DATOS Y VISUALIZACIÓN
library(summarytools)
library(ggplot2)
library(GGally)
## Registered S3 method overwritten by 'GGally':
## method from
## +.gg ggplot2
library(readxl)
Reg_1 <- read_excel("Reg_1.xlsx")
datos_expo <- Reg_1
vista_datos<-view(dfSummary(datos_expo))
## Switching method to 'browser'
## Output file written: C:\Users\romer\AppData\Local\Temp\RtmpimBSN7\file294c1afa4238.html
vista_datos
## [1] "C:\\Users\\romer\\AppData\\Local\\Temp\\RtmpimBSN7\\file294c1afa4238.html"
shapiro.test(datos_expo$Publ_TV)
##
## Shapiro-Wilk normality test
##
## data: datos_expo$Publ_TV
## W = 0.92377, p-value = 0.1171
shapiro.test(datos_expo$Publ_radio)
##
## Shapiro-Wilk normality test
##
## data: datos_expo$Publ_radio
## W = 0.9034, p-value = 0.04779
shapiro.test(datos_expo$Publ_periodicos)
##
## Shapiro-Wilk normality test
##
## data: datos_expo$Publ_periodicos
## W = 0.73628, p-value = 0.0001118
ggpairs(datos_expo)
summary(datos_expo)
## Ventas Publ_TV Publ_radio Publ_periodicos
## Min. : 8.00 Min. :0.800 Min. : 50.00 Min. :0.300
## 1st Qu.:10.75 1st Qu.:1.000 1st Qu.: 60.00 1st Qu.:0.400
## Median :12.50 Median :1.425 Median : 67.00 Median :0.450
## Mean :13.43 Mean :1.413 Mean : 70.60 Mean :0.561
## 3rd Qu.:16.00 3rd Qu.:1.762 3rd Qu.: 76.25 3rd Qu.:0.575
## Max. :22.00 Max. :2.000 Max. :110.00 Max. :1.100
Base matricial
#Solución al ejercicio propuesto en la presentación
datos_expo2 <- Reg_1[6:11, ]
y <- c(14,16,12,14,11,10)
X <- cbind(
1,
c(1.70, 1.75,1.30, 1.45, 0.90, 0.80), #Publ_TV
c(65,69, 67, 68, 67, 97), #Publ_radio
c(0.44, 0.40, 0.44, 0.46, 0.46, 0.45) #Publ_periodicos
)
colnames(X) <- c("Intercepto", "Publ_TV", "Publ_radio", "Publ_periodicos")
list(y = y, X = X)
## $y
## [1] 14 16 12 14 11 10
##
## $X
## Intercepto Publ_TV Publ_radio Publ_periodicos
## [1,] 1 1.70 65 0.44
## [2,] 1 1.75 69 0.40
## [3,] 1 1.30 67 0.44
## [4,] 1 1.45 68 0.46
## [5,] 1 0.90 67 0.46
## [6,] 1 0.80 97 0.45
beta <- c("β_0", "β_1", "β_2", "β_3")
epsilon <- paste0("ε_", 1:6)
cat("\nβ =\n")
##
## β =
print(matrix(beta, ncol = 1))
## [,1]
## [1,] "β_0"
## [2,] "β_1"
## [3,] "β_2"
## [4,] "β_3"
cat("\nε =\n")
##
## ε =
print(matrix(epsilon, ncol = 1))
## [,1]
## [1,] "ε_1"
## [2,] "ε_2"
## [3,] "ε_3"
## [4,] "ε_4"
## [5,] "ε_5"
## [6,] "ε_6"
Estimador de mínimos cuadrados
XtX <- t(X) %*% X
Xty <- t(X) %*% y
beta_hat <- solve(XtX) %*% Xty
colnames(beta_hat) <- "Estimacion"
rownames(beta_hat) <- c("Intercepto", "Publ_TV", "Publ_radio", "Publ_periodicos")
beta_hat
## Estimacion
## Intercepto 13.774114461
## Publ_TV 4.635378565
## Publ_radio -0.008443403
## Publ_periodicos -14.569125959
lm(datos_expo2$Ventas~datos_expo2$Publ_TV+datos_expo2$Publ_radio+datos_expo2$Publ_periodicos)
##
## Call:
## lm(formula = datos_expo2$Ventas ~ datos_expo2$Publ_TV + datos_expo2$Publ_radio +
## datos_expo2$Publ_periodicos)
##
## Coefficients:
## (Intercept) datos_expo2$Publ_TV
## 13.774114 4.635379
## datos_expo2$Publ_radio datos_expo2$Publ_periodicos
## -0.008443 -14.569126