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Gracia María Lemus Mejía
LM21017

Matriz de información

library(readr)
library(kableExtra)
load("C:/Users/02lmg/OneDrive/Escritorio/Ciclo 6/METODO PARA EL ANALISIS ECONOMICO/unidad 2/Graacia María Lemus Mejía - 6-2.RData")
mat_X<-X6_2
mat_X %>% 
 head() %>% 
  kable(caption ="Matriz de información:" ,align = "c",digits = 6) %>% 
  kable_material(html_font = "sans-serif")
Matriz de información:
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
4 1 4 3 3 2 4 4 4 4
5 5 4 4 3 3 4 1 1 3
2 1 3 1 4 2 1 5 4 5
1 1 1 1 4 4 2 5 5 4
1 1 2 1 5 5 4 3 3 2
5 5 5 5 3 3 4 2 2 1

Literal A

Matriz de varianza covarianza

1. De forma “manual”

library(dplyr)
library(kableExtra)
centrado<-function(x){
  x-mean(x)
}
Xc<-apply(X = mat_X,MARGIN = 2,centrado)
Xc %>% head() %>% 
  kable(caption ="Matriz de Variables centradas:",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif")
Matriz de Variables centradas:
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
0.3 -2.4 0.5 0.2 -0.7 -1.7 0.35 1.15 1.2 1.35
1.3 1.6 0.5 1.2 -0.7 -0.7 0.35 -1.85 -1.8 0.35
-1.7 -2.4 -0.5 -1.8 0.3 -1.7 -2.65 2.15 1.2 2.35
-2.7 -2.4 -2.5 -1.8 0.3 0.3 -1.65 2.15 2.2 1.35
-2.7 -2.4 -1.5 -1.8 1.3 1.3 0.35 0.15 0.2 -0.65
1.3 1.6 1.5 2.2 -0.7 -0.7 0.35 -0.85 -0.8 -1.65 
n_obs<-nrow(mat_X)
mat_V<-t(Xc)%*%Xc/(n_obs-1) 
mat_V %>% kable(caption ="Cálculo de V(X) forma manual:" ,
                align = "c",
                digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))
Cálculo de V(X) forma manual:
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
V1 1.80 1.92 1.32 1.73 -0.62 -0.31 0.36 -1.21 -1.27 -0.90
V2 1.92 2.67 1.42 2.14 -0.66 -0.14 0.52 -1.78 -1.81 -1.54
V3 1.32 1.42 1.42 1.53 -0.53 -0.32 0.29 -0.92 -1.11 -0.87
V4 1.73 2.14 1.53 2.48 -0.80 -0.48 0.35 -1.61 -1.83 -1.39
V5 -0.62 -0.66 -0.53 -0.80 0.85 0.80 0.21 0.37 0.46 0.15
V6 -0.31 -0.14 -0.32 -0.48 0.80 1.38 0.63 0.22 0.09 -0.37
V7 0.36 0.52 0.29 0.35 0.21 0.63 1.61 -0.53 -0.34 -0.71
V8 -1.21 -1.78 -0.92 -1.61 0.37 0.22 -0.53 1.92 1.81 1.37
V9 -1.27 -1.81 -1.11 -1.83 0.46 0.09 -0.34 1.81 2.17 1.56
V10 -0.90 -1.54 -0.87 -1.39 0.15 -0.37 -0.71 1.37 1.56 1.82

2. Usando el comando cov de R base

library(dplyr)
library(kableExtra)
cov(mat_X) %>% 
  kable(caption="Cálculo de V(X) a través de R base",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))
Cálculo de V(X) a través de R base
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
V1 1.80 1.92 1.32 1.73 -0.62 -0.31 0.36 -1.21 -1.27 -0.90
V2 1.92 2.67 1.42 2.14 -0.66 -0.14 0.52 -1.78 -1.81 -1.54
V3 1.32 1.42 1.42 1.53 -0.53 -0.32 0.29 -0.92 -1.11 -0.87
V4 1.73 2.14 1.53 2.48 -0.80 -0.48 0.35 -1.61 -1.83 -1.39
V5 -0.62 -0.66 -0.53 -0.80 0.85 0.80 0.21 0.37 0.46 0.15
V6 -0.31 -0.14 -0.32 -0.48 0.80 1.38 0.63 0.22 0.09 -0.37
V7 0.36 0.52 0.29 0.35 0.21 0.63 1.61 -0.53 -0.34 -0.71
V8 -1.21 -1.78 -0.92 -1.61 0.37 0.22 -0.53 1.92 1.81 1.37
V9 -1.27 -1.81 -1.11 -1.83 0.46 0.09 -0.34 1.81 2.17 1.56
V10 -0.90 -1.54 -0.87 -1.39 0.15 -0.37 -0.71 1.37 1.56 1.82

Literal B

matriz de correlación

1.De forma “manual”

