#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. estimación del modelo

library(stargazer)
modelo_E<-lm(formula = price~lotsize+sqrft+bdrms, data = hprice1)
stargazer(modelo_E, title = 'Estimación del moodelo',type = 'text')
## 
## Estimación del moodelo
## ===============================================
##                         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)

##2.1 calculo de matriz (X’X)

library(stargazer)
matriz_X<-model.matrix(modelo_E)
stargazer(head(matriz_X,n=6),type="text")
## 
## =================================
##   (Intercept) lotsize sqrft bdrms
## ---------------------------------
## 1      1       6,126  2,438   4  
## 2      1       9,903  2,076   3  
## 3      1       5,200  1,374   3  
## 4      1       4,600  1,448   3  
## 5      1       6,095  2,514   4  
## 6      1       8,566  2,754   5  
## ---------------------------------
matriz_XX<-t(matriz_X)%*%matriz_X
stargazer(matriz_XX,type = "text")
## 
## ==============================================================
##             (Intercept)    lotsize         sqrft       bdrms  
## --------------------------------------------------------------
## (Intercept)     88         793,748        177,205       314   
## lotsize       793,748   16,165,159,010 1,692,290,257 2,933,767
## sqrft         177,205   1,692,290,257   385,820,561   654,755 
## bdrms           314       2,933,767       654,755      1,182  
## --------------------------------------------------------------

##2.2 matriz Sn

library(stargazer)
options(scipen = 999)
Sn<-solve(diag(sqrt(diag(matriz_XX))))
stargazer(Sn,type = "text",title = 'Sn')
## 
## Sn
## ==========================
## 0.107    0      0      0  
## 0     0.00001   0      0  
## 0        0    0.0001   0  
## 0        0      0    0.029
## --------------------------

##2.2 matriz (X’X) normalizada

library(stargazer)
nor_XX<-(Sn%*%matriz_XX)%*%Sn
stargazer(nor_XX,type = "text",digits = 4)
## 
## ===========================
## 1      0.6655 0.9617 0.9736
## 0.6655   1    0.6776 0.6712
## 0.9617 0.6776   1    0.9696
## 0.9736 0.6712 0.9696   1   
## ---------------------------

a) Indice de condición

Autovalores de matriz (X’X) normalizada

library(stargazer)

Lambdas<-eigen(nor_XX,symmetric = TRUE)
stargazer(Lambdas$values,type = "text", title = "Lambdas")
## 
## Lambdas
## =======================
## 3.482 0.455 0.039 0.025
## -----------------------

Indice de condición

K<-sqrt(max(Lambdas$values)/min(Lambdas$values))
print(K)
## [1] 11.86778

El índice de condición es 11.86778 lo que nos dice que la multolinealidad es leve y no se debe considerar un problema.

Obtencion del indice de condición usando la libreria (mctest)

library(mctest) 
eigprop(mod = modelo_E)
## 
## Call:
## eigprop(mod = modelo_E)
## 
##   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 Farrar-Glaubar

m<-ncol(matriz_X[,-1]) # cantidad de variables explicativas k-1
n<-nrow(matriz_X)
determinante_R<- det(cor(matriz_X[,-1])) # determinanre de la matriz de correlacion
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)
print(VC)
## [1] 7.814728

#Prueba de Farrar-Glaubar Uso de la libreria psych

library(psych)
library(fastGraph)
FG_test<-cortest.bartlett(matriz_X[,-1])
VC_1<-qchisq(0.05,FG_test$df,lower.tail = FALSE)
print(FG_test)
## $chisq
## [1] 31.38122
## 
## $p.value
## [1] 0.0000007065806
## 
## $df
## [1] 3
library(fastGraph)
shadeDist(xshade = chi_FG,ddist = "dchisq",parm1 = gl,lower.tail = FALSE,sub=paste("VC:",VC,"FG:",chi_FG))

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

Uso de la librería (car) y “mctest”

library(car)
VIFs<-vif(modelo_E)
print(VIFs)
##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663

Uso de la librería (mctest)

library(mctest)
mc.plot(modelo_E,vif = 3)