Para una empresa se ha estimado un modelo que relaciona las ventas de 200 empresas, con su gasto en tv, radio, periodicos y la interaccion entre tv y periodicos.
options(scipen = 99999)
load("C:/Users/gusta_000/Desktop/Econometria/Guia/modelo_ventas.RData")
matriz_X_1 <- model.matrix(modelo_ventas)
matriz_XX_1 <- t(matriz_X_1)%*%matriz_X_1
#Calculo de la matriz A
#solo se muestra una parte de las matrices para no saturar la pagina, pero internamente las matrices mantienen sus dimensiones.
matriz_A_1 <- solve(matriz_XX_1)%*%t(matriz_X_1)
matriz_A_1[1:4,1:4]## 1 2 3 4
## (Intercept) -0.01128647020 0.01410377973 0.0350639188 0.0004283381
## tv -0.00006704103 0.00003094914 -0.0006120193 -0.0002120642
## periodico 0.00139818182 -0.00190724690 -0.0025468816 0.0002293243
## radio -0.00058002134 0.00064866654 -0.0001093284 -0.0001899710#Calculo de la matriz P
matriz_P_1 <- matriz_X_1%*%matriz_A_1
matriz_P_1[1:4,1:4]## 1 2 3 4
## 1 0.03181459 0.00370346 0.01758786 0.02250872
## 2 0.00370346 0.02460480 0.03447285 0.01212022
## 3 0.01758786 0.03447285 0.06766822 0.02641047
## 4 0.02250872 0.01212022 0.02641047 0.02031981#Calculo de la matriz M
n_1 <- nrow(matriz_X_1)
matriz_M_1 <- diag(n_1)-matriz_P_1
matriz_M_1[1:4,1:4]## 1 2 3 4
## 1 0.96818541 -0.00370346 -0.01758786 -0.02250872
## 2 -0.00370346 0.97539520 -0.03447285 -0.01212022
## 3 -0.01758786 -0.03447285 0.93233178 -0.02641047
## 4 -0.02250872 -0.01212022 -0.02641047 0.97968019library(magrittr)
residuos_modelo_ventas <- modelo_ventas$residuals
datos_modelo_1 <- modelo_ventas$model
residuos_matrices_1 <- matriz_M_1%*%datos_modelo_1$ventas
cbind(residuos_matrices_1,residuos_modelo_ventas, residuos_modelo_ventas-residuos_matrices_1)%>%round(digits = 2) %>% as.data.frame() -> comparacion_1
names(comparacion_1) <- c("Por matrices", "En el modelo", "Diferencias")
#Se muestran solo 10 observaciones para no saturar la pagina
head(comparacion_1, n = 10)## Por matrices En el modelo Diferencias
## 1 -15.93 -15.93 0
## 2 19.33 19.33 0
## 3 38.02 38.02 0
## 4 -15.43 -15.43 0
## 5 5.16 5.16 0
## 6 80.22 80.22 0
## 7 -16.35 -16.35 0
## 8 -22.89 -22.89 0
## 9 -34.40 -34.40 0
## 10 46.09 46.09 0eigen(x = matriz_XX_1, symmetric = TRUE) -> descomposicion_1
auto_valores_1 <- descomposicion_1$values
print(auto_valores_1)## [1] 311421698.6388 70252.5341 40973.4590 3714.3627 12.7735print(auto_valores_1>0)## [1] TRUE TRUE TRUE TRUE TRUEPara una empresa se desea estimar un modelo que relaciona el tiempo (en minutos) en acomodar cajas en una bodega, en funcion de la distancia (en metros) y del numero de cajas nota: las cajas son todas iguales. Los datos se encuentra en "datos_cajas.RData"
load("C:/Users/gusta_000/Desktop/Econometria/Guia/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: 0.0003325matriz_x_2 <- model.matrix(modelo_cajas)
matriz_xx_2 <- t(matriz_x_2)%*%matriz_x_2
#Calculando Matriz A
matriz_A_2 <- solve(matriz_xx_2)%*%t(matriz_x_2)
print(matriz_A_2)## 1 2 3 4 5
## (Intercept) 0.459747079 0.505626389 -0.317731768 0.707001469 0.053149816
## Distancia -0.003015297 -0.009318829 0.018819615 -0.019989342 -0.006641453
## N_cajas -0.017147338 -0.009890695 -0.007919488 -0.004479623 0.011082085
## 6 7 8 9 10
## (Intercept) -0.166576988 0.633594572 -0.125532551 0.1260628274 -0.90735239
## Distancia 0.006550474 -0.009903692 0.009409808 0.0003379213 0.02334256
## N_cajas 0.002768355 -0.016090251 -0.003959744 -0.0038254420 0.01780152
## 11 12 13 14 15
## (Intercept) 0.277217608 0.368482344 0.487274665 -0.3674581822 -0.73350489
## Distancia -0.011931220 -0.007473259 -0.006797416 0.0001559637 0.01645417
## N_cajas 0.006862401 -0.005142468 -0.012793352 0.0238754370 0.01885861#Calculando Matriz P
matriz_P_2 <- matriz_x_2%*%matriz_A_2
