Guía de ejercicios MCO
Miguel Ángel López Ayala
2026-03-10
Ejercicio 1
##numeral 1
options(scipen=9999)
load("C:/Users/MINEDUCYT/Downloads/modelo_ventas.RData")
# obtener la matrix X
matriz_X <- model.matrix(modelo_ventas)
#matrix XX
matriz_XX <- t(matriz_X)%*%matriz_X
#matriz A
matriz_A <- solve(matriz_XX)%*%t(matriz_X)
#matriz P
matriz_P <- matriz_X%*%matriz_A
#matriz M
#conocer numero de filas
n<-nrow(matriz_X)
#hacer la matriz M
matriz_M <-diag(n) - matriz_PNumeral 2
#residuos del modelo (objeto 1)
residuos_modelo_ventas <- modelo_ventas$residuals
datos_modelo <-modelo_ventas$model
#residuos matriz (objeto 2)
residuos_matrices <- matriz_M%*%datos_modelo$ventas
#verificar
cbind(residuos_modelo_ventas,residuos_matrices,residuos_modelo_ventas-residuos_matrices) |> round(digits = 2) |> as.data.frame()-> comparacion
#agrgar nombre
names(comparacion) <- c("por matrices","En modelo","Diferencia")
comparacion## por matrices En modelo Diferencia
## 1 -15.93 -15.93 0
## 2 19.33 19.33 0
## 3 38.02 38.02 0
## 4 -15.43 -15.43 0
## 5 5.16 5.16 0
## 6 80.22 80.22 0
## 7 -16.35 -16.35 0
## 8 -22.89 -22.89 0
## 9 -34.40 -34.40 0
## 10 46.09 46.09 0
## 11 -40.56 -40.56 0
## 12 9.25 9.25 0
## 13 5.82 5.82 0
## 14 -19.64 -19.64 0
## 15 -2.74 -2.74 0
## 16 -20.58 -20.58 0
## 17 -4.89 -4.89 0
## 18 -0.83 -0.83 0
## 19 -36.61 -36.61 0
## 20 -8.11 -8.11 0
## 21 11.00 11.00 0
## 22 56.50 56.50 0
## 23 -7.55 -7.55 0
## 24 31.71 31.71 0
## 25 -40.48 -40.48 0
## 26 86.80 86.80 0
## 27 -1.44 -1.44 0
## 28 35.92 35.92 0
## 29 24.51 24.51 0
## 30 -38.94 -38.94 0
## 31 25.44 25.44 0
## 32 -17.24 -17.24 0
## 33 -44.11 -44.11 0
## 34 47.62 47.62 0
## 35 -38.06 -38.06 0
## 36 104.56 104.56 0
## 37 -22.01 -22.01 0
## 38 6.26 6.26 0
## 39 -20.85 -20.85 0
## 40 -8.14 -8.14 0
## 41 3.52 3.52 0
## 42 7.13 7.13 0
## 43 39.33 39.33 0
## 44 29.22 29.22 0
## 45 -13.40 -13.40 0
## 46 8.21 8.21 0
## 47 -42.24 -42.24 0
## 48 -15.16 -15.16 0
## 49 36.15 36.15 0
## 50 -42.33 -42.33 0
## 51 29.60 29.60 0
## 52 -27.94 -27.94 0
## 53 -25.78 -25.78 0
## 54 -16.15 -16.15 0
## 55 20.52 20.52 0
## 56 -34.10 -34.10 0
## 57 32.84 32.84 0
## 58 -8.84 -8.84 0
## 59 -25.90 -25.90 0
## 60 4.38 4.38 0
## 61 -56.13 -56.13 0
## 62 -5.97 -5.97 0
## 63 34.06 34.06 0
## 64 -22.00 -22.00 0
## 65 -22.92 -22.92 0
## 66 -33.91 -33.91 0
## 67 -25.98 -25.98 0
## 68 -24.10 -24.10 0
## 69 15.18 15.18 0
## 70 -12.96 -12.96 0
## 71 -2.78 -2.78 0
## 72 -39.34 -39.34 0
## 73 9.10 9.10 0
## 74 -23.58 -23.58 0
## 75 16.53 16.53 0
## 76 41.92 41.92 0
## 77 -61.13 -61.13 0
## 78 -11.80 -11.80 0
## 79 42.30 42.30 0
## 80 -28.28 -28.28 0
## 81 -18.10 -18.10 0
## 82 55.90 55.90 0
## 83 -32.84 -32.84 0
## 84 1.99 1.99 0
