Ejercicios-MCO-R.R

#Ejercicio 1
options(scipen=999999999)
#Creando matriz xx
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

#Creando matriz xy
matriz_xy<-matrix(data = c(55331,
                           12524626,
                           4374490),nrow = 3,ncol=1)
matriz_xy

##          [,1]
## [1,]    55331
## [2,] 12524626
## [3,]  4374490

inver_matriz_xx<-solve(matriz_xx)
print(inver_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

beta<-inver_matriz_xx%*%matriz_xy
beta

##             [,1]
## [1,] -45.8830775
## [2,]  12.5399333
## [3,]  -0.5104348

#ejercicio 2
options(scipen = 999999999)
#creando matriz xx
matriz_xx<-matrix(data =c(26,5857,131,
                          5857,1675143,28173,
                          131,28173,869),nrow=3,ncol=3,byrow = TRUE)
#creando matriz xy
matriz_xx

##      [,1]    [,2]  [,3]
## [1,]   26    5857   131
## [2,] 5857 1675143 28173
## [3,]  131   28173   869

matriz_xy<-matrix(data=c(1181,
                         298629,
                         6068),nrow=3,ncol=1,byrow=TRUE)
matriz_xy

##        [,1]
## [1,]   1181
## [2,] 298629
## [3,]   6068

#inversa de matriz xx
inver_matriz_xx<-solve(matriz_xx)
inver_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

beta<-inver_matriz_xx%*%matriz_xy
beta

##             [,1]
## [1,] 17.86018879
## [2,]  0.09602564
## [3,]  1.17719778