexo edad antg sala
id 196.00 -17.60 1.09 0.95 39.20 18.21 3327.02
ausen -17.60 14.34 0.43 -0.20 -34.84 -27.74 -1223.19
taller 1.09 0.43 0.19 0.02 -0.89 -0.50 -22.34
sexo 0.95 -0.20 0.02 0.25 0.24 1.33 118.24
edad 39.20 -34.84 -0.89 0.24 185.61 121.65 2081.76
antg 18.21 -27.74 -0.50 1.33 121.65 104.92 2175.43
sala 3327.02 -1223.19 -22.34 118.24 2081.76 2175.43 234470.21round(cor(data), 2) # matriz de correlaciones id ausen taller sexo edad antg sala
id 1.00 -0.33 0.18 0.13 0.21 0.13 0.49
ausen -0.33 1.00 0.26 -0.11 -0.68 -0.72 -0.67
taller 0.18 0.26 1.00 0.07 -0.15 -0.11 -0.11
sexo 0.13 -0.11 0.07 1.00 0.03 0.26 0.49
edad 0.21 -0.68 -0.15 0.03 1.00 0.87 0.32
antg 0.13 -0.72 -0.11 0.26 0.87 1.00 0.44
sala 0.49 -0.67 -0.11 0.49 0.32 0.44 1.00# Estimación del modelo
attach(data)
modelo1=lm(ausen ~ taller + sexo + edad + antg + sala , data=data)
summary(modelo1)
Call:
lm(formula = ausen ~ taller + sexo + edad + antg + sala, data = data)
Residuals:
Min 1Q Median 3Q Max
-7.0713 -0.5383 0.3031 0.9391 3.5793
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 12.4436075 1.6404323 7.586 2.14e-09 ***
taller 0.9684600 0.6688242 1.448 0.15504
sexo 2.0492914 0.7122235 2.877 0.00628 **
edad -0.0372111 0.0469913 -0.792 0.43288
antg -0.1507700 0.0652833 -2.309 0.02590 *
sala -0.0044288 0.0007348 -6.027 3.63e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.964 on 42 degrees of freedom
Multiple R-squared: 0.7597, Adjusted R-squared: 0.7311
F-statistic: 26.56 on 5 and 42 DF, p-value: 5.282e-12# diagnostico
coefficients(modelo1) # coeficientes estimados (Intercept) taller sexo edad antg sala
12.443607478 0.968459990 2.049291411 -0.037211075 -0.150770045 -0.004428793 yhat=fitted(modelo1) # valores estimados
u=residuals(modelo1) # residuales
anova(modelo1) # tabla de anovaAnalysis of Variance Table
Response: ausen
Df Sum Sq Mean Sq F value Pr(>F)
taller 1 44.444 44.444 11.5262 0.001510 **
sexo 1 10.612 10.612 2.7522 0.104573
edad 1 275.299 275.299 71.3956 1.331e-10 ***
antg 1 41.613 41.613 10.7919 0.002062 **
sala 1 140.080 140.080 36.3283 3.629e-07 ***
Residuals 42 161.950 3.856
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1vcov(modelo1) # matriz de varianzas covarianza de parámetros ( de los betas) (Intercept) taller sexo edad
(Intercept) 2.6910180499 -0.4609636984 -0.1696280253 -5.605492e-02
taller -0.4609636984 0.4473257798 -0.0535216133 2.117073e-03
sexo -0.1696280253 -0.0535216133 0.5072623436 1.228218e-02
edad -0.0560549171 0.0021170730 0.0122821769 2.208178e-03
antg 0.0686105842 -0.0008662038 -0.0163953239 -2.692865e-03
sala -0.0006247407 0.0000588528 -0.0002178462 -6.131445e-07
antg sala
(Intercept) 6.861058e-02 -6.247407e-04
taller -8.662038e-04 5.885280e-05
sexo -1.639532e-02 -2.178462e-04
edad -2.692865e-03 -6.131445e-07
antg 4.261912e-03 -7.447761e-06
sala -7.447761e-06 5.399159e-07# Stepwise Regression
library(MASS)
modelo2=lm(ausen ~ taller + sexo + edad + antg + sala , data=data)
step=stepAIC(modelo2, direction="both")Start: AIC=70.37
ausen ~ taller + sexo + edad + antg + sala
Df Sum of Sq RSS AIC
- edad 1 2.418 164.37 69.084
<none> 161.95 70.372
- taller 1 8.085 170.03 70.711
- antg 1 20.566 182.52 74.111
- sexo 1 31.923 193.87 77.008
- sala 1 140.080 302.03 98.288
Step: AIC=69.08
ausen ~ taller + sexo + antg + sala
Df Sum of Sq RSS AIC
<none> 164.37 69.084
- taller 1 8.731 173.10 69.568
