#trabajando con datos imputadosya fui
USArrests <- read.csv("mcs.csv",head=T,sep=",")
head(USArrests)
## acidezfija acidezvolátil ácidocÃtrico azúcarresidual cloruros
## 1 7.0 0.27 0.36 20.7 0.045
## 2 6.3 0.30 0.34 1.6 0.049
## 3 8.1 0.28 0.40 6.9 0.050
## 4 7.2 0.23 0.32 8.5 0.058
## 5 7.2 0.23 0.32 8.5 0.058
## 6 8.1 0.28 0.40 6.9 0.050
## dióxidodeazufrelibre dióxidodeazufretotal densidad pH sulfatos alcohol
## 1 45 170 1.0010 3.00 0.45 8.8
## 2 14 132 0.9940 3.30 0.49 9.5
## 3 30 97 0.9951 3.26 0.44 10.1
## 4 47 186 0.9956 3.19 0.40 9.9
## 5 47 186 0.9956 3.19 0.40 9.9
## 6 30 97 0.9951 3.26 0.44 10.1
## calidad
## 1 6
## 2 6
## 3 6
## 4 6
## 5 6
## 6 6
str(USArrests)
## 'data.frame': 4898 obs. of 12 variables:
## $ acidezfija : num 7 6.3 8.1 7.2 7.2 8.1 6.2 7 6.3 8.1 ...
## $ acidezvolátil : num 0.27 0.3 0.28 0.23 0.23 0.28 0.32 0.27 0.3 0.22 ...
## $ ácidocÃtrico : num 0.36 0.34 0.4 0.32 0.32 0.4 0.16 0.36 0.34 0.43 ...
## $ azúcarresidual : num 20.7 1.6 6.9 8.5 8.5 6.9 7 20.7 1.6 1.5 ...
## $ cloruros : num 0.045 0.049 0.05 0.058 0.058 0.05 0.045 0.045 0.049 0.044 ...
## $ dióxidodeazufrelibre: num 45 14 30 47 47 30 30 45 14 28 ...
## $ dióxidodeazufretotal: num 170 132 97 186 186 97 136 170 132 129 ...
## $ densidad : num 1.001 0.994 0.995 0.996 0.996 ...
## $ pH : num 3 3.3 3.26 3.19 3.19 3.26 3.18 3 3.3 3.22 ...
## $ sulfatos : num 0.45 0.49 0.44 0.4 0.4 0.44 0.47 0.45 0.49 0.45 ...
## $ alcohol : num 8.8 9.5 10.1 9.9 9.9 10.1 9.6 8.8 9.5 11 ...
## $ calidad : int 6 6 6 6 6 6 6 6 6 6 ...
boxplot(USArrests,col=11:15)
par(mfrow=c(1,1))
hist(USArrests$acidezfija, freq = TRUE, main = "Histograma de frecuencias",
xlab = "acidezfija", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$acidezvolátil, freq = TRUE, main = "Histograma de frecuencias",
xlab = "acidezvolátil", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$ácidocÃtrico, freq = TRUE, main = "Histograma de frecuencias",
xlab = "ácidocÃtrico", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$azúcarresidual, freq = TRUE, main = "Histograma de frecuencias",
xlab = "azúcarresidual", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$cloruros, freq = TRUE, main = "Histograma de frecuencias",
xlab = "cloruros", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$dióxidodeazufrelibre, freq = TRUE, main = "Histograma de frecuencias",
xlab = "dióxidodeazufrelibre", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$dióxidodeazufretotal, freq = TRUE, main = "Histograma de frecuencias",
xlab = "dióxidodeazufretotal", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$densidad, freq = TRUE, main = "Histograma de frecuencias",
xlab = "densidad", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$pH, freq = TRUE, main = "Histograma de frecuencias",
xlab = "pH", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$sulfatos, freq = TRUE, main = "Histograma de frecuencias",
xlab = "sulfatos", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$alcohol, freq = TRUE, main = "Histograma de frecuencias",
xlab = "alcohol", ylab = "Frecuencia", col = "#009ACD")
hist(USArrests$calidad, freq = TRUE, main = "Histograma de frecuencias",
xlab = "calidad", ylab = "Frecuencia", col = "#009ACD")
#Histogramas escaladas
require(psych)
## Loading required package: psych
## Warning: package 'psych' was built under R version 4.0.3
multi.hist(x = USArrests,dcol = c("blue", "red"), dlty = c("dotted", "solid"),
main = "")
summary(USArrests)
## acidezfija acidezvolátil ácidocÃtrico azúcarresidual
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.600