print(matriz_P_2)## 1 2 3 4 5 6
## 1 0.19781478 0.127154573 0.16766180 0.062524965 -0.03527291 0.057620774
## 2 0.12715457 0.124295239 0.03396629 0.140073563 0.05334477 0.038710181
## 3 0.16766180 0.033966286 0.35585795 -0.137368460 -0.10168744 0.123125512
## 4 0.06252497 0.140073563 -0.13736846 0.257600846 0.15524536 0.006698639
## 5 -0.03527291 0.053344771 -0.10168744 0.155245361 0.18408997 0.046742309
## 6 0.05762077 0.038710181 0.12312551 0.006698639 0.04674231 0.086318088
## 7 0.17558129 0.144648497 0.07654437 0.133523089 0.01345706 0.036955589
## 8 0.11716423 0.050316476 0.21126231 -0.035350897 -0.01751039 0.094896089
## 9 0.09794605 0.077129229 0.10132526 0.055636570 0.03786105 0.067680430
## 10 -0.02906036 -0.056765574 0.20436525 -0.131155907 0.05122193 0.136694350
## 11 -0.01209498 0.081873124 -0.13140718 0.199703669 0.18629079 0.030873007
## 12 0.09285990 0.104513848 0.01812731 0.131114317 0.07550894 0.044246890
## 13 0.15541865 0.125438973 0.08744449 0.109054124 0.01789770 0.046274418
## 14 -0.12402490 -0.005427535 -0.12246527 0.112857904 0.23285894 0.067134558
## 15 -0.05129385 -0.039271650 0.11324781 -0.060157783 0.09995191 0.116029165
## 7 8 9 10 11 12
## 1 0.17558129 0.11716423 0.09794605 -0.02906036 -0.01209498 0.092859897
## 2 0.14464850 0.05031648 0.07712923 -0.05676557 0.08187312 0.104513848
## 3 0.07654437 0.21126231 0.10132526 0.20436525 -0.13140718 0.018127310
## 4 0.13352309 -0.03535090 0.05563657 -0.13115591 0.19970367 0.131114317
## 5 0.01345706 -0.01751039 0.03786105 0.05122193 0.18629079 0.075508940
## 6 0.03695559 0.09489609 0.06768043 0.13669435 0.03087301 0.044246890
## 7 0.18301556 0.07160552 0.08894348 -0.08682757 0.04935470 0.112467995
## 8 0.07160552 0.13896449 0.08399596 0.13551596 -0.03237026 0.042396988
## 9 0.08894348 0.08399596 0.07465547 0.05440619 0.04101064 0.069478345
## 10 -0.08682757 0.13551596 0.05440619 0.34795579 -0.01326471 -0.021162536
## 11 0.04935470 -0.03237026 0.04101064 -0.01326471 0.20329083 0.095597926
## 12 0.11246799 0.04239699 0.06947834 -0.02116254 0.09559793 0.094228911
## 13 0.15702161 0.07705558 0.08545596 -0.04568349 0.04428588 0.099852268
## 14 -0.07689788 -0.02789930 0.01907176 0.16357209 0.20867158 0.042323339
## 15 -0.07939330 0.08995724 0.04540362 0.29018859 0.04818497 -0.001554438
## 13 14 15
## 1 0.15541865 -0.124024902 -0.051293849
## 2 0.12543897 -0.005427535 -0.039271650
## 3 0.08744449 -0.122465266 0.113247813
## 4 0.10905412 0.112857904 -0.060157783
## 5 0.01789770 0.232858944 0.099951911
## 6 0.04627442 0.067134558 0.116029165
## 7 0.15702161 -0.076897883 -0.079393301
## 8 0.07705558 -0.027899299 0.089957240
## 9 0.08545596 0.019071756 0.045403621
## 10 -0.04568349 0.163572088 0.290188586
## 11 0.04428588 0.208671580 0.048184973
## 12 0.09985227 0.042323339 -0.001554438
## 13 0.13743085 -0.052866482 -0.044080529
## 14 -0.05286648 0.352392093 0.210699107
## 15 -0.04408053 0.210699107 0.262089133#Calculando Matriz M
n_2 <- nrow(matriz_x_2)
matriz_M_2 <- diag(n_2)-matriz_P_2
print(matriz_M_2)## 1 2 3 4 5 6