## 85 -7.85 -7.85 0
## 86 2.06 2.06 0
## 87 -18.80 -18.80 0
## 88 -12.42 -12.42 0
## 89 -34.44 -34.44 0
## 90 -0.71 -0.71 0
## 91 -19.86 -19.86 0
## 92 -71.04 -71.04 0
## 93 5.47 5.47 0
## 94 -1.83 -1.83 0
## 95 -22.68 -22.68 0
## 96 -9.60 -9.60 0
## 97 30.46 30.46 0
## 98 2.80 2.80 0
## 99 -1.39 -1.39 0
## 100 -6.92 -6.92 0
## 101 47.13 47.13 0
## 102 13.67 13.67 0
## 103 74.24 74.24 0
## 104 8.29 8.29 0
## 105 5.20 5.20 0
## 106 -23.16 -23.16 0
## 107 -39.16 -39.16 0
## 108 -36.55 -36.55 0
## 109 -51.39 -51.39 0
## 110 14.93 14.93 0
## 111 31.77 31.77 0
## 112 0.85 0.85 0
## 113 3.55 3.55 0
## 114 20.05 20.05 0
## 115 1.25 1.25 0
## 116 -6.04 -6.04 0
## 117 -5.24 -5.24 0
## 118 -59.49 -59.49 0
## 119 -9.08 -9.08 0
## 120 -15.33 -15.33 0
## 121 -22.74 -22.74 0
## 122 -6.98 -6.98 0
## 123 52.60 52.60 0
## 124 -7.38 -7.38 0
## 125 6.99 6.99 0
## 126 -36.29 -36.29 0
## 127 51.55 51.55 0
## 128 -45.71 -45.71 0
## 129 -38.99 -38.99 0
## 130 -49.74 -49.74 0
## 131 137.77 137.77 0
## 132 68.15 68.15 0
## 133 29.49 29.49 0
## 134 4.04 4.04 0
## 135 2.44 2.44 0
## 136 24.96 24.96 0
## 137 14.83 14.83 0
## 138 18.65 18.65 0
## 139 -13.45 -13.45 0
## 140 -17.13 -17.13 0
## 141 -36.00 -36.00 0
## 142 -7.79 -7.79 0
## 143 -5.46 -5.46 0
## 144 -38.02 -38.02 0
## 145 -33.90 -33.90 0
## 146 -7.02 -7.02 0
## 147 57.02 57.02 0
## 148 -24.42 -24.42 0
## 149 5.76 5.76 0
## 150 -21.33 -21.33 0
## 151 60.96 60.96 0
## 152 -37.40 -37.40 0
## 153 3.70 3.70 0
## 154 -11.53 -11.53 0
## 155 5.57 5.57 0
## 156 20.34 20.34 0
## 157 -6.39 -6.39 0
## 158 0.10 0.10 0
## 159 35.21 35.21 0
## 160 -12.86 -12.86 0
## 161 -0.28 -0.28 0
## 162 -5.49 -5.49 0
## 163 7.07 7.07 0
## 164 -11.48 -11.48 0
## 165 -17.07 -17.07 0
## 166 43.48 43.48 0
## 167 30.49 30.49 0
## 168 32.76 32.76 0
## 169 9.33 9.33 0
## 170 79.25 79.25 0
## 171 -32.15 -32.15 0
## 172 -2.32 -2.32 0
## 173 -19.07 -19.07 0
## 174 11.45 11.45 0
## 175 56.81 56.81 0
## 176 -20.90 -20.90 0
## 177 10.72 10.72 0
## 178 10.72 10.72 0
## 179 99.16 99.16 0
## 180 0.68 0.68 0
## 181 8.07 8.07 0
## 182 43.24 43.24 0
## 183 -53.93 -53.93 0
## 184 -14.41 -14.41 0
## 185 33.06 33.06 0
## 186 -26.80 -26.80 0
## 187 -11.78 -11.78 0
## 188 2.02 2.02 0
## 189 75.55 75.55 0
## 190 -31.29 -31.29 0
## 191 11.46 11.46 0
## 192 -34.64 -34.64 0
## 193 -47.21 -47.21 0
## 194 -20.94 -20.94 0
## 195 -16.29 -16.29 0
## 196 -54.55 -54.55 0
## 197 -31.98 -31.98 0
## 198 8.34 8.34 0
## 199 -9.58 -9.58 0
## 200 49.59 49.59 0numeral 3
eigen(x = matriz_XX, symmetric = TRUE) -> descomposicion
auto_valores <- descomposicion$values
print(auto_valores)## [1] 311421698.6388 70252.5341 40973.4590 3714.3627 12.7735print(auto_valores > 0)## [1] TRUE TRUE TRUE TRUE TRUE#Ejercicio 2 Literal 1
