# UNIVERSIDAD NACIONAL DEL ALTIPLANO PUNO
# INGENIERIA ESTADISTICA E INFORMATICA
# TECNICAS ESTADISTICAS MULTIVARIADAS
# ANALISIS DE COMPONENTES PRINCIPALES
library(FactoMineR)
## Warning: package 'FactoMineR' was built under R version 4.1.3
library(psych)
## Warning: package 'psych' was built under R version 4.1.3
library(shiny)
## Warning: package 'shiny' was built under R version 4.1.3
library(Factoshiny)
## Warning: package 'Factoshiny' was built under R version 4.1.3
## Loading required package: FactoInvestigate
## Warning: package 'FactoInvestigate' was built under R version 4.1.3
## Loading required package: ggplot2
## Warning: package 'ggplot2' was built under R version 4.1.3
##
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
##
## %+%, alpha
library(colourpicker)
## Warning: package 'colourpicker' was built under R version 4.1.3
##
## Attaching package: 'colourpicker'
## The following object is masked from 'package:shiny':
##
## runExample
datos <- read.csv("usarrest.csv", header = T, sep = ";", row.names = 1)
datos
## Asesinatos Asaltos Poblac_urbanana Violaciones
## Alabama 13.2 236 58 21.2
## Alaska 10.0 263 48 44.5
## Arizona 8.1 294 80 31.0
## Arkansas 8.8 190 50 19.5
## California 9.0 276 91 40.6
## Colorado 7.9 204 78 38.7
## Connecticut 3.3 110 77 11.1
## Delaware 5.9 238 72 15.8
## Florida 15.4 335 80 31.9
## Georgia 17.4 211 60 25.8
## Hawaii 5.3 46 83 20.2
## Idaho 2.6 120 54 14.2
## Illinois 10.4 249 83 24.0
## Indiana 7.2 113 65 21.0
## Iowa 2.2 56 57 11.3
## Kansas 6.0 115 66 18.0
## Kentucky 9.7 109 52 16.3
## Louisiana 15.4 249 66 22.2
## Maine 2.1 83 51 7.8
## Maryland 11.3 300 67 27.8
## Massachusetts 4.4 149 85 16.3
## Michigan 12.1 255 74 35.1
## Minnesota 2.7 72 66 14.9
## Mississippi 16.1 259 44 17.1
## Missouri 9.0 178 70 28.2
## Montana 6.0 109 53 16.4
## Nebraska 4.3 102 62 16.5
## Nevada 12.2 252 81 46.0
## New Hampshire 2.1 57 56 9.5
## New Jersey 7.4 159 89 18.8
## New Mexico 11.4 285 70 32.1
## New York 11.1 254 86 26.1
## North Carolina 13.0 337 45 16.1
## North Dakota 0.8 45 44 7.3
## Ohio 7.3 120 75 21.4
## Oklahoma 6.6 151 68 20.0
## Oregon 4.9 159 67 29.3
## Pennsylvania 6.3 106 72 14.9
## Rhode Island 3.4 174 87 8.3
## South Carolina 14.4 279 48 22.5
## South Dakota 3.8 86 45 12.8
## Tennessee 13.2 188 59 26.9
## Texas 12.7 201 80 25.5
## Utah 3.2 120 80 22.9
## Vermont 2.2 48 32 11.2
## Virginia 8.5 156 63 20.7
## Washington 4.0 145 73 26.2
## West Virginia 5.7 81 39 9.3
## Wisconsin 2.6 53 66 10.8
## Wyoming 6.8 161 60 15.6
#View(datos)
str(datos)
## 'data.frame': 50 obs. of 4 variables:
## $ Asesinatos : num 13.2 10 8.1 8.8 9 7.9 3.3 5.9 15.4 17.4 ...
## $ Asaltos : int 236 263 294 190 276 204 110 238 335 211 ...
## $ Poblac_urbanana: int 58 48 80 50 91 78 77 72 80 60 ...
## $ Violaciones : num 21.2 44.5 31 19.5 40.6 38.7 11.1 15.8 31.9 25.8 ...
head(datos)
## Asesinatos Asaltos Poblac_urbanana Violaciones
## Alabama 13.2 236 58 21.2
## Alaska 10.0 263 48 44.5
## Arizona 8.1 294 80 31.0
## Arkansas 8.8 190 50 19.5
## California 9.0 276 91 40.6
## Colorado 7.9 204 78 38.7
summary(datos)
## Asesinatos Asaltos Poblac_urbanana Violaciones
## Min. : 0.800 Min. : 45.0 Min. :32.00 Min. : 7.30
## 1st Qu.: 4.075 1st Qu.:109.0 1st Qu.:54.50 1st Qu.:15.07
## Median : 7.250 Median :159.0 Median :66.00 Median :20.10
## Mean : 7.788 Mean :170.8 Mean :65.54 Mean :21.23
## 3rd Qu.:11.250 3rd Qu.:249.0 3rd Qu.:77.75 3rd Qu.:26.18
## Max. :17.400 Max. :337.0 Max. :91.00 Max. :46.00
cor(datos)
## Asesinatos Asaltos Poblac_urbanana Violaciones
## Asesinatos 1.00000000 0.8018733 0.06957262 0.5635788
## Asaltos 0.80187331 1.0000000 0.25887170 0.6652412
## Poblac_urbanana 0.06957262 0.2588717 1.00000000 0.4113412
## Violaciones 0.56357883 0.6652412 0.41134124 1.0000000
# Prueba de Esfericidad de Bartlett
cortest.bartlett(cor(datos),n=dim(datos))
## $chisq
## [1] 88.288147 1.570963
##
## $p.value
## [1] 6.868423e-17 9.546421e-01
##
## $df
## [1] 6
# Indicador Kaiser-Meyer-Olkinn KMO y MSA
KMO(datos)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = datos)
## Overall MSA = 0.65
## MSA for each item =
## Asesinatos Asaltos Poblac_urbanana Violaciones
## 0.62 0.64 0.50 0.78
modelo <- prcomp(datos)
modelo
## Standard deviations (1, .., p=4):
## [1] 83.732400 14.212402 6.489426 2.482790
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## Asesinatos 0.04170432 -0.04482166 0.07989066 -0.99492173
## Asaltos 0.99522128 -0.05876003 -0.06756974 0.03893830
## Poblac_urbanana 0.04633575 0.97685748 -0.20054629 -0.05816914
## Violaciones 0.07515550 0.20071807 0.97408059 0.07232502
# Grafico
biplot(modelo)
# observando los resultados de 2 componentes
result<- PCA(datos,scale.unit = T, ncp=2,graph = T)
# PCAshiny(datos)