paquetes <- c("wooldridge", "lmtest", "fastGraph")
instalar <- paquetes[!sapply(paquetes, requireNamespace, quietly = TRUE)]
if(length(instalar) > 0) install.packages(instalar)
# 1) Cargar librerías y base de datos
library(wooldridge)
## Warning: package 'wooldridge' was built under R version 4.5.3
library(lmtest)
## Cargando paquete requerido: zoo
## 
## Adjuntando el paquete: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(fastGraph)
## Warning: package 'fastGraph' was built under R version 4.5.3
head(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

1. Estimación del modelo.

modelo <- lm(price ~ lotsize + sqrft + bdrms, data = hprice1)

summary(modelo)
## 
## Call:
## lm(formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -120.026  -38.530   -6.555   32.323  209.376 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.177e+01  2.948e+01  -0.739  0.46221    
## lotsize      2.068e-03  6.421e-04   3.220  0.00182 ** 
## sqrft        1.228e-01  1.324e-02   9.275 1.66e-14 ***
## bdrms        1.385e+01  9.010e+00   1.537  0.12795    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 59.83 on 84 degrees of freedom
## Multiple R-squared:  0.6724, Adjusted R-squared:  0.6607 
## F-statistic: 57.46 on 3 and 84 DF,  p-value: < 2.2e-16

a) Prueba de White (heterocedasticidad)

# Usando "lmtest" con terminos cruzados

bptest(modelo, ~ lotsize + sqrft + bdrms +
    I(lotsize^2) + I(sqrft^2) + I(bdrms^2) +
    I(lotsize * sqrft) + I(lotsize * bdrms) + I(sqrft * bdrms),
  data = hprice1)
## 
##  studentized Breusch-Pagan test
## 
## data:  modelo
## BP = 33.732, df = 9, p-value = 9.953e-05

INTERPRETACION: como el p-value > 0.05 No hay hetocedasticidad; P-value < 0.05 Si hay heterocedasticidad.

Obtener residuos y valores ajustados

residuos <- residuals(modelo)
ajustados <- fitted(modelo)

head(residuos)
##          1          2          3          4          5          6 
## -45.639765  74.848732  -8.236558 -12.081520  18.093192  62.939597
head(ajustados)
##        1        2        3        4        5        6 
## 345.6398 295.1513 199.2366 207.0815 354.9068 403.3354

b) Gráficos con fastGraph

plot(ajustados, residuos,
           main = "Residuos vs Valores Ajustados",
           xlab = "Valores Ajustados",
           ylab = "Residuos")

abline(h = 0, col = "purple")