Matriz de Información X

library(readr)
library(kableExtra)
url_link<-"http://halweb.uc3m.es/esp/Personal/personas/agrane/libro/ficheros_datos/capitulo_7/datos_prob_7_3.txt"
mat_X<-read_table2(url_link,col_names = FALSE)

mat_X %>% head() %>% 
  kable(caption ="Matriz de información:" ,align = "c",digits = 6) %>% 
  kable_material(html_font = "sans-serif")
Matriz de información:
X1 X2 X3 X4 X5 X6 X7 X8
30 41 670 3903 12 94 341 1.2
124 46 410 955 6 57 89 0.5
95 48 370 6 5 26 20 0.1
90 43 680 435 8 20 331 1.6
112 41 100 1293 2 51 22 0.1
73 51 390 6115 4 35 93 0.2

Cálculo de V(X):

Cálculo “Manual”

library(dplyr)
library(kableExtra)
centrado<-function(x){
  x-mean(x)
}
Xcentrada<-apply(X = mat_X,MARGIN = 2,centrado)
Xcentrada %>% head() %>% 
  kable(caption ="Matriz de Variables centradas:",
        align = "c",
        digits = 2) %>% 
  kable_material(html_font = "sans-serif")
Matriz de Variables centradas:
X1 X2 X3 X4 X5 X6 X7 X8
-49.67 -0.67 303.89 1463.5 2.94 -60.17 196.72 0.71
44.33 4.33 43.89 -1484.5 -3.06 -97.17 -55.28 0.01
15.33 6.33 3.89 -2433.5 -4.06 -128.17 -124.28 -0.39
10.33 1.33 313.89 -2004.5 -1.06 -134.17 186.72 1.11
32.33 -0.67 -266.11 -1146.5 -7.06 -103.17 -122.28 -0.39
-6.67 9.33 23.89 3675.5 -5.06 -119.17 -51.28 -0.29 
n_obs<-nrow(mat_X)
mat_V<-t(Xcentrada)%*%Xcentrada/(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:
X1 X2 X3 X4 X5 X6 X7 X8
X1 716.12 45.06 -2689.61 -16082.06 -121.63 -1019.06 -1844.37 -5.15
X2 45.06 46.94 -144.31 2756.71 -24.63 -938.41 -205.25 -0.42
X3 -2689.61 -144.31 36389.87 123889.71 740.82 838.33 17499.38 73.48
X4 -16082.06 2756.71 123889.71 5736372.38 3078.97 6672.44 140343.50 412.79
X5 -121.63 -24.63 740.82 3078.97 51.47 405.58 565.22 1.59
X6 -1019.06 -938.41 838.33 6672.44 405.58 26579.56 3149.77 -2.96
X7 -1844.37 -205.25 17499.38 140343.50 565.22 3149.77 16879.39 64.51
X8 -5.15 -0.42 73.48 412.79 1.59 -2.96 64.51 0.28

Cálculo con 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
X1 X2 X3 X4 X5 X6 X7 X8
X1 716.12 45.06 -2689.61 -16082.06 -121.63 -1019.06 -1844.37 -5.15
X2 45.06 46.94 -144.31 2756.71 -24.63 -938.41 -205.25 -0.42
X3 -2689.61 -144.31 36389.87 123889.71 740.82 838.33 17499.38 73.48
X4 -16082.06 2756.71 123889.71 5736372.38 3078.97 6672.44 140343.50 412.79
X5 -121.63 -24.63 740.82 3078.97 51.47 405.58 565.22 1.59
X6 -1019.06 -938.41 838.33 6672.44 405.58 26579.56 3149.77 -2.96
X7 -1844.37 -205.25 17499.38 140343.50 565.22 3149.77 16879.39 64.51
X8 -5.15 -0.42 73.48 412.79 1.59 -2.96 64.51 0.28

Cálculo de R(X)