+ edad 1 2.418 161.95 70.372
- sexo 1 44.720 209.09 78.635
- sala 1 140.779 305.15 96.781
- antg 1 151.697 316.07 98.468step$anova # display resultsStepwise Model Path
Analysis of Deviance Table
Initial Model:
ausen ~ taller + sexo + edad + antg + sala
Final Model:
ausen ~ taller + sexo + antg + sala
Step Df Deviance Resid. Df Resid. Dev AIC
1 42 161.9505 70.37230
2 - edad 1 2.417928 43 164.3684 69.08364modelo3=lm(ausen ~ taller + sexo + antg + sala , data=data)
summary(modelo3)
Call:
lm(formula = ausen ~ taller + sexo + antg + sala, data = data)
Residuals:
Min 1Q Median 3Q Max
-6.989 -0.597 0.310 1.041 3.826
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.4989988 1.1211859 10.256 3.98e-13 ***
taller 1.0041358 0.6644050 1.511 0.13802
sexo 2.2562643 0.6596516 3.420 0.00138 **
antg -0.1961488 0.0311366 -6.300 1.34e-07 ***
sala -0.0044391 0.0007315 -6.069 2.91e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.955 on 43 degrees of freedom
Multiple R-squared: 0.7561, Adjusted R-squared: 0.7334
F-statistic: 33.33 on 4 and 43 DF, p-value: 1.15e-12modelo4=lm(ausen ~ sexo + antg + sala , data=data)
summary(modelo4)
Call:
lm(formula = ausen ~ sexo + antg + sala, data = data)
Residuals:
Min 1Q Median 3Q Max
-6.8757 -0.9888 0.2701 1.3332 4.0126
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 12.4172771 0.9559277 12.990 < 2e-16 ***
sexo 2.4035082 0.6618691 3.631 0.000732 ***
antg -0.2000174 0.0314808 -6.354 1.02e-07 ***
sala -0.0045732 0.0007366 -6.208 1.67e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 1.983 on 44 degrees of freedom
Multiple R-squared: 0.7432, Adjusted R-squared: 0.7257
F-statistic: 42.44 on 3 and 44 DF, p-value: 4.805e-13uhat=modelo4$residuals
#-----------------------------------------------------------------
# Examen de normalidad de errores
shapiro.test(uhat)
Shapiro-Wilk normality test
data: uhat
W = 0.92696, p-value = 0.005279# Supuesto de no autocorrelacion
# install.packages("lmtest")
library(lmtest)Loading required package: zoo
Attaching package: 'zoo'The following objects are masked from 'package:base':
as.Date, as.Date.numeric# Prueba de D-W - autocorrelacion
# Ho: los erreres no estan autocorrelacionados
dwtest(modelo4)
Durbin-Watson test
data: modelo4
DW = 1.8731, p-value = 0.3097
alternative hypothesis: true autocorrelation is greater than 0# Supuesto de homoscedasticidad
# Prueba de Goldfeld-Quandt
# Ho no existe heteroscedasticidad
gqtest(modelo4)
Goldfeld-Quandt test
data: modelo4
GQ = 0.46949, df1 = 20, df2 = 20, p-value = 0.9506
alternative hypothesis: variance increases from segment 1 to 2# Supuesto de correcta especificacion
# Prueba de especificacion
# Prueba RESET
resettest(modelo4, power=2, type="regressor")
RESET test
data: modelo4
RESET = 1.7756, df1 = 3, df2 = 41, p-value = 0.1669modelo5=lm(ausen ~ antg + sala , data=data)
summary(modelo5)
Call:
lm(formula = ausen ~ antg + sala, data = data)
Residuals:
Min 1Q Median 3Q Max
-5.508 -1.103 0.033 1.914 3.610
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 11.9557841 1.0680594 11.194 1.35e-14 ***
antg -0.1934922 0.0354307 -5.461 1.95e-06 ***
sala -0.0034216 0.0007495 -4.565 3.85e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2.236 on 45 degrees of freedom
Multiple R-squared: 0.6662, Adjusted R-squared: 0.6514
F-statistic: 44.91 on 2 and 45 DF, p-value: 1.898e-11