Heterocedasticidad

library(wooldridge)
data(hprice1)
head(force(hprice1),n=5)

##   price assess bdrms lotsize sqrft colonial   lprice  lassess llotsize   lsqrft
## 1   300  349.1     4    6126  2438        1 5.703783 5.855359 8.720297 7.798934
## 2   370  351.5     3    9903  2076        1 5.913503 5.862210 9.200593 7.638198
## 3   191  217.7     3    5200  1374        0 5.252274 5.383118 8.556414 7.225482
## 4   195  231.8     3    4600  1448        1 5.273000 5.445875 8.433811 7.277938
## 5   373  319.1     4    6095  2514        1 5.921578 5.765504 8.715224 7.829630

MODELO ESTIMADO

library(stargazer)

## 
## Please cite as:

##  Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.

##  R package version 5.2.3. https://CRAN.R-project.org/package=stargazer

modelo_estimado <-lm(formula = price ~ lotsize +sqrft+ bdrms, data = hprice1)
stargazer(modelo_estimado, title = "Ejercicio de pruebas de Heterocedasticidad", type = "text")

## 
## Ejercicio de pruebas de Heterocedasticidad
## ===============================================
##                         Dependent variable:    
##                     ---------------------------
##                                price           
## -----------------------------------------------
## lotsize                      0.002***          
##                               (0.001)          
##                                                
## sqrft                        0.123***          
##                               (0.013)          
##                                                
## bdrms                         13.853           
##                               (9.010)          
##                                                
## Constant                      -21.770          
##                              (29.475)          
##                                                
## -----------------------------------------------
## Observations                    88             
## R2                             0.672           
## Adjusted R2                    0.661           
## Residual Std. Error      59.833 (df = 84)      
## F Statistic           57.460*** (df = 3; 84)   
## ===============================================
## Note:               *p<0.1; **p<0.05; ***p<0.01

1. PRUEBA DE WHITE USANDO “LMTEST”, INCLUYENDO TÉRMINOS CRUZADOS.

library(lmtest)

## Loading required package: zoo

## 
## Attaching package: 'zoo'

## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric

white_test<-bptest(modelo_estimado,~I(lotsize^2)+I(sqrft^2)+I(bdrms^2)+lotsize*sqrft+lotsize*bdrms+sqrft*bdrms,data = hprice1)
print(white_test)

## 
##  studentized Breusch-Pagan test
## 
## data:  modelo_estimado
## BP = 33.732, df = 9, p-value = 9.953e-05

Como 0.00009953 ≤ 0.05 Se rechaza Ho, es decir que hay evidencia de que la varianza de los residuos es Heterocedástica.

GRÁFICA.

library(fastGraph)
alphan_sig<-0.05
gl<-3+3+3
u_i<-modelo_estimado$residuals
data_prueba_white<-as.data.frame(cbind(u_i,hprice1))
regresion_auxiliar<-lm(formula = I(u_i^2)~lotsize+sqrft+bdrms+I(lotsize^2)+I(sqrft^2)+I(bdrms^2)+lotsize*sqrft+lotsize*bdrms+sqrft*bdrms,data = data_prueba_white)
sumario<-summary(regresion_auxiliar)
n<-nrow(data_prueba_white)
R_2<-sumario$r.squared
LM_w<-n*R_2
VC<-qchisq(p = 0.95,df = gl)
shadeDist(LM_w,ddist = "dchisq",
          parm1 = gl,
          lower.tail = FALSE, xmin = 0,
          sub=paste("VC:", round(VC,2)," ","LM_w", round(LM_w,2)))