#CARGA DE LA MATRIZ A UTILIZAR mat_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)

## Parsed with column specification:
## cols(
##   X1 = col_double(),
##   X2 = col_double(),
##   X3 = col_double(),
##   X4 = col_double(),
##   X5 = col_double(),
##   X6 = col_double(),
##   X7 = col_double(),
##   X8 = col_double()
## )

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)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:kableExtra':
## 
##     group_rows

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

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

Número de observaciones

 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 = "Calculo de V(X) a través de R base",
        align = "c",
        digits = 2) %>%
  kable_material(html_font = "sans-serif") %>%
  kable_styling(bootstrap_options = c("stripped", "hover"))

Calculo 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

#Calculo 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

Número de observaciones

n_obs<-nrow(mat_X)
mat_R<-t(Zx)%*%Zx/(n_obs-1)
mat_R %>% kable(caption = "Calculo de R(X) formula manual:" ,
                align = "c",
                digits = 2) %>%
  kable_material(html_font = "sans-serif") %>%
  kable_styling(bootstrap_options = c("striped", "hover"))

Calculo de R(X) formula 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

#Creación y presentación de matriz de correlación usando corrplot # Ejemplo 1

library(corrplot)

## corrplot 0.84 loaded

library(grDevices)
library(Hmisc)

## Loading required package: lattice

## Loading required package: survival

## Loading required package: Formula

## Loading required package: ggplot2

## 
## Attaching package: 'Hmisc'

## The following objects are masked from 'package:dplyr':
## 
##     src, summarize

## The following objects are masked from 'package:base':
## 
##     format.pval, units

Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="lower",
         tl.col="purple",
         tl.srt = 22,
         order = "hclust",
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         method = "circle",
         col = c("pink", "green","yellow","blue","orange"), bg = "light blue")

Ejemplo 2

Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         method="color",
         type="full",
         order="FPC",
         tl.col="brown",
         tl.srt = 18,
         pch.col = "blue",
         insig = "p-value",
         sig.level = -1,
         col = heat.colors(100))

Ejemplo 3

blackandred <- c("light blue", "blue")

Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,# r es la matriz de correlación
         p.mat = Mat_R$r,
         method="number",
         type="full",
         order="hclust",
         addrect=3,
         tl.col="blue",
         tl.srt = 20,
         pch.col = "Brown",
         insig = "p-value",
         sig.level = -1,
         col = blackandred)

Ejemplo 4

library(corrplot)
library(grDevices)
library(Hmisc)
col4 <- colorRampPalette(c("#7F0000", "pink", "#FF7F00", "yellow", "#7FFF7F",
                           "cyan", "#007FFF", "purple", "#00007F"))
Mat_R<-rcorr(as.matrix(mat_X))
corrplot(Mat_R$r,
         p.mat = Mat_R$r,
         type="upper",
         tl.col="red",
         tl.srt = 15,
         pch.col = "black",
         insig = "p-value",
         sig.level = -1,
         order = "hclust",
         method = "circle",
         addrect = 3,
         col = col4(100))

Ejemplo 5

col2 <- 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="pie",
         type="full",
         order="hclust",
         addrect=2,
         tl.col="black",
         tl.srt = 22,
         pch.col = "Black",
         insig = "p-value",
         sig.level = -1,
         col = col2(80))

Componentes Principales y Análisis factorial

Jessica Lissette Gamez Cuellar,GC13028

16/10/2020

Cálculo de V(X)

Número de observaciones

Número de observaciones

Ejemplo 2

Ejemplo 3

Ejemplo 4

Ejemplo 5