Literal a) calculo de residuos

options(scipen = 9999999)
load("C:/Users/miguel/Desktop/Economia/Econometria/R studio/Ejercicios/consumption_equation.RData")
n<-nrow(P)
M<-diag(n)-P
residuos<-M%*%C
print(residuos)
##          [,1]
## 1   -5.859103
## 2    2.605057
## 3   45.765735
## 4   31.102448
## 5  -21.037889
## 6    7.008120
## 7   17.859663
## 8   10.705631
## 9   22.002328
## 10  -2.689665
## 11   7.784083
## 12 -13.127696
## 13  17.521565
## 14  17.304695
## 15 -16.308260
## 16  -5.255508
## 17   2.788211
## 18 -16.379339
## 19 -14.327554
## 20  11.749135
## 21 -31.424669
## 22 -23.329596
## 23  22.171806
## 24  -5.040038
## 25 -36.191398
## 26 -25.211753
## 27 -21.411271
## 28   1.410519
## 29 -24.229564
## 30  20.971808
## 31  43.342653
## 32  36.808458
## 33  17.882297
## 34 -33.100273
## 35 -37.819995
## 36 -49.370820
## 37  23.456143
## 38 -25.510341
## 39 -11.960629
## 40  -9.234201
## 41  21.949616
## 42   3.211123
## 43 -14.511436
## 44   3.197576
## 45 -62.396763
## 46 -66.854500
## 47   8.330745
## 48  91.963380
## 49  61.620735
## 50  48.148861
## 51 -10.717721
## 52 -84.069717
## 53 -56.426627
## 54 125.113605

Literal b) lcalculo de la varianza del error

#Sigma cuadrado
k<-4
var_error=t(residuos)%*%residuos/(n-k)
print(var_error)
##          [,1]
## [1,] 1428.746

Literal c) Matriz de Var-Cov

var_error<-as.vector(var_error)
var.cov<-var_error*solve(XX)
print(var.cov)
##               (Intercept)             Yd               W             I
## (Intercept) 164.522304918 -0.09333539523  0.009670913575 10.5186890800
## Yd           -0.093335395  0.00018911268 -0.000032769561 -0.0072901023
## W             0.009670914 -0.00003276956  0.000006165749  0.0004193421
## I            10.518689080 -0.00729010228  0.000419342092  5.3203789879

Literal d) Calculo de las estimaciones

C_estimada<-P%*%C
cuadro<-as.data.frame(cbind(C,C_estimada,residuos))
names(cuadro)<-c("C","C_estimada","Residuos")
print(head(cuadro))
##        C C_estimada   Residuos
## 1  976.4   982.2591  -5.859103
## 2  998.1   995.4949   2.605057
## 3 1025.3   979.5343  45.765735
## 4 1090.9  1059.7976  31.102448
## 5 1107.1  1128.1379 -21.037889
## 6 1142.4  1135.3919   7.008120