Cálculo “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:
X1 X2 X3 X4 X5 X6 X7 X8
-1.86 -0.10 1.59 0.61 0.41 -0.37 1.51 1.34
1.66 0.63 0.23 -0.62 -0.43 -0.60 -0.43 0.02
0.57 0.92 0.02 -1.02 -0.57 -0.79 -0.96 -0.73
0.39 0.19 1.65 -0.84 -0.15 -0.82 1.44 2.09
1.21 -0.10 -1.39 -0.48 -0.98 -0.63 -0.94 -0.73
-0.25 1.36 0.13 1.53 -0.70 -0.73 -0.39 -0.54 
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:
X1 X2 X3 X4 X5 X6 X7 X8
X1 1.00 0.25 -0.53 -0.25 -0.63 -0.23 -0.53 -0.36
X2 0.25 1.00 -0.11 0.17 -0.50 -0.84 -0.23 -0.12
X3 -0.53 -0.11 1.00 0.27 0.54 0.03 0.71 0.73
X4 -0.25 0.17 0.27 1.00 0.18 0.02 0.45 0.32
X5 -0.63 -0.50 0.54 0.18 1.00 0.35 0.61 0.42
X6 -0.23 -0.84 0.03 0.02 0.35 1.00 0.15 -0.03
X7 -0.53 -0.23 0.71 0.45 0.61 0.15 1.00 0.93
X8 -0.36 -0.12 0.73 0.32 0.42 -0.03 0.93 1.00

Cálculo usando 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
X1 X2 X3 X4 X5 X6 X7 X8
X1 1.00 0.25 -0.53 -0.25 -0.63 -0.23 -0.53 -0.36
X2 0.25 1.00 -0.11 0.17 -0.50 -0.84 -0.23 -0.12
X3 -0.53 -0.11 1.00 0.27 0.54 0.03 0.71 0.73
X4 -0.25 0.17 0.27 1.00 0.18 0.02 0.45 0.32
X5 -0.63 -0.50 0.54 0.18 1.00 0.35 0.61 0.42
X6 -0.23 -0.84 0.03 0.02 0.35 1.00 0.15 -0.03
X7 -0.53 -0.23 0.71 0.45 0.61 0.15 1.00 0.93
X8 -0.36 -0.12 0.73 0.32 0.42 -0.03 0.93 1.00

Versiones gráficas de R(X)

Usando el paquete PerformanceAnalytics

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

Usando el paquete 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))

Ejemplo 2 usando paquete corrplot

library(corrplot)
library(grDevices)
library(Hmisc)
colQ <- colorRampPalette(c("#7F0000", "red", "#FF7F00", "yellow", "#7FFF7F",
                           "cyan", "#007FFF", "blue", "#00007F"))
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         method = "color",
         type="lower",
         tl.col="blue",
         tl.srt = 17,
         pch.col = "white",
         insig = "p-value",
         sig.level = -1,
         col = colQ(100))

Ejemplo 3 usando paquete corrplot

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         method = "shade",
         type="full",
         tl.col="red",
         tl.srt = 17,
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         col = heat.colors(100))

Ejemplo 4 usando paquete corrplot

library(corrplot)
library(grDevices)
library(Hmisc)
col1 <- colorRampPalette(c("#67001F", "#B2182B", "#D6604D", "#F4A582",
                           "#FDDBC7", "#FFFFFF", "#D1E5F0", "#92C5DE",
                           "#4393C3", "#2166AC", "#053061"))
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         method = "ellipse",
         is.corr = FALSE,
         type="full",
         tl.col="black",
         tl.srt = 20,
         pch.col = "blue",
         insig = "p-value",
         sig.level = -1,
         order = "hclust",
         addrect = 2,
         col = col1(100))

Ejemplo 5 usando paquete “corrplot”

library(corrplot)
library(grDevices)
library(Hmisc)
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         method = "ellipse",
         type="upper",
         order = "hclust",
         col= c("yellow","white"),bg="lightblue",
         insig = "p-value",
         sig.level = -1)