load("C:/Users/MINEDUCYT/Downloads/datos_cajas.RData")
modelo_cajas <-lm(formula = Tiempo ~ Distancia+N_cajas, data= datos_cajas)
summary(modelo_cajas)##
## Call:
## lm(formula = Tiempo ~ Distancia + N_cajas, data = datos_cajas)
##
## Residuals:
## Min 1Q Median 3Q Max
## -9.2716 -0.5405 0.5212 1.4051 2.9381
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.3112 5.8573 0.395 0.70007
## Distancia 0.4559 0.1468 3.107 0.00908 **
## N_cajas 0.8772 0.1530 5.732 0.0000943 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 3.141 on 12 degrees of freedom
## Multiple R-squared: 0.7368, Adjusted R-squared: 0.6929
## F-statistic: 16.8 on 2 and 12 DF, p-value: 0.0003325Numeral 2
#matriz X
matriz_X2 <- model.matrix(modelo_cajas)
#matriz XX
matriz_XX2 <-t(matriz_X2)%*%matriz_X2
#Matriz A
matriz_A2 <- solve(matriz_XX2)%*%t(matriz_X2)
#Matriz P
Matriz_P2 <- matriz_X2%*%matriz_A2 #alternativamente se puede matriz_P2<-matriz_X%*%solve(matriz_XX)%*%t(matriz_X)
#matriz M
n2 <-nrow(matriz_X2)
matriz_M2 <- diag(n2)-Matriz_P2numeral 3
library(matlib)## Warning: package 'matlib' was built under R version 4.5.2#residuos del modelo
residuos_modelo2 <-modelo_cajas$residuals
matriz_y <-datos_cajas$Tiempo
#residuos de la matriz
residuos_por_matrices2 <-matriz_M2%*%matriz_y
# unir columnas (comparativa)
cbind(residuos_modelo2,
residuos_por_matrices2,
residuos_por_matrices2-residuos_por_matrices2) |> as.data.frame() |> round(digits=2) ->comparativa2
names(comparativa2) <- c("residuos modelo",
"residuos matrices",
"diferencia")
print(comparativa2)## residuos modelo residuos matrices diferencia
## 1 -0.76 -0.76 0
## 2 0.13 0.13 0
## 3 -0.32 -0.32 0
## 4 2.94 2.94 0
## 5 -9.27 -9.27 0
## 6 0.77 0.77 0
## 7 1.31 1.31 0
## 8 -2.09 -2.09 0
## 9 1.43 1.43 0
## 10 0.52 0.52 0
## 11 0.52 0.52 0
## 12 1.38 1.38 0
## 13 -1.02 -1.02 0
## 14 2.89 2.89 0
## 15 1.59 1.59 0literal 4
#verificar autovalores
descomposicion2 <-eigen (matriz_XX2)
autovalores2 <-descomposicion2$values
#visualizarlo
print(autovalores2)## [1] 16976.7781334 709.9345923 0.2872743#otra forma de verlo
print(autovalores2>0)## [1] TRUE TRUE TRUE#Ejercicio 3 Calcule las matrices A, P, M
load("C:/Users/MINEDUCYT/Downloads/modelo_estimado.RData")
#calcular X
Matriz_X3 <- model.matrix(modelo_estimado_1)
#calcular XX
matrix_xx3 <- t(Matriz_X3) %*% Matriz_X3
# Calcular A
matriz_a3 <- solve(matrix_xx3) %*% t(Matriz_X3)
# Calcular P
matriz_p3 <- Matriz_X3 %*% matriz_a3
#Calcular M
n3 <- diag(matriz_p3)
matriz_m3 <- diag(n3) - matriz_p3Compruebe que los residuos en el objeto “modelo_estimado” son iguales al producto de M*y, donde “y” es la variable endógena en el modelo (“crime”
