Carga de Datos

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

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

options(scipen = 9999)
library(stargazer)
modelo.price <- lm(formula = price~lotsize+sqrft+bdrms,data = hprice1)
stargazer(modelo.price,title = "Modelo Price", type = "html")
Modelo Price
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 través de:

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

Indice de Condición Manual

# Cálculo Manual
#Matriz X
x_mat<-model.matrix(modelo.price)
#Sigma Matriz
xx_mat<-t(x_mat)%*%x_mat
print(xx_mat)
##             (Intercept)     lotsize      sqrft   bdrms
## (Intercept)          88      793748     177205     314
## lotsize          793748 16165159010 1692290257 2933767
## sqrft            177205  1692290257  385820561  654755
## bdrms               314     2933767     654755    1182
#Construccion de Sn
Sn<-solve(diag(sqrt(diag(xx_mat))))
print(Sn)
##           [,1]           [,2]          [,3]       [,4]
## [1,] 0.1066004 0.000000000000 0.00000000000 0.00000000
## [2,] 0.0000000 0.000007865204 0.00000000000 0.00000000
## [3,] 0.0000000 0.000000000000 0.00005091049 0.00000000
## [4,] 0.0000000 0.000000000000 0.00000000000 0.02908649
#Sn normalizada
xx_mat.norm<-(Sn%*%xx_mat)%*%Sn
print(xx_mat.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
#Atovalores
lambdas<-eigen(xx_mat.norm,symmetric = TRUE)$values
print(lambdas)
## [1] 3.48158596 0.45518380 0.03851083 0.02471941
#Indice de Condicion
k<-sqrt(max(lambdas)/min(lambdas))
print(k)
## [1] 11.86778

Indice de condición con McTest

library(mctest)
mctest(modelo.price)
## 
## Call:
## omcdiag(mod = mod, Inter = TRUE, detr = detr, red = red, conf = conf, 
##     theil = theil, cn = cn)
## 
## 
## Overall Multicollinearity Diagnostics
## 
##                        MC Results detection
## Determinant |X'X|:         0.6918         0
## Farrar Chi-Square:        31.3812         1
## Red Indicator:             0.3341         0
## Sum of Lambda Inverse:     3.8525         0
## Theil's Method:           -0.7297         0
## Condition Number:         11.8678         0
## 
## 1 --> COLLINEARITY is detected by the test 
## 0 --> COLLINEARITY is not detected by the test

Prueba Farrar Glauber

library(psych)
library(fastGraph)
FG<-cortest.bartlett(x_mat[,-1])
print(FG)
## $chisq
## [1] 31.38122
## 
## $p.value
## [1] 0.0000007065806
## 
## $df
## [1] 3
vc<-qchisq(0.05,FG$df,lower.tail = FALSE)
shadeDist(xshade = FG$chisq,
          ddist = "dchisq",
          parm1 = FG$df,
          lower.tail = FALSE,
          sub=paste("VC:",vc,"FG:",FG$chisq))

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

#VIF de forma tabular
library(car)
VIF<-vif(modelo.price)
print(VIF)
##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663
#VIF de forma gráfica
library(mctest)
mc.plot(modelo.price,vif = 2)