## 1 0.80218522 -0.127154573 -0.16766180 -0.062524965 0.03527291 -0.057620774
## 2 -0.12715457 0.875704761 -0.03396629 -0.140073563 -0.05334477 -0.038710181
## 3 -0.16766180 -0.033966286 0.64414205 0.137368460 0.10168744 -0.123125512
## 4 -0.06252497 -0.140073563 0.13736846 0.742399154 -0.15524536 -0.006698639
## 5 0.03527291 -0.053344771 0.10168744 -0.155245361 0.81591003 -0.046742309
## 6 -0.05762077 -0.038710181 -0.12312551 -0.006698639 -0.04674231 0.913681912
## 7 -0.17558129 -0.144648497 -0.07654437 -0.133523089 -0.01345706 -0.036955589
## 8 -0.11716423 -0.050316476 -0.21126231 0.035350897 0.01751039 -0.094896089
## 9 -0.09794605 -0.077129229 -0.10132526 -0.055636570 -0.03786105 -0.067680430
## 10 0.02906036 0.056765574 -0.20436525 0.131155907 -0.05122193 -0.136694350
## 11 0.01209498 -0.081873124 0.13140718 -0.199703669 -0.18629079 -0.030873007
## 12 -0.09285990 -0.104513848 -0.01812731 -0.131114317 -0.07550894 -0.044246890
## 13 -0.15541865 -0.125438973 -0.08744449 -0.109054124 -0.01789770 -0.046274418
## 14 0.12402490 0.005427535 0.12246527 -0.112857904 -0.23285894 -0.067134558
## 15 0.05129385 0.039271650 -0.11324781 0.060157783 -0.09995191 -0.116029165
## 7 8 9 10 11 12
## 1 -0.17558129 -0.11716423 -0.09794605 0.02906036 0.01209498 -0.092859897
## 2 -0.14464850 -0.05031648 -0.07712923 0.05676557 -0.08187312 -0.104513848
## 3 -0.07654437 -0.21126231 -0.10132526 -0.20436525 0.13140718 -0.018127310
## 4 -0.13352309 0.03535090 -0.05563657 0.13115591 -0.19970367 -0.131114317
## 5 -0.01345706 0.01751039 -0.03786105 -0.05122193 -0.18629079 -0.075508940
## 6 -0.03695559 -0.09489609 -0.06768043 -0.13669435 -0.03087301 -0.044246890
## 7 0.81698444 -0.07160552 -0.08894348 0.08682757 -0.04935470 -0.112467995
## 8 -0.07160552 0.86103551 -0.08399596 -0.13551596 0.03237026 -0.042396988
## 9 -0.08894348 -0.08399596 0.92534453 -0.05440619 -0.04101064 -0.069478345
## 10 0.08682757 -0.13551596 -0.05440619 0.65204421 0.01326471 0.021162536
## 11 -0.04935470 0.03237026 -0.04101064 0.01326471 0.79670917 -0.095597926
## 12 -0.11246799 -0.04239699 -0.06947834 0.02116254 -0.09559793 0.905771089
## 13 -0.15702161 -0.07705558 -0.08545596 0.04568349 -0.04428588 -0.099852268
## 14 0.07689788 0.02789930 -0.01907176 -0.16357209 -0.20867158 -0.042323339
## 15 0.07939330 -0.08995724 -0.04540362 -0.29018859 -0.04818497 0.001554438
## 13 14 15
## 1 -0.15541865 0.124024902 0.051293849
## 2 -0.12543897 0.005427535 0.039271650
## 3 -0.08744449 0.122465266 -0.113247813
## 4 -0.10905412 -0.112857904 0.060157783
## 5 -0.01789770 -0.232858944 -0.099951911
## 6 -0.04627442 -0.067134558 -0.116029165
## 7 -0.15702161 0.076897883 0.079393301
## 8 -0.07705558 0.027899299 -0.089957240
## 9 -0.08545596 -0.019071756 -0.045403621
## 10 0.04568349 -0.163572088 -0.290188586
## 11 -0.04428588 -0.208671580 -0.048184973
## 12 -0.09985227 -0.042323339 0.001554438
## 13 0.86256915 0.052866482 0.044080529
## 14 0.05286648 0.647607907 -0.210699107
## 15 0.04408053 -0.210699107 0.737910867library(magrittr)
residuos_modelo_cajas <- modelo_cajas$residuals
residuos_matrices_2 <- matriz_M_2%*%datos_cajas$Tiempo
cbind(residuos_matrices_2,residuos_modelo_cajas,residuos_matrices_2-residuos_modelo_cajas)%>%round(digits = 2)%>%as.data.frame() -> comparacion_2
names(comparacion_2) <- c("Por matrices", "en el modelo", "Diferencia")
print(comparacion_2)## Por matrices en el modelo 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 0options(scipen = 999999)
descomposicion_2 <- eigen(x = matriz_xx_2,symmetric = TRUE)
auto_valores_2 <- descomposicion_2$values
print(auto_valores_2)## [1] 16976.7781334 709.9345923 0.2872743print(auto_valores_2>0)## [1] TRUE TRUE TRUEPara los EEUU se ha estimado un modelo que relaciona el "numero de crimenes" en un estado con el "Nivel de pobreza" y la cantidad de solteros en el mismo.
