Ejercicio #1
Matriz X’X
options(scipen = 99999999)
matriz_xx<-matrix(data = c(25,4586, 2018,
4586, 1030398, 364545,
2018, 364545, 204312),nrow = 3,ncol = 3,byrow = TRUE)
print(matriz_xx)
## [,1] [,2] [,3]
## [1,] 25 4586 2018
## [2,] 4586 1030398 364545
## [3,] 2018 364545 204312
Matriz X’Y
matriz_xy<-matrix(data=c(55331,
12524626,
4374490), nrow = 3,ncol = 1,byrow = TRUE)
print(matriz_xy)
## [,1]
## [1,] 55331
## [2,] 12524626
## [3,] 4374490
Inversa de X’X
inv_matriz_xx<-solve(matriz_xx)
print(inv_matriz_xx)
## [,1] [,2] [,3]
## [1,] 0.397982654 -0.0010321198463 -0.0020893284104
## [2,] -0.001032120 0.0000053085599 0.0000007224679
## [3,] -0.002089328 0.0000007224679 0.0000242418099
Estimador de parametros β
beta<-inv_matriz_xx%*%matriz_xy
print(beta)
## [,1]
## [1,] -45.8830775
## [2,] 12.5399333
## [3,] -0.5104348
Ejercico #2
Matriz X’X
options(scipen = 99999999)
matriz_xx<-matrix(data = c(26, 5857, 131,
5857, 1675143, 28173,
131, 28173, 869), nrow = 3, ncol = 3, byrow = TRUE)
print(matriz_xx)
## [,1] [,2] [,3]
## [1,] 26 5857 131
## [2,] 5857 1675143 28173
## [3,] 131 28173 869
Matriz X’Y
matriz_xy<-matrix(data = c(1181,
298629,
6068), nrow = 3, ncol = 1, byrow = TRUE)
print(matriz_xy)
## [,1]
## [1,] 1181
## [2,] 298629
## [3,] 6068
Inversa de X’X
inv_matriz_xx<-solve(matriz_xx)
print(inv_matriz_xx)
## [,1] [,2] [,3]
## [1,] 0.3509517581 -0.000741721931 -0.02885862872
## [2,] -0.0007417219 0.000002880324 0.00001843291
## [3,] -0.0288586287 0.000018432909 0.00490353282
Estimador de parámetros β
beta2<-inv_matriz_xx%*%matriz_xy
print(beta2)
## [,1]
## [1,] 17.86018879
## [2,] 0.09602564
## [3,] 1.17719778