## 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700 1st Qu.: 1.700
## Median : 6.800 Median :0.2600 Median :0.3200 Median : 5.200
## Mean : 6.855 Mean :0.2782 Mean :0.3342 Mean : 6.391
## 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900 3rd Qu.: 9.900
## Max. :14.200 Max. :1.1000 Max. :1.6600 Max. :65.800
## cloruros dióxidodeazufrelibre dióxidodeazufretotal densidad
## Min. :0.00900 Min. : 2.00 Min. : 9.0 Min. :0.9871
## 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0 1st Qu.:0.9917
## Median :0.04300 Median : 34.00 Median :134.0 Median :0.9937
## Mean :0.04577 Mean : 35.31 Mean :138.4 Mean :0.9940
## 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0 3rd Qu.:0.9961
## Max. :0.34600 Max. :289.00 Max. :440.0 Max. :1.0390
## pH sulfatos alcohol calidad
## Min. :2.720 Min. :0.2200 Min. : 8.00 Min. :3.000
## 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50 1st Qu.:5.000
## Median :3.180 Median :0.4700 Median :10.40 Median :6.000
## Mean :3.188 Mean :0.4898 Mean :10.51 Mean :5.878
## 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40 3rd Qu.:6.000
## Max. :3.820 Max. :1.0800 Max. :14.20 Max. :9.000
library(psych)
describe(USArrests)
## vars n mean sd median trimmed mad min max
## acidezfija 1 4898 6.85 0.84 6.80 6.82 0.74 3.80 14.20
## acidezvolátil 2 4898 0.28 0.10 0.26 0.27 0.09 0.08 1.10
## ácidocÃtrico 3 4898 0.33 0.12 0.32 0.33 0.09 0.00 1.66
## azúcarresidual 4 4898 6.39 5.07 5.20 5.80 5.34 0.60 65.80
## cloruros 5 4898 0.05 0.02 0.04 0.04 0.01 0.01 0.35
## dióxidodeazufrelibre 6 4898 35.31 17.01 34.00 34.36 16.31 2.00 289.00
## dióxidodeazufretotal 7 4898 138.36 42.50 134.00 136.96 43.00 9.00 440.00
## densidad 8 4898 0.99 0.00 0.99 0.99 0.00 0.99 1.04
## pH 9 4898 3.19 0.15 3.18 3.18 0.15 2.72 3.82
## sulfatos 10 4898 0.49 0.11 0.47 0.48 0.10 0.22 1.08
## alcohol 11 4898 10.51 1.23 10.40 10.43 1.48 8.00 14.20
## calidad 12 4898 5.88 0.89 6.00 5.85 1.48 3.00 9.00
## range skew kurtosis se
## acidezfija 10.40 0.65 2.17 0.01
## acidezvolátil 1.02 1.58 5.08 0.00
## ácidocÃtrico 1.66 1.28 6.16 0.00
## azúcarresidual 65.20 1.08 3.46 0.07
## cloruros 0.34 5.02 37.51 0.00
## dióxidodeazufrelibre 287.00 1.41 11.45 0.24
## dióxidodeazufretotal 431.00 0.39 0.57 0.61
## densidad 0.05 0.98 9.78 0.00
## pH 1.10 0.46 0.53 0.00
## sulfatos 0.86 0.98 1.59 0.00
## alcohol 6.20 0.49 -0.70 0.02
## calidad 6.00 0.16 0.21 0.01
summary(USArrests)
## acidezfija acidezvolátil ácidocÃtrico azúcarresidual
## Min. : 3.800 Min. :0.0800 Min. :0.0000 Min. : 0.600
## 1st Qu.: 6.300 1st Qu.:0.2100 1st Qu.:0.2700 1st Qu.: 1.700
## Median : 6.800 Median :0.2600 Median :0.3200 Median : 5.200
## Mean : 6.855 Mean :0.2782 Mean :0.3342 Mean : 6.391
## 3rd Qu.: 7.300 3rd Qu.:0.3200 3rd Qu.:0.3900 3rd Qu.: 9.900
## Max. :14.200 Max. :1.1000 Max. :1.6600 Max. :65.800
## cloruros dióxidodeazufrelibre dióxidodeazufretotal densidad
## Min. :0.00900 Min. : 2.00 Min. : 9.0 Min. :0.9871
## 1st Qu.:0.03600 1st Qu.: 23.00 1st Qu.:108.0 1st Qu.:0.9917
## Median :0.04300 Median : 34.00 Median :134.0 Median :0.9937
## Mean :0.04577 Mean : 35.31 Mean :138.4 Mean :0.9940
## 3rd Qu.:0.05000 3rd Qu.: 46.00 3rd Qu.:167.0 3rd Qu.:0.9961
## Max. :0.34600 Max. :289.00 Max. :440.0 Max. :1.0390
## pH sulfatos alcohol calidad
## Min. :2.720 Min. :0.2200 Min. : 8.00 Min. :3.000
## 1st Qu.:3.090 1st Qu.:0.4100 1st Qu.: 9.50 1st Qu.:5.000
## Median :3.180 Median :0.4700 Median :10.40 Median :6.000
## Mean :3.188 Mean :