# 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("Estudiantes.csv", header = T, sep = ";", row.names = 1)
datos
## Matematicas Ciencias Español Historia EdFidica
## Lucia 7.0 6.5 9.2 8.6 8.0
## Pedro 7.5 9.4 7.3 7.0 7.0
## Ines 7.6 9.2 8.0 8.0 7.5
## Luis 5.0 6.5 6.5 7.0 9.0
## Andres 6.0 6.0 7.8 8.9 7.3
## Ana 7.8 9.6 7.7 8.0 6.5
## Carlos 6.3 6.4 8.2 9.0 7.2
## Jose 7.9 9.7 7.5 8.0 6.0
## Sonia 6.0 6.0 6.5 5.5 8.7
## Maria 6.8 7.2 8.7 9.0 7.0
#View(datos)
str(datos)
## 'data.frame': 10 obs. of 5 variables:
## $ Matematicas: num 7 7.5 7.6 5 6 7.8 6.3 7.9 6 6.8
## $ Ciencias : num 6.5 9.4 9.2 6.5 6 9.6 6.4 9.7 6 7.2
## $ Español : num 9.2 7.3 8 6.5 7.8 7.7 8.2 7.5 6.5 8.7
## $ Historia : num 8.6 7 8 7 8.9 8 9 8 5.5 9
## $ EdFidica : num 8 7 7.5 9 7.3 6.5 7.2 6 8.7 7
head(datos)
## Matematicas Ciencias Español Historia EdFidica
## Lucia 7.0 6.5 9.2 8.6 8.0
## Pedro 7.5 9.4 7.3 7.0 7.0
## Ines 7.6 9.2 8.0 8.0 7.5
## Luis 5.0 6.5 6.5 7.0 9.0
## Andres 6.0 6.0 7.8 8.9 7.3
## Ana 7.8 9.6 7.7 8.0 6.5
summary(datos)
## Matematicas Ciencias Español Historia EdFidica
## Min. :5.000 Min. :6.000 Min. :6.50 Min. :5.500 Min. :6.000
## 1st Qu.:6.075 1st Qu.:6.425 1st Qu.:7.35 1st Qu.:7.250 1st Qu.:7.000
## Median :6.900 Median :6.850 Median :7.75 Median :8.000 Median :7.250
## Mean :6.790 Mean :7.650 Mean :7.74 Mean :7.900 Mean :7.420
## 3rd Qu.:7.575 3rd Qu.:9.350 3rd Qu.:8.15 3rd Qu.:8.825 3rd Qu.:7.875
## Max. :7.900 Max. :9.700 Max. :9.20 Max. :9.000 Max. :9.000
cor(datos)
## Matematicas Ciencias Español Historia EdFidica
## Matematicas 1.0000000 0.85407878 0.38457424 0.20719425 -0.7871627
## Ciencias 0.8540788 1.00000000 -0.02005218 -0.02153942 -0.6877206
## Español 0.3845742 -0.02005218 1.00000000 0.82091619 -0.3655434
## Historia 0.2071943 -0.02153942 0.82091619 1.00000000 -0.5080013
## EdFidica -0.7871627 -0.68772056 -0.36554342 -0.50800132 1.0000000
# Prueba de Esfericidad de Bartlett
cortest.bartlett(cor(datos),n=dim(datos))
## $chisq
## [1] 41.150599 9.496292
##
## $p.value
## [1] 1.061203e-05 4.857378e-01
##
## $df
## [1] 10
# Indicador Kaiser-Meyer-Olkinn KMO y MSA
KMO(datos)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = datos)
## Overall MSA = 0.3
## MSA for each item =
## Matematicas Ciencias Español Historia EdFidica
## 0.33 0.34 0.23 0.25 0.37
modelo <- prcomp(datos)
modelo
## Standard deviations (1, .., p=5):
## [1] 1.97155026 1.41162417 0.54854909 0.40981080 0.09255745
##
## Rotation (n x k) = (5 x 5):
## PC1 PC2 PC3 PC4 PC5
## Matematicas -0.4554991 -0.0301873 -0.47296282 -0.39587804 -0.6412457
## Ciencias -0.7730822 0.3366382 0.04147109 0.49953935 0.1943173
## Español -0.1117975 -0.5349732 -0.62844982 0.02458048 0.5529481
## Historia -0.1416005 -0.7479026 0.35163283 0.39973889 -0.3703433
## EdFidica 0.4028835 0.2005213 -0.50595602 0.65828993 -0.3288450
# Grafico
biplot(modelo)
# observando los resultados de 2 componentes
result<- PCA(datos,scale.unit = T, ncp=2,graph = T)
# PCAshiny(datos)