Zx<-scale(x = mat_X,center =TRUE)
Zx %>% head() %>% 
  kable(caption ="Matriz de Variables Estandarizadas:",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif")
Matriz de Variables Estandarizadas:
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
0.22 -1.47 0.42 0.13 -0.76 -1.45 0.28 0.83 0.81 1.00
0.97 0.98 0.42 0.76 -0.76 -0.60 0.28 -1.33 -1.22 0.26
-1.27 -1.47 -0.42 -1.14 0.32 -1.45 -2.09 1.55 0.81 1.74
-2.01 -1.47 -2.10 -1.14 0.32 0.26 -1.30 1.55 1.49 1.00
-2.01 -1.47 -1.26 -1.14 1.41 1.11 0.28 0.11 0.14 -0.48
0.97 0.98 1.26 1.40 -0.76 -0.60 0.28 -0.61 -0.54 -1.22 
n_obs<-nrow(mat_X)
mat_R<-t(Zx)%*%Zx/(n_obs-1) 
mat_R %>% kable(caption ="Cálculo de R(X) forma manual:" ,
                align = "c",
                digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))
Cálculo de R(X) forma manual:
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
V1 1.00 0.87 0.82 0.82 -0.50 -0.19 0.21 -0.65 -0.64 -0.50
V2 0.87 1.00 0.73 0.83 -0.44 -0.07 0.25 -0.78 -0.75 -0.70
V3 0.82 0.73 1.00 0.81 -0.48 -0.23 0.19 -0.56 -0.63 -0.54
V4 0.82 0.83 0.81 1.00 -0.55 -0.26 0.17 -0.74 -0.79 -0.65
V5 -0.50 -0.44 -0.48 -0.55 1.00 0.74 0.18 0.29 0.34 0.12
V6 -0.19 -0.07 -0.23 -0.26 0.74 1.00 0.42 0.13 0.05 -0.24
V7 0.21 0.25 0.19 0.17 0.18 0.42 1.00 -0.30 -0.18 -0.41
V8 -0.65 -0.78 -0.56 -0.74 0.29 0.13 -0.30 1.00 0.89 0.73
V9 -0.64 -0.75 -0.63 -0.79 0.34 0.05 -0.18 0.89 1.00 0.78
V10 -0.50 -0.70 -0.54 -0.65 0.12 -0.24 -0.41 0.73 0.78 1.00

2. Usando el comando cor de R base

library(dplyr)
library(kableExtra)
cor(mat_X) %>% 
  kable(caption="Cálculo de R(X) a través de R base",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("striped", "hover"))
Cálculo de R(X) a través de R base
V1 V2 V3 V4 V5 V6 V7 V8 V9 V10
V1 1.00 0.87 0.82 0.82 -0.50 -0.19 0.21 -0.65 -0.64 -0.50
V2 0.87 1.00 0.73 0.83 -0.44 -0.07 0.25 -0.78 -0.75 -0.70
V3 0.82 0.73 1.00 0.81 -0.48 -0.23 0.19 -0.56 -0.63 -0.54
V4 0.82 0.83 0.81 1.00 -0.55 -0.26 0.17 -0.74 -0.79 -0.65
V5 -0.50 -0.44 -0.48 -0.55 1.00 0.74 0.18 0.29 0.34 0.12
V6 -0.19 -0.07 -0.23 -0.26 0.74 1.00 0.42 0.13 0.05 -0.24
V7 0.21 0.25 0.19 0.17 0.18 0.42 1.00 -0.30 -0.18 -0.41
V8 -0.65 -0.78 -0.56 -0.74 0.29 0.13 -0.30 1.00 0.89 0.73
V9 -0.64 -0.75 -0.63 -0.79 0.34 0.05 -0.18 0.89 1.00 0.78
V10 -0.50 -0.70 -0.54 -0.65 0.12 -0.24 -0.41 0.73 0.78 1.00

3. Presenta la matriz de correlación

PerformanceAnalytics

library(PerformanceAnalytics)
chart.Correlation(as.matrix(mat_X),histogram = TRUE,pch=12)

Corrplot

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="upper",
         tl.col="black",
         tl.srt = 20,
         pch.col = "blue",
         insig = "p-value",
         sig.level = -1,
         col = terrain.colors(100))

Literal C

Extracción de los Componentes usando R

library(dplyr)
library(factoextra)
library(kableExtra)
library(stargazer)
library(ggplot2)
options(scipen = 99999)
PC<-princomp(x = mat_X,cor = TRUE,fix_sign = FALSE)
factoextra::get_eig(PC) %>% kable(caption="Resumen de PCA",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif") %>% 
  kable_styling(bootstrap_options = c("hover"))
Resumen de PCA
eigenvalue variance.percent cumulative.variance.percent
Dim.1 5.70 57.01 57.01
Dim.2 2.07 20.69 77.70
Dim.3 0.72 7.20 84.91
Dim.4 0.55 5.48 90.39
Dim.5 0.32 3.16 93.54
Dim.6 0.27 2.71 96.25
Dim.7 0.15 1.46 97.72
Dim.8 0.13 1.28 99.00
Dim.9 0.07 0.68 99.68
Dim.10 0.03 0.32 100.00

Graficos

fviz_eig(PC,
         choice = "eigenvalue",
         barcolor = "red",
         barfill = "red",
         addlabels = TRUE, 
       )+labs(title = "Gráfico de Sedimentación",subtitle = "Usando princomp, con Autovalores")+
  xlab(label = "Componentes")+
  ylab(label = "Autovalores")+geom_hline(yintercept = 1)

fviz_eig(PC,
         choice = "variance",
         barcolor = "green",
         barfill = "green",
         addlabels = TRUE,
       )+labs(title = "Gráfico de Sedimentación",
              subtitle = "Usando princomp, con %Varianza Explicada")+
  xlab(label = "Componentes")+
  ylab(label = "%Varianza")

a. ¿Cuántas Componentes habría que retener?

De acuerdo al criterio del codo se sugiere retener tres componentes principales. Estas tres componentes principales explican aproximadamente el 84.91% de la varianza acumulativa en los datos de la encuesta sobre las preferencias del público en la compra de automóviles.

Esto significa que las tres primeras componentes capturan una proporción sustancial de la variabilidad en los datos, lo que facilita el análisis y la interpretación de las preferencias del público en la compra de automóviles en relación con las diez características evaluadas.