Heterocedasticidad
Hernández Gutiérrez German Alejandro HG19046.
2023-05-21
1. Importacion de datos
library(wooldridge)
data(hprice1)
head(force(hprice1))## price assess bdrms lotsize sqrft colonial lprice lassess llotsize
## 1 300.000 349.1 4 6126 2438 1 5.703783 5.855359 8.720297
## 2 370.000 351.5 3 9903 2076 1 5.913503 5.862210 9.200593
## 3 191.000 217.7 3 5200 1374 0 5.252274 5.383118 8.556414
## 4 195.000 231.8 3 4600 1448 1 5.273000 5.445875 8.433811
## 5 373.000 319.1 4 6095 2514 1 5.921578 5.765504 8.715224
## 6 466.275 414.5 5 8566 2754 1 6.144775 6.027073 9.055556
## lsqrft
## 1 7.798934
## 2 7.638198
## 3 7.225482
## 4 7.277938
## 5 7.829630
## 6 7.920810library(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=stargazermodelo_heterocedasticidad<-lm(price = ˆα + ˆα1(lotsize) + ˆα2(sqrft) + ˆα3(bdrms) +ε, data = hprice1)## Warning: In lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...) :
## extra argument 'price' will be disregardedstargazer(modelo_heterocedasticidad,title = "Modelo para Ejemplo", type = "text")##
## Modelo para Ejemplo
## ===============================================
## Dependent variable:
## ---------------------------
## NA
## -----------------------------------------------
## assess 1.233***
## (0.097)
##
## bdrms 2.652
## (2.118)
##
## lotsize 0.00003
## (0.0003)
##
## sqrft 0.008
## (0.019)
##
## colonial -0.410
## (3.390)
##
## lprice 276.094***
## (10.186)
##
## lassess -396.819***
## (38.182)
##
## llotsize 1.755
## (5.791)
##
## lsqrft -3.954
## (41.502)
##
## Constant 606.372**
## (246.442)
##
## -----------------------------------------------
## Observations 88
## R2 0.986
## Adjusted R2 0.984
## Residual Std. Error 12.921 (df = 78)
## F Statistic 602.196*** (df = 9; 78)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01summary(modelo_heterocedasticidad)##
## Call:
## lm(data = hprice1, price = ˆα + ˆα1(lotsize) + ˆα2(sqrft) +
## ˆα3(bdrms) + ε)
##
## Residuals:
## Min 1Q Median 3Q Max
## -41.299 -4.117 0.383 4.547 53.462
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.064e+02 2.464e+02 2.461 0.0161 *
## assess 1.233e+00 9.706e-02 12.704 < 2e-16 ***
## bdrms 2.652e+00 2.118e+00 1.252 0.2143
## lotsize 3.452e-05 2.524e-04 0.137 0.8916
## sqrft 8.147e-03 1.859e-02 0.438 0.6624
## colonial -4.100e-01 3.390e+00 -0.121 0.9041
## lprice 2.761e+02 1.019e+01 27.107 < 2e-16 ***
## lassess -3.968e+02 3.818e+01 -10.393 2.23e-16 ***
## llotsize 1.755e+00 5.791e+00 0.303 0.7627
## lsqrft -3.954e+00 4.150e+01 -0.095 0.9243
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 12.92 on 78 degrees of freedom
## Multiple R-squared: 0.9858, Adjusted R-squared: 0.9842
## F-statistic: 602.2 on 9 and 78 DF, p-value: < 2.2e-162. Verificacion de varianza residual, si es homocedastica o no.
a) Prueba de white con calculos a mano
library(stargazer)
u_i<-modelo_heterocedasticidad$residuals
data_prueba_white<-as.data.frame(cbind(u_i,hprice1))
regresion_auxiliar<-lm(I(u_i^2)~lotsize+sqrft+bdrms+I(lotsize^2)+I(sqrft^2)+I(bdrms^2)+lotsize*sqrft*bdrms, data= data_prueba_white)
sumario<-summary(regresion_auxiliar)
n<-nrow(data_prueba_white)
R_2<-sumario$r.squared
LM_w<-n*R_2
gl=3+3+1
p_value<-1-pchisq(q=LM_w,df=gl)
VC<-qchisq(p=0.95,df=gl)
salida_white<-c(LM_w,VC,p_value)
names(salida_white)<-c("LMw","valor critico","p value")
stargazer(salida_white,title = "Resultados prueba white", type="text", digits = 6)##
## Resultados prueba white
## ================================
## LMw valor critico p value
## --------------------------------
## 10.975530 14.067140 0.139690
## --------------------------------como 0.139690 es > 0.05 no se rechaza la H0 por lo tanto hay evidencia que la varianza de los residuos es homocedastica.
Calculo mediante libreria LMTEST
library(lmtest)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericprueba_white<-bptest(modelo_heterocedasticidad,~I(lotsize^2)+I(sqrft^2)+I(bdrms^2)+lotsize*sqrft*bdrms,data = hprice1)
print(prueba_white)##
## studentized Breusch-Pagan test
##
## data: modelo_heterocedasticidad
## BP = 10.976, df = 10, p-value = 0.3594como 0.3594 es > 0.05 no se rechaza la H0 por lo tanto hay evidencia que la varianza de los residuos es homocedastica.
library(fastGraph)
LM_W<-n*R_2
gl<-3*2+choose(3,2)
vc<-qchisq(p=0.95,df=gl)
shadeDist(xshade = prueba_white$statistic,
ddist = "dchisq",
parm1 = VC,
lower.tail = FALSE, col = c("black","orange"),
sub=paste("VC:",VC,"White:",LM_w))