Ejercicios MCO

## Ejercicio 1
## 1. Generando la matriz X'X
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

## 2. Generando la matriz X'Y
matriz_xy<-matrix(data = c(55331,12524626,4774490),nrow = 3,ncol = 1,byrow = TRUE)
print(matriz_xy)

##          [,1]
## [1,]    55331
## [2,] 12524626
## [3,]  4774490

## 3. Calculando la inversa de X'X
inv_matriz_xx<-solve(matriz_xx)
print(inv_matriz_xx)

##              [,1]          [,2]          [,3]
## [1,]  0.397982654 -1.032120e-03 -2.089328e-03
## [2,] -0.001032120  5.308560e-06  7.224679e-07
## [3,] -0.002089328  7.224679e-07  2.424181e-05

## 4. Calculando el estimador de parametros B
beta<-inv_matriz_xx%*%matriz_xy
print(beta)

##             [,1]
## [1,] -881.614442
## [2,]   12.828921
## [3,]    9.186289

## Ejercicio 2
## 1. Generando la matriz X'X
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

## 2. Generando la 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

## 3. Calculando la inversa de X'X
inv_matriz_xx<-solve(matriz_xx)
print(inv_matriz_xx)

##               [,1]          [,2]          [,3]
## [1,]  0.3509517581 -7.417219e-04 -2.885863e-02
## [2,] -0.0007417219  2.880324e-06  1.843291e-05
## [3,] -0.0288586287  1.843291e-05  4.903533e-03

## 4. Calculando el estimador de parametros B
beta<-inv_matriz_xx%*%matriz_xy
print(beta)

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