Carga de Datos

library(wooldridge)
## Warning: package 'wooldridge' was built under R version 4.3.3
data(hprice1)
head(force(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

1. estime el siguiente modelo,price = ˆα + ˆα1(lotsize) + ˆα2(sqrft) + ˆα3(bdrms) + E

modelo_estimado <- lm( formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
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
stargazer(modelo_estimado, title = 'Modelo estimado', type = 'html')
Modelo estimado
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

2. Verifique si hay evidencia de la independencia de los regresores (no colinealidad)

a) Indice de condición y prueba de FG, presente sus resultados de manera tabular en ambos casos y para la prueba de FG presente también sus resultados de forma gráfica usando la librería fastGraph

Indice de condición

matrizX <- model.matrix(modelo_estimado)
MatrizXX <- t(matrizX) %*% matrizX
#Sn matriz de normailizacion
Sn <- solve(diag(sqrt(diag(MatrizXX))))
print( Sn)
##           [,1]         [,2]         [,3]       [,4]
## [1,] 0.1066004 0.000000e+00 0.000000e+00 0.00000000
## [2,] 0.0000000 7.865204e-06 0.000000e+00 0.00000000
## [3,] 0.0000000 0.000000e+00 5.091049e-05 0.00000000
## [4,] 0.0000000 0.000000e+00 0.000000e+00 0.02908649
##Matriz normalizada

Matriz_norm <- (Sn %*% MatrizXX) %*% Sn
print(Matriz_norm)
##           [,1]      [,2]      [,3]      [,4]
## [1,] 1.0000000 0.6655050 0.9617052 0.9735978
## [2,] 0.6655050 1.0000000 0.6776293 0.6711613
## [3,] 0.9617052 0.6776293 1.0000000 0.9695661
## [4,] 0.9735978 0.6711613 0.9695661 1.0000000
#Encontrar los autovalores
lambdas <- eigen(Matriz_norm, symmetric = TRUE)$values

#Calculando K (indice de correlacion)
K <- sqrt(max(lambdas)/ min(lambdas))
print(K)
## [1] 11.86778
#con libreria
library(mctest)
indice_condicion<- eigprop( mod = modelo_estimado)
print(indice_condicion)
## 
## Call:
## eigprop(mod = modelo_estimado)
## 
##   Eigenvalues      CI (Intercept) lotsize  sqrft  bdrms
## 1      3.4816  1.0000      0.0037  0.0278 0.0042 0.0029
## 2      0.4552  2.7656      0.0068  0.9671 0.0061 0.0051
## 3      0.0385  9.5082      0.4726  0.0051 0.8161 0.0169
## 4      0.0247 11.8678      0.5170  0.0000 0.1737 0.9750
## 
## ===============================
## Row 2==> lotsize, proportion 0.967080 >= 0.50 
## Row 3==> sqrft, proportion 0.816079 >= 0.50 
## Row 4==> bdrms, proportion 0.975026 >= 0.50

#Prueba FG con libreria

library(psych)
## Warning: package 'psych' was built under R version 4.3.2
FG <- cortest.bartlett(matrizX[,-1])
## R was not square, finding R from data
print(FG)
## $chisq
## [1] 31.38122
## 
## $p.value
## [1] 7.065806e-07
## 
## $df
## [1] 3
library(fastGraph)
## Warning: package 'fastGraph' was built under R version 4.3.3
vC_1 <-qchisq(0.05, FG$df, lower.tail = FALSE)

#Prueba FG a paso

library(fastGraph)

m <- ncol(matrizX[,-1])
n <- nrow(matrizX)
Determinante_R <- det(cor(matrizX[,- 1]))
Chi_FG <- -(n-1 - (2*m + 5)/6)*log(Determinante_R)
print(Chi_FG)
## [1] 31.38122
#Valor critico
gl<- m*(m-1)/2
Vc<- qchisq(0.05,gl, lower.tail = FALSE)

#Graficar FG
shadeDist(xshade = Chi_FG, ddist = "dchisq", parm1 = gl, lower.tail = FALSE, sub = paste("VC:", Vc))

b) Factores inflacionarios de la varianza, presente sus resultados de forma tabular y de forma gráfica.

#VIF manual

VIFmanual <- diag(solve(cor(matrizX[,-1])))
print(VIFmanual)
##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663

#VIF libreria car

library(car)
## Warning: package 'car' was built under R version 4.3.2
## Loading required package: carData
## 
## Attaching package: 'car'
## The following object is masked from 'package:psych':
## 
##     logit
VIF <- vif(modelo_estimado)
print(VIF)
##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663

#VIF con libreria mctest (FORMA GRAFICA)

library(mctest)
mc.plot(modelo_estimado, vif = 2)