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
modelo_precio<-lm(formula = price~lotsize+sqrft+bdrms, data=hprice1)
summary(modelo_precio)
## 
## Call:
## lm(formula = price ~ lotsize + sqrft + bdrms, data = hprice1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -120.026  -38.530   -6.555   32.323  209.376 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -2.177e+01  2.948e+01  -0.739  0.46221    
## lotsize      2.068e-03  6.421e-04   3.220  0.00182 ** 
## sqrft        1.228e-01  1.324e-02   9.275 1.66e-14 ***
## bdrms        1.385e+01  9.010e+00   1.537  0.12795    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 59.83 on 84 degrees of freedom
## Multiple R-squared:  0.6724, Adjusted R-squared:  0.6607 
## F-statistic: 57.46 on 3 and 84 DF,  p-value: < 2.2e-16
options(scipen = 99999)
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
library(fastGraph)
X<-model.matrix(modelo_precio)
stargazer(head(X,n=5),type = "text",align=FALSE,no.space=FALSE)
## 
## =================================
##   (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  
## ---------------------------------
XX<-t(X)%*%X
stargazer(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  
## --------------------------------------------------------------
library (stargazer)
options (scipen = 99999)
Sn<-solve(diag(sqrt(diag(XX))))
stargazer(Sn,type="text")
## 
## ==========================
## 0.107    0      0      0  
## 0     0.00001   0      0  
## 0        0    0.0001   0  
## 0        0      0    0.029
## --------------------------
XX_norm<-(Sn%*%XX)%*%Sn
stargazer(XX_norm,type="text")
## 
## =======================
## 1     0.666 0.962 0.974
## 0.666   1   0.678 0.671
## 0.962 0.678   1   0.970
## 0.974 0.671 0.970   1  
## -----------------------
library(stargazer)
lambdas<-eigen(XX,symmetric = TRUE)
stargazer(lambdas$values,type="text")
## 
## ===============================================
## 16,344,612,181.000 206,368,583.000 73.019 3.974
## -----------------------------------------------
K<-sqrt(max(lambdas$values)/(lambdas$values))
print(K)
## [1]     1.000000     8.899498 14961.305923 64134.107095
library(stargazer)
Zn<-scale(X[,-1])
stargazer(head(Zn,n=5),type="text")
## 
## =======================
##   lotsize sqrft  bdrms 
## -----------------------
## 1 -0.284  0.735  0.513 
## 2  0.087  0.108  -0.675
## 3 -0.375  -1.108 -0.675
## 4 -0.434  -0.980 -0.675
## 5 -0.287  0.867  0.513 
## -----------------------
library(stargazer)
n<-nrow(Zn)
R<-(t(Zn)%*%Zn)*(1/(n-1))
stargazer(R,digits = 4,type="text")
## 
## =============================
##         lotsize sqrft  bdrms 
## -----------------------------
## lotsize    1    0.1838 0.1363
## sqrft   0.1838    1    0.5315
## bdrms   0.1363  0.5315   1   
## -----------------------------
det_R<-det(R)
print(det_R)
## [1] 0.6917931
m<-ncol(X[,-1])
n<-nrow(X[,-1])
chi_FG<--(n-1-(2*m+5)/6)*log(det_R)
print(chi_FG)
## [1] 31.38122
gl<-m*(m-1)/2
VC<-qchisq(p=0.95,df=gl)
print(VC)
## [1] 7.814728
library(fastGraph)
shadeDist(xshade = chi_FG ,ddist = "dchisq", parm1 = gl, lower.tail = FALSE,col=c("black","magenta"), sub = paste("VC: ", VC,   "FG: ", chi_FG) )

#Hay evidencia de que hay multicolinealidad entre las variables #Factores inflacionarios de la varianza.

IR<-solve(R)
print(IR)
##             lotsize      sqrft       bdrms
## lotsize  1.03721145 -0.1610145 -0.05582352
## sqrft   -0.16101454  1.4186543 -0.73202696
## bdrms   -0.05582352 -0.7320270  1.39666321
VIF<-diag(IR)
print(VIF)
##  lotsize    sqrft    bdrms 
## 1.037211 1.418654 1.396663