#residuos del modelo
residuos_modelo3 <- modelo_estimado_1$residuals
# residuos matriz.
datos_modelo3 <-modelo_estimado_1$model
residuos_matriz3 <- matriz_m3 %*% datos_modelo3$crime
#verificar
tabla <- cbind(residuos_modelo3, residuos_matriz3, residuos_modelo3-residuos_matriz3) |> as.data.frame() |> round(digits = 2)
names(tabla) <- c("En modelo", "por matrices", "diferencia")
print(tabla)## En modelo por matrices diferencia
## 1 -311.71 -949.72 638.01
## 2 116.80 -638.65 755.46
## 3 45.25 -501.16 546.41
## 4 -34.45 -733.47 699.03
## 5 243.00 -797.72 1040.72
## 6 -145.12 -677.99 532.88
## 7 86.13 -346.37 432.50
## 8 88.31 -568.16 656.47
## 9 689.82 -457.91 1147.73
## 10 -163.29 -855.69 692.40
## 11 60.90 -184.58 245.48
## 12 126.92 -184.21 311.13
## 13 -19.27 -291.17 271.91
## 14 322.59 -617.47 940.07
## 15 -22.44 -499.88 477.44
## 16 128.18 -353.42 481.61
## 17 -70.82 -492.77 421.94
## 18 -227.95 -1118.51 890.56
## 19 287.10 -491.24 778.34
## 20 303.88 -633.52 937.40
## 21 -341.99 -463.97 121.99
## 22 -107.18 -873.02 765.83
## 23 -30.63 -347.85 317.22
## 24 189.45 -533.79 723.24
## 25 -811.14 -1190.15 379.02
## 26 -351.77 -525.67 173.90
## 27 102.71 -562.66 665.38
## 28 -23.36 -100.62 77.25
## 29 73.38 -252.10 325.47
## 30 -91.63 -223.52 131.89
## 31 324.03 -280.91 604.94
## 32 -115.85 -1002.26 886.40
## 33 113.65 -700.56 814.21
## 34 217.94 -825.60 1043.54
## 35 -112.70 -605.56 492.86
## 36 21.38 -570.84 592.23
## 37 -88.91 -578.01 489.10
## 38 99.42 -304.30 403.72
## 39 -102.65 -493.03 390.38
## 40 217.88 -765.70 983.59
## 41 -84.09 -283.19 199.09
## 42 137.78 -581.71 719.50
## 43 48.89 -690.51 739.40
## 44 -67.16 -358.29 291.13
## 45 -39.29 -396.59 357.31
## 46 -415.78 -525.17 109.38
## 47 -145.50 -645.33 499.83
## 48 -183.61 -441.31 257.71
## 49 -138.39 -309.29 170.90
## 50 -232.91 -512.91 280.00
## 51 434.17 -921.58 1355.75Muestre que los autovalores de x’x son positivos (use el comando eigen)
descomposicion3 <-eigen(matrix_xx3)
autovalores3 <- descomposicion3$values
#visualizar
print(autovalores3)## [1] 17956.580914 279.157317 1.681762print(autovalores3>0)## [1] TRUE TRUE TRUEEjercicio 4
Literal 1
library(readxl)
Investiment_Equation <- read_excel("C:/Users/MINEDUCYT/Downloads/Investiment_Equation.xlsx")
#estimar modelo
ecuacion_inversion <- lm(formula = InvReal ~ Trend + Inflation + PNBr + Interest, data = Investiment_Equation)
#norma apa
library(stargazer)
stargazer(ecuacion_inversion, title = "Ecuación de Inversión", type = "text")##
