1) Estimando el modelo
library(stargazer)
modelo_estimado<-lm(price~lotsize+sqrft+bdrms,data = hprice1)
stargazer(modelo_estimado,type = "html",title = "Modelo Estimado")
Modelo Estimado
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Dependent variable:
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price
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lotsize
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0.002***
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(0.001)
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sqrft
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0.123***
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(0.013)
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bdrms
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13.853
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(9.010)
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Constant
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-21.770
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(29.475)
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Observations
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88
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R2
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0.672
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Adjusted R2
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0.661
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Residual Std. Error
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59.833 (df = 84)
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F Statistic
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57.460*** (df = 3; 84)
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Note:
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p<0.1; p<0.05;
p<0.01
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2) Verificando si hay evidencia de la independencia de los
regresores(no colinealidad)
Indice de Condición
library(stargazer)
X_mat<-model.matrix(modelo_estimado)
stargazer(head(X_mat,n=5),type = "html")
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(Intercept)
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lotsize
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sqrft
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bdrms
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1
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1
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6,126
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2,438
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4
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2
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1
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9,903
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2,076
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3
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3
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1
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5,200
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1,374
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3
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4
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1
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4,600
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1,448
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3
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5
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1
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6,095
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2,514
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4
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XX_matrix<-t(X_mat)%*%X_mat
stargazer(XX_matrix,type = "html")
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(Intercept)
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lotsize
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sqrft
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bdrms
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(Intercept)
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88
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793,748
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177,205
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314
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lotsize
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793,748
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16,165,159,010
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1,692,290,257
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2,933,767
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sqrft
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177,205
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1,692,290,257
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385,820,561
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654,755
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bdrms
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314
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2,933,767
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654,755
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1,182
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Cálculo de la matriz de normalización
options(scipen = 999)
library(stargazer)
Sn<-solve(diag(sqrt(diag(XX_matrix))))
stargazer(Sn,type = "html")
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0.107
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0
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0
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0
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0
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0.00001
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0
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0
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0
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0
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0.0001
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0
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0
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0
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0
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0.029
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library(stargazer)
XX_norm<-(Sn%*%XX_matrix)%*%Sn
stargazer(XX_norm,type = "html",digits = 4)
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1
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0.6655
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0.9617
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0.9736
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0.6655
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1
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0.6776
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0.6712
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0.9617
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0.6776
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1
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0.9696
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0.9736
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0.6712
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0.9696
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1
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library(stargazer)
#autovalores
lambdas<-eigen(XX_norm,symmetric = TRUE)
stargazer(lambdas$values,type = "html")
Cálculo de k(x)
k<-sqrt(max(lambdas$values)/min(lambdas$values))
print(k)
## [1] 11.86778
R/ La multicolinealidad es leve porque k(x)=11.86778 es decir, que es
inferior a 20, por tanto no se considera un problema.
Prueba de Farrar-Glaubar
Cálculo de |R|
library(stargazer)
Zn<-scale(X_mat[,-1])
stargazer(head(Zn,n=5),type = "html")
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lotsize
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sqrft
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bdrms
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1
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-0.284
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0.735
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0.513
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2
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0.087
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0.108
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-0.675
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3
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-0.375
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-1.108
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-0.675
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4
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-0.434
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-0.980
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-0.675
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5
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-0.287
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0.867
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0.513
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Cálculo de la matriz R
library(stargazer)
n<-nrow(Zn)
R<-(t(Zn)%*%Zn)*(1/(n-1))
stargazer(R,type = "html",digits = 4)
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lotsize
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sqrft
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bdrms
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lotsize
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1
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0.1838
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0.1363
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sqrft
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0.1838
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1
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0.5315
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bdrms
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0.1363
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0.5315
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1
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Cálculo de |R|
determinante_R<-det(R)
print(determinante_R)
## [1] 0.6917931
Aplicando la prueba de Farrer Glaubar
m<-ncol(X_mat[,-1])
n<-nrow(X_mat[,-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(p=0.95,df=gl)
print(VC)
## [1] 7.814728
R/ Se rechaza la Hipótesis nula dado que 31.38122>7.814728, por lo
tanto hay evidencia de multicolinealidad en los regresores.
Factores Inflacionarios de la Varianza (FIV)
library(performance)
VIFs<-multicollinearity(x = modelo_estimado,verbose=FALSE)
VIFs
## # Check for Multicollinearity
##
## Low Correlation
##
## Term VIF VIF 95% CI Increased SE Tolerance Tolerance 95% CI
## lotsize 1.04 [1.00, 11.02] 1.02 0.96 [0.09, 1.00]
## sqrft 1.42 [1.18, 1.98] 1.19 0.70 [0.51, 0.85]
## bdrms 1.40 [1.17, 1.95] 1.18 0.72 [0.51, 0.86]
R/ No hay multicolinealidad en las variables explicativas.
