Prueba de normalidad 3 variables

PRUEBAS DE NORMALIDAD CON 3 VARIABLES.

-Datos

library(readr)
library(stargazer)
library(fitdistrplus)
library(normtest)
ejemplo_regresion1<-read.csv("C:\\Users\\AD_be\\Desktop\\Econometria\\Datos_practica_2.csv")
head(ejemplo_regresion1,n = 10)

##      Y  X1   X2     X3
## 1  320  50  7.4  370.0
## 2  450  53  5.1  270.3
## 3  370  60  4.2  252.0
## 4  470  63  3.9  245.7
## 5  420  69  1.4   96.6
## 6  500  82  2.2  180.4
## 7  570 100  7.0  700.0
## 8  640 104  5.7  592.8
## 9  670 113 13.1 1480.3
## 10 780 130 16.4 2132.0

Modelo de Regresion Lineal

reg_lineal<-lm(formula= Y~X1+X2+X3, data = ejemplo_regresion1)
stargazer(reg_lineal, title = "Regresion multiple", type = "text", digits = 3)

## 
## Regresion multiple
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                  Y             
## -----------------------------------------------
## X1                           2.329***          
##                               (0.477)          
##                                                
## X2                           -25.071**         
##                              (11.485)          
##                                                
## X3                           0.286***          
##                               (0.077)          
##                                                
## Constant                    303.504***         
##                              (71.547)          
##                                                
## -----------------------------------------------
## Observations                    20             
## R2                             0.963           
## Adjusted R2                    0.957           
## Residual Std. Error      67.678 (df = 16)      
## F Statistic           140.441*** (df = 3; 16)  
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

Ajuste de los residuos a la Distribucion Normal.

-Verificando el ajuste de los residuos.

fit_normal<-fitdist(data = reg_lineal$residuals,distr = "norm")
plot(fit_normal)

Estimacion.

summary(fit_normal)

## Fitting of the distribution ' norm ' by maximum likelihood 
## Parameters : 
##          estimate Std. Error
## mean 1.064556e-15  13.535551
## sd   6.053282e+01   9.571082
## Loglikelihood:  -110.4425   AIC:  224.885   BIC:  226.8764 
## Correlation matrix:
##      mean sd
## mean    1  0
## sd      0  1

Prueba de normalidad Jarque-Bera.

jb.norm.test(reg_lineal$residuals)

## 
##  Jarque-Bera test for normality
## 
## data:  reg_lineal$residuals
## JB = 0.58681, p-value = 0.6705

qqnorm(reg_lineal$residuals)
qqline(reg_lineal$residuals)

Histograma JB

hist(reg_lineal$residuals, main = "HIstograma de los residuos", xlab = "Residuos", ylab = "Frecuencia")

Prueba de normalidad Kolmogorov-Smirnov.

library(nortest)

## Warning: package 'nortest' was built under R version 3.5.2

lillie.test(reg_lineal$residuals)

## 
##  Lilliefors (Kolmogorov-Smirnov) normality test
## 
## data:  reg_lineal$residuals
## D = 0.14222, p-value = 0.3594

qqnorm(reg_lineal$residuals)
qqline(reg_lineal$residuals)

Histograma KS

hist(reg_lineal$residuals, main = "Histograma de los Residuos", xlab = "Residuos", ylab = "Frecuencia")

Prueba de normalidad Shapiro-Wilk.

shapiro.test(reg_lineal$residuals)

## 
##  Shapiro-Wilk normality test
## 
## data:  reg_lineal$residuals
## W = 0.95957, p-value = 0.5352