## Ecuación de Inversión
## ===============================================
## Dependent variable:
## ---------------------------
## InvReal
## -----------------------------------------------
## Trend -0.016***
## (0.002)
##
## Inflation 0.00002
## (0.001)
##
## PNBr 0.665***
## (0.054)
##
## Interest -0.240*
## (0.120)
##
## Constant -0.503***
## (0.054)
##
## -----------------------------------------------
## Observations 15
## R2 0.973
## Adjusted R2 0.962
## Residual Std. Error 0.007 (df = 10)
## F Statistic 90.089*** (df = 4; 10)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Literal 2
#crear matrix X
model.matrix(ecuacion_inversion) -> Mat_X4
#Matriz M
n4 <- nrow(Mat_X4)
Mat_M <- diag(n4)-Mat_X4%*%solve(t(Mat_X4)%*%Mat_X4)%*%t(Mat_X4)
#Residuos
Y4 <-Investiment_Equation$InvReal
Residuos4 <- Mat_M%*%Y4
print(Residuos4)## [,1]
## 1 -0.0100602233
## 2 -0.0009290882
## 3 0.0029656679
## 4 0.0078576839
## 5 0.0028109133
## 6 0.0006259732
## 7 0.0075909286
## 8 -0.0055352778
## 9 -0.0037254127
## 10 0.0006953129
## 11 0.0019904770
## 12 -0.0001288433
## 13 -0.0101976729
## 14 0.0068712384
## 15 -0.0008316770literal 3
#Intervalo de confianza
confint(object = ecuacion_inversion, parm = "PNBr", level = .93)## 3.5 % 96.5 %
## PNBr 0.554777 0.774317Podemos concluir que el 93% de las estimaciones que hacemos el experimento se esperaria que el impacto de 1 un millón en el PNBr, se tradujece en un cambio esperado en un minimo de 0.55477 (millones) y un máximo 0.774317 (millones)
Ejercicio 5
Literal 1
load("C:/Users/MINEDUCYT/Downloads/consumption_equation.RData")
n5 <-nrow(P)
m5 <- diag(n5)-P
#residuos
residuos5 <- m5%*%C
print(residuos5)## [,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
## 54 125.113605Calcular de la varianza del error
#Numero de parametros (mirrar matriz XX)
K5 <- 4
#varianza del error
var_error5=t(residuos5)%*%residuos5/(n5-K5)
print(var_error5)## [,1]
## [1,] 1428.746Matriz de Var-Cov
#varianza covianza
#transformar la varianza del error a vector
var_error_5 <- as.vector(var_error5)
#Varainza por la inversa de XX
Var.cov5 <- var_error_5 * solve(XX)
print(Var.cov5)## (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 5.3203789879Estimaciones del consumo
C_estimado<-P%*%C
plot(C_estimado)
#Comparar C estimado con su valor real, incluyendo residuos
cuadro <- as.data.frame(cbind(C,C_estimado,residuos5))
names(cuadro) <- c("C","estimado","Residuos")
print(cuadro)## C estimado 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
## 7 1197.2 1179.3403 17.859663
## 8 1221.9 1211.1944 10.705631
## 9 1310.4 1288.3977 22.002328
## 10 1348.8 1351.4897 -2.689665
## 11 1381.8 1374.0159 7.784083
## 12 1393.0 1406.1277 -13.127696
## 13 1470.7 1453.1784 17.521565
## 14 1510.8 1493.4953 17.304695
## 15 1541.2 1557.5083 -16.308260
## 16 1617.3 1622.5555 -5.255508
## 17 1684.0 1681.2118 2.788211
## 18 1784.8 1801.1793 -16.379339
## 19 1897.6 1911.9276 -14.327554
## 20 2006.1 1994.3509 11.749135
## 21 2066.2 2097.6247 -31.424669
## 22 