Importacion 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. Estimacion del Modelo

modelo_estimado<-lm(formula = price~lotsize+sqrft+bdrms,data = hprice1)
stargazer::stargazer(modelo_estimado,type = "text",title = "Modelo Estimado")
## 
## 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. Verificar si hay evidencia de la independencia de los regresores

a) Indice de condicion y Prueba de FG

Indice de Condicion

library(mctest)
source(file = "D:/DOCUMENTOS EN GENERAL/Econo/Pruebas/correccion_eigprop.R")
my_eigprop(mod = modelo_estimado)
## 
## Call:
## my_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

options(scipen = 999999999)
library(mctest)
mctest(modelo_estimado)
## 
## 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
Xmat<-model.matrix(modelo_estimado)
library(psych)
library(fastGraph)
FG_test<-cortest.bartlett(Xmat[,-1])
vc_2<-qchisq(0.05,FG_test$df,lower.tail = FALSE)
print(FG_test)

$chisq [1] 31.38122

$p.value [1] 0.0000007065806

$df [1] 3

# Prueba FG (forma grafica) utilizando fastGraph
shadeDist(xshade = FG_test$chisq,ddist = "dchisq",parm1 = FG_test$df,lower.tail = FALSE,sub=paste("VC:",vc_2,"FG:",FG_test$chisq))

Hay evidencia estadistica de no rechazar la hipotesis nula ya que el P value es mayor que el nivel de significancia, por lo tanto nuestro modelo presenta evidencia de no Multicolinealidad.

b) Factores Inflacionarios de la Varianza

library(car)
VIF_car<-vif(modelo_estimado)
print(VIF_car)
##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663
library(mctest)
mc.plot(modelo_estimado,vif = 2)