options(scipen = 999999)
load("C:/Users/gusta_000/Desktop/Econometria/Guia/modelo_estimado.RData")
matriz_x_3 <- model.matrix(modelo_estimado_1)
#solo se muestra una parte de las matrices para no saturar la pagina, pero internamente las matrices mantienen sus dimensiones.
#Matriz A
matriz_A_3 <- solve(t(matriz_x_3)%*%matriz_x_3)%*%t(matriz_x_3)
matriz_A_3[,1:4]## 1 2 3 4
## (Intercept) -0.12023796 0.007496216 0.043732382 -0.019624196
## poverty -0.01182361 0.003994776 0.008825494 0.000303668
## single 0.02723384 -0.003960021 -0.013241432 0.003081729#Matriz P
matriz_P_3 <- matriz_x_3%*%matriz_A_3
matriz_P_3[1:4,1:4]## 1 2 3 4
## 1 0.16161108 -0.01277963 -0.06530809 0.02720791
## 2 -0.01277963 0.03146508 0.04501952 0.02109951
## 3 -0.06530809 0.04501952 0.07855895 0.01942366
## 4 0.02720791 0.02109951 0.01942366 0.02234121#Matriz M
n_3 <- nrow(matriz_x_3)
matriz_M_3 <- diag(n_3)-matriz_P_3
matriz_M_3[1:4,1:4]## 1 2 3 4
## 1 0.83838892 0.01277963 0.06530809 -0.02720791
## 2 0.01277963 0.96853492 -0.04501952 -0.02109951
## 3 0.06530809 -0.04501952 0.92144105 -0.01942366
## 4 -0.02720791 -0.02109951 -0.01942366 0.97765879library(magrittr)
Y_3 <- modelo_estimado_1$model$crime
residuos_estimados_3 <- matriz_M_3%*%Y_3
as.data.frame(cbind(residuos_estimados_3, modelo_estimado_1$residuals, residuos_estimados_3-modelo_estimado_1$residuals))%>%round(digits = 2)%>%as.data.frame() -> comparativo_3
names(comparativo_3) <- c("residuos_estimados_3", "modelo_estimado_1$residuals", "Diferencia")
#Se muestran solo 10 observaciones para no saturar la pagina
head(comparativo_3,n = 10)## residuos_estimados_3 modelo_estimado_1$residuals Diferencia
## 1 -311.71 -311.71 0
## 2 116.80 116.80 0
## 3 45.25 45.25 0
## 4 -34.45 -34.45 0
## 5 243.00 243.00 0
## 6 -145.12 -145.12 0
## 7 86.13 86.13 0
## 8 88.31 88.31 0
## 9 689.82 689.82 0
## 10 -163.29 -163.29 0descomposicion_3 <- eigen(x = t(matriz_x_3)%*%matriz_x_3, symmetric = TRUE)
auto_valores_3 <- descomposicion_3$values
print(auto_valores_3)## [1] 17956.580914 279.157317 1.681762print(auto_valores_3>0)## [1] TRUE TRUE TRUEDentro del archivo "Investiment_Equation.xlsx" se encuentran datos para estimar una funcion de inversion, para un pais, y contiene las siguientes variables:
InvReal = Inversion Real en millones de US$,
Trend = tendencia, Inflation = inflacion,
PNBr = Producto Nacional Bruto Real en US$,
Interest = Tasa de interes.
