Modelación Regresión
Dr. Víctor Chung
1/9/2019
Paquetes Utilizados
library("foreign")
library("olsrr")
library("mctest")
library("GGally")
library("ggplot2")Base de datos
auto<-read.dta("auto.dta")
head(auto)## make price mpg rep78 headroom trunk weight length turn
## 1 AMC Concord 4099 22 3 2.5 11 2930 186 40
## 2 AMC Pacer 4749 17 3 3.0 11 3350 173 40
## 3 AMC Spirit 3799 22 NA 3.0 12 2640 168 35
## 4 Buick Century 4816 20 3 4.5 16 3250 196 40
## 5 Buick Electra 7827 15 4 4.0 20 4080 222 43
## 6 Buick LeSabre 5788 18 3 4.0 21 3670 218 43
## displacement gear_ratio foreign
## 1 121 3.58 Domestic
## 2 258 2.53 Domestic
## 3 121 3.08 Domestic
## 4 196 2.93 Domestic
## 5 350 2.41 Domestic
## 6 231 2.73 DomesticReegresión Simple: mpg vs weight
Diagrama de Dispersión
ggplot(auto, aes(x=weight, y=mpg)) +
geom_point() + theme_light()
Estimación del Modelo
modelo1<-lm(mpg~weight,data=auto)
summary(modelo1)##
## Call:
## lm(formula = mpg ~ weight, data = auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.9593 -1.9325 -0.3713 0.8885 13.8174
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.4402835 1.6140031 24.44 <2e-16 ***
## weight -0.0060087 0.0005179 -11.60 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.439 on 72 degrees of freedom
## Multiple R-squared: 0.6515, Adjusted R-squared: 0.6467
## F-statistic: 134.6 on 1 and 72 DF, p-value: < 2.2e-16Modelo
\[ mpg = 39.4403 - 0.0060*weight \] ## Evaluación de los residuales
Normalidad
Gráfico Q-Q
ols_plot_resid_qq(modelo1)
Prueba de Normalidad
\[ H_0: Los \ residuales \ siguen \ una \ Distribución \ Normal \]
ols_test_normality(modelo1)## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.8959 0.0000
## Kolmogorov-Smirnov 0.1593 0.0416
## Cramer-von Mises 6.3706 0.0000
## Anderson-Darling 2.4253 0.0000
## -----------------------------------------------Correlación entre residuos observados y esperados
ols_test_correlation(modelo1)## [1] 0.9423747Gráfico residuales vs ajustados
ols_plot_resid_fit(modelo1)
Histograma de los residuales
ols_plot_resid_hist(modelo1)
ols_plot_diagnostics(modelo1)
Modelo de Regresión distinguiendo procedencia del auto.
Diagrama de Dispersión
ggplot(auto,aes(weight,mpg,color=foreign))+geom_point()
ggplot(auto, aes(x = weight, y = mpg))+
geom_point(aes(color = foreign))+
facet_wrap(~foreign, ncol = 2, nrow = 1)
Modelo Autos Domésticos
modelo.domestico<-lm(mpg~weight,data=subset(auto,foreign=="Domestic"))
summary(modelo.domestico)##
## Call:
## lm(formula = mpg ~ weight, data = subset(auto, foreign == "Domestic"))
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.8130 -1.5041 -0.2844 0.4845 7.8318
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 39.6469645 1.5766224 25.15 <2e-16 ***
## weight -0.0059751 0.0004654 -12.84 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.311 on 50 degrees of freedom
## Multiple R-squared: 0.7673, Adjusted R-squared: 0.7626
## F-statistic: 164.8 on 1 and 50 DF, p-value: < 2.2e-16Modelo Autos Domésticos
\[ mpg = 39.64696 - 0.0059751*weight \] ## Evaluación de los residuales
Normalidad
Gráfico Q-Q
ols_plot_resid_qq(modelo.domestico)
ols_test_normality(modelo.domestico)## -----------------------------------------------
## Test Statistic pvalue
## -----------------------------------------------
## Shapiro-Wilk 0.8369 0.0000
## Kolmogorov-Smirnov 0.1741 0.0754
## Cramer-von Mises 5.2468 0.0000
## Anderson-Darling 2.3618 0.0000
## -----------------------------------------------Gráfico residuales vs ajustados
ols_plot_resid_fit(modelo.domestico)
ols_plot_diagnostics(modelo.domestico)
Modelo con foreign
modelo.foreign<-lm(mpg ~ weight + as.numeric(foreign),data=auto)
summary(modelo.foreign)##
## Call:
## lm(formula = mpg ~ weight + as.numeric(foreign), data = auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -6.1529 -1.9712 -0.4534 0.8083 14.4096
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 43.3297314 2.9983312 14.451 < 2e-16 ***
## weight -0.0065879 0.0006371 -10.340 8.28e-16 ***
## as.numeric(foreign) -1.6500291 1.0759941 -1.533 0.13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.407 on 71 degrees of freedom
## Multiple R-squared: 0.6627, Adjusted R-squared: 0.6532
## F-statistic: 69.75 on 2 and 71 DF, p-value: < 2.2e-16\[ mpg=43.3297-0.0065879*weight-1.6500291*foreign \]
Modelo Cuadrático
auto$weight2<-auto$weight^2modelo.cuadratico<-lm(mpg ~ weight + weight2 + as.numeric(foreign),data=auto)
summary(modelo.cuadratico)##
## Call:
## lm(formula = mpg ~ weight + weight2 + as.numeric(foreign), data = auto)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.6361 -1.8989 -0.3020 0.8105 13.8517
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 5.874e+01 6.707e+00 8.758 7.34e-13 ***
## weight -1.657e-02 3.969e-03 -4.175 8.43e-05 ***
## weight2 1.591e-06 6.249e-07 2.546 0.0131 *
## as.numeric(foreign) -2.204e+00 1.059e+00 -2.080 0.0412 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.283 on 70 degrees of freedom
## Multiple R-squared: 0.6913, Adjusted R-squared: 0.6781
## F-statistic: 52.25 on 3 and 70 DF, p-value: < 2.2e-16\[ mpg=58.874-0.001657*weight + 0.000001591*weight^2-2.204*foreign \]
ols_plot_diagnostics(modelo.cuadratico)
