GUIA 1

library(wooldridge)
data(hprice1)
head(hprice1, n = 5) #mostrar las primeras 5 observaciones

##   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 <- 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

# Calcula el estadístico de prueba de JarqueBera
n <- length(modelo$residuals)
JB_stat <- (n / 6) * (sum(modelo$residuals^3)/sd(modelo$residuals)^3)^2 +
            (n / 24) * (sum(modelo$residuals^4)/sd(modelo$residuals)^4) - 3 * (n - 1)

# Grados de libertad para la distribución chi-cuadrado
df <- 2

# Valor p
p_value_JB <- pchisq(JB_stat, df, lower.tail = FALSE)

# Imprimir resultados
cat("Estadística de prueba de Jarque-Bera:", JB_stat, "\n")

## Estadística de prueba de Jarque-Bera: 102688.2

cat("Valor p:", p_value_JB, "\n")

## Valor p: 0

# Prueba de Kolmogorov-Smirnov
ks.test <- ks.test(modelo$residuals, "pnorm", mean(modelo$residuals), sd(modelo$residuals))
ks.test

## 
##  Exact one-sample Kolmogorov-Smirnov test
## 
## data:  modelo$residuals
## D = 0.075439, p-value = 0.67
## alternative hypothesis: two-sided

# Prueba de Shapiro-Wilk
shapiro.test <- shapiro.test(modelo$residuals)
shapiro.test

## 
##  Shapiro-Wilk normality test
## 
## data:  modelo$residuals
## W = 0.94132, p-value = 0.0005937