2184.2 2207.5296 -23.329596
## 23 2264.8 2242.6282 22.171806
## 24 2317.5 2322.5400 -5.040038
## 25 2405.2 2441.3914 -36.191398
## 26 2550.5 2575.7118 -25.211753
## 27 2675.9 2697.3113 -21.411271
## 28 2653.7 2652.2895 1.410519
## 29 2710.9 2735.1296 -24.229564
## 30 2868.9 2847.9282 20.971808
## 31 2992.1 2948.7573 43.342653
## 32 3124.7 3087.8915 36.808458
## 33 3203.2 3185.3177 17.882297
## 34 3193.0 3226.1003 -33.100273
## 35 3236.0 3273.8200 -37.819995
## 36 3275.5 3324.8708 -49.370820
## 37 3454.3 3430.8439 23.456143
## 38 3640.6 3666.1103 -25.510341
## 39 3820.9 3832.8606 -11.960629
## 40 3981.2 3990.4342 -9.234201
## 41 4113.4 4091.4504 21.949616
## 42 4279.5 4276.2889 3.211123
## 43 4393.7 4408.2114 -14.511436
## 44 4474.5 4471.3024 3.197576
## 45 4466.6 4528.9968 -62.396763
## 46 4594.5 4661.3545 -66.854500
## 47 4748.9 4740.5693 8.330745
## 48 4928.1 4836.1366 91.963380
## 49 5075.6 5013.9793 61.620735
## 50 5237.5 5189.3511 48.148861
## 51 5423.9 5434.6177 -10.717721
## 52 5683.7 5767.7697 -84.069717
## 53 5968.4 6024.8266 -56.426627
## 54 6257.8 6132.6864 125.113605#Ejericio 6 Estima la ecuación de ventas, presenta sus resultados en formato APA.
load("C:/Users/MINEDUCYT/Downloads/datos_ventas (1).RData")
modelo_ventas2 <- lm(formula = ventas~tv+radio+periodico,data = datos_ventas)
stargazer(modelo_ventas2,title = "Modelo ventas",type = "text")##
## Modelo ventas
## ===============================================
## Dependent variable:
## ---------------------------
## ventas
## -----------------------------------------------
## tv 0.045
## (0.118)
##
## radio -3.450***
## (0.206)
##
## periodico 18.485***
## (0.563)
##
## Constant -33.289***
## (7.172)
##
## -----------------------------------------------
## Observations 200
## R2 0.847
## Adjusted R2 0.844
## Residual Std. Error 33.875 (df = 196)
## F Statistic 360.758*** (df = 3; 196)
## ===============================================
## Note: *p<0.1; **p<0.05; ***p<0.01Calcule los residuos a través de la matriz M
matriz_X6 <- model.matrix(modelo_ventas2)
#matriz M
n6 <- nrow(matriz_X6)
matriz_m6 <- diag(n6)-matriz_X6%*%solve(t(matriz_X6)%*%matriz_X6)%*%t(matriz_X6)
residuos_modelo6 <- modelo_ventas2$residuals
matriz_y <- datos_ventas$ventas
mresiduos_matrices <- residuos_modelo6%*%matriz_yCalcule un intervalo de confianza del 96.8% para el impacto del gasto de publicidad en TV, en las ventas, e interprételo.
confint(object = modelo_ventas2, parm = "tv", level = .968)## 1.6 % 98.4 %
## tv -0.2097376 0.2998052Interpretación. podemos concluir que el 96.8% de las estimaciones que hacemos el experimento se esperaria que el impacto de una unidad en la TV, se tradujece en un cambio esperado en un minimo de -0.2097376 y un máximo 0.2998052