Se solicita:
library(readxl)
Investiment_Equation <- read_excel("C:/Users/gusta_000/Desktop/Econometria/Guia/Investiment_Equation.xlsx")
ecuacion_inversion <- lm(formula = InvReal~Trend+Inflation+PNBr+Interest, data = Investiment_Equation)
library(stargazer)
stargazer(ecuacion_inversion, title = "Ecuacion de inversion", type = "text")##
## Ecuacion de inversion
## ===============================================
## 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<0.01model.matrix(ecuacion_inversion) -> matriz_x_4
n_4 <- nrow(matriz_x_4)
matriz_M_4 <- diag(n_4)-matriz_x_4%*%solve(t(matriz_x_4)%*%matriz_x_4)%*%t(matriz_x_4)
Y_4 <- Investiment_Equation$InvReal
residuos_4 <- matriz_M_4%*%Y_4
print(residuos_4)## [,1]
## 1 -0.0100602233
## 2 -0.0009290882
## 3 0.0029656679
## 4 0.0078576839
## 5 0.0028109133
## 6 0.0006259732
## 7 0.0075909286
## 8 -0.0055352778
## 9 -0.0037254127
## 10 0.0006953129
## 11 0.0019904770
## 12 -0.0001288433
## 13 -0.0101976729
## 14 0.0068712384
## 15 -0.0008316770confint(object = ecuacion_inversion, parm = "PNBr", level = 0.93)## 3.5 % 96.5 %
## PNBr 0.554777 0.774317Interpretacion: En el 93% de las ocasiones que estimemos la ecuacion, se esperaria que el impacto de un millon de dolares del PNB real se traduzca en un minimo de 0.55 millones de dolares en inversion real hasta un maximo de 0.77 millones de dolares.
Dentro del archivo "consumption_equation.RData" se encuentran objetos relacionados a una funcion de consumo, que se construyo usando las variables: C=Consumo en millones de US$, Yd=Ingreso disponible, W=Riqueza, I=Tasa de interes
load("C:/Users/gusta_000/Desktop/Econometria/Guia/consumption_equation.RData")
n_5 <- nrow(P)
M_5 <- diag(n_5)-P
residuos_5 <- M_5%*%C
#Se muestran los primeros 10 residuos para no saturar la pagina
head(residuos_5, n = 10)## [,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#Sigma cuadrado
k <- 4
var_error <- t(residuos_5)%*%residuos_5/(n_5-k)
print(var_error)## [,1]
## [1,] 1428.746options(scipen = 999999)
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 5.3203789879C_estimada <- P%*%C
#Se muestran las 10 primeras estimaciones para no saturar la pagina
head(C_estimada, n = 10)## [,1]
## 1 982.2591
## 2 995.4949
## 3 979.5343
## 4 1059.7976
## 5 1128.1379
## 6 1135.3919
## 7 1179.3403
## 8 1211.1944
## 9 1288.3977
## 10 1351.4897Dentro del archivo "datos_ventas.RData" se encuentran los datos para estimar una funcion de ventas, para una empresa, y contiene las siguientes variables:
ventas = Ventas en millones de US$,
tv = gasto en publicidad en TV en millones de US$,
radio = gasto en publicidad en radio en millones de US$,
periodico = gasto en publicidad en periodico en millones de US$.
Se solicita:
library(stargazer)
options(scipen = 999999)
load("C:/Users/gusta_000/Desktop/Econometria/Guia/datos_ventas.RData")
ventas_ecuacion<-lm(formula = ventas~tv+radio+periodico,data = datos_ventas)
stargazer(ventas_ecuacion,title = "Ecuacion de Ventas",type = "text")##
## Ecuacion de 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<0.01#Creando matriz M
matriz_x_6 <- model.matrix(ventas_ecuacion)
matriz_xx_6 <- t(matriz_x_6)%*%matriz_x_6
n_6 <- nrow(matriz_x_6)
matriz_M_6 <- diag(n_6)-matriz_x_6%*%solve(t(matriz_x_6)%*%matriz_x_6)%*%t(matriz_x_6)
Y_6 <- datos_ventas$ventas
residuos_6 <- matriz_M_6%*%Y_6
#Se muestran solo 10 observaciones para no saturar la pagina
head(residuos_6, n = 10)## [,1]
## 1 -17.85246
## 2 19.08216
## 3 33.79319
## 4 -17.35090
## 5 10.25721
## 6 74.20385
## 7 -15.24652
## 8 -23.42430
## 9 -39.64052
## 10 45.16139confint(object = ventas_ecuacion, parm = "tv", level = 0.968)## 1.6 % 98.4 %
## tv -0.2097376 0.2998052Interpretacion: el gasto en publicidad en TV no es estadisticamente significativo de forma individual, ya que incluye "0" dentro del intervalo.