library(nortest)
data("mtcars")
head(mtcars)
## mpg cyl disp hp drat wt qsec vs am gear carb
## Mazda RX4 21.0 6 160 110 3.90 2.620 16.46 0 1 4 4
## Mazda RX4 Wag 21.0 6 160 110 3.90 2.875 17.02 0 1 4 4
## Datsun 710 22.8 4 108 93 3.85 2.320 18.61 1 1 4 1
## Hornet 4 Drive 21.4 6 258 110 3.08 3.215 19.44 1 0 3 1
## Hornet Sportabout 18.7 8 360 175 3.15 3.440 17.02 0 0 3 2
## Valiant 18.1 6 225 105 2.76 3.460 20.22 1 0 3 1
plot(mtcars$wt, mtcars$mpg)
grid()
boxplot(mtcars)
boxplot(mtcars[, c(1,2,5:11)])
hist(mtcars$mpg)
plot(density(mtcars$mpg))
shapiro.test(mtcars$mpg)
##
## Shapiro-Wilk normality test
##
## data: mtcars$mpg
## W = 0.94756, p-value = 0.1229
#Regresión
modelo1 = lm(mpg ~ wt, data= mtcars)
summary(modelo1)
##
## Call:
## lm(formula = mpg ~ wt, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.5432 -2.3647 -0.1252 1.4096 6.8727
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 37.2851 1.8776 19.858 < 2e-16 ***
## wt -5.3445 0.5591 -9.559 1.29e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.046 on 30 degrees of freedom
## Multiple R-squared: 0.7528, Adjusted R-squared: 0.7446
## F-statistic: 91.38 on 1 and 30 DF, p-value: 1.294e-10
## mpg (rendimineto se estima en 37,2851 menos la pendiente -5.3441 por el peso wt)
## el menos -5.34 dice que por canda unidad de peso el redimiento perdido es de -5.3441
## SUPUESTO DE NORMALODAD
u= modelo1$residuals
#media de 0.
summary(u)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## -4.5432 -2.3647 -0.1252 0.0000 1.4096 6.8727
#Ho: errores con distribución normal
shapiro.test(u)
##
## Shapiro-Wilk normality test
##
## data: u
## W = 0.94508, p-value = 0.1044
#p-value = 0.1044 se asume que tiene una distribucionj normal.
# test de normalidad de anderson
ad.test(u)
##
## Anderson-Darling normality test
##
## data: u
## A = 0.46842, p-value = 0.233
# p-value = 0.233 confrima la distribucon normal
# kolmogorov smirnoff
lillie.test(u)
##
## Lilliefors (Kolmogorov-Smirnov) normality test
##
## data: u
## D = 0.082516, p-value = 0.8379
# p-value = 0.8379 confrima la distribucon normal
## VARIANZA DE LOS ERRORES
##bruspegan para heterecedasticiad
lmtest::bptest(modelo1)
##
## studentized Breusch-Pagan test
##
## data: modelo1
## BP = 0.040438, df = 1, p-value = 0.8406
# p-value = 0.8406 se asume que la varianza es constante
##errores indpendientes - no autocorrelacion
lmtest::dwtest(modelo1)
##
## Durbin-Watson test
##
## data: modelo1
## DW = 1.2517, p-value = 0.0102
## alternative hypothesis: true autocorrelation is greater than 0
## p-value = 0.0102 hay relaxcion con los errores, el modelo cumple todo menos la autocorrelacion de los errores.
library(MASS)
boxcox(lm(mpg ~ wt, data = mtcars))
## cuando lamda esta mas cerca de 0 la mejor trasnformacion es la logaritmica.
modelo2= lm(log(mpg) ~ wt, data = mtcars)
summary(modelo2)
##
## Call:
## lm(formula = log(mpg) ~ wt, data = mtcars)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.210346 -0.085932 -0.006136 0.061335 0.308623
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.83191 0.08396 45.64 < 2e-16 ***
## wt -0.27178 0.02500 -10.87 6.31e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1362 on 30 degrees of freedom
## Multiple R-squared: 0.7976, Adjusted R-squared: 0.7908
## F-statistic: 118.2 on 1 and 30 DF, p-value: 6.31e-12
## por un incremento unitario en el peso el rendimeinto se va a reduri en un -27,178%
lmtest::bptest(modelo2)
##
## studentized Breusch-Pagan test
##
## data: modelo2
## BP = 1.7974, df = 1, p-value = 0.18
u2=modelo2$residuals
shapiro.test(u2)
##
## Shapiro-Wilk normality test
##
## data: u2
## W = 0.96184, p-value = 0.3081
lmtest::bptest(modelo2)
##
## studentized Breusch-Pagan test
##
## data: modelo2
## BP = 1.7974, df = 1, p-value = 0.18
lmtest::dwtest(modelo2)
##
## Durbin-Watson test
##
## data: modelo2
## DW = 1.5016, p-value = 0.06009
## alternative hypothesis: true autocorrelation is greater than 0
boxplot(mtcars$wt)
modelo3 = lm(mpg ~log(wt), data = mtcars)
modelo4 = lm(log(mpg) ~ log(wt), data = mtcars)
stargazer::stargazer(modelo1, modelo2, modelo3, modelo4, type="text", df=FALSE)
##
## ==============================================================
## Dependent variable:
## ------------------------------------------
## mpg log(mpg) mpg log(mpg)
## (1) (2) (3) (4)
## --------------------------------------------------------------
## wt -5.344*** -0.272***
## (0.559) (0.025)
##
## log(wt) -17.086*** -0.842***
## (1.510) (0.075)
##
## Constant 37.285*** 3.832*** 39.257*** 3.902***
## (1.878) (0.084) (1.758) (0.088)
##
## --------------------------------------------------------------
## Observations 32 32 32 32
## R2 0.753 0.798 0.810 0.806
## Adjusted R2 0.745 0.791 0.804 0.799
## Residual Std. Error 3.046 0.136 2.669 0.133
## F Statistic 91.375*** 118.191*** 128.016*** 124.360***
## ==============================================================
## Note: *p<0.1; **p<0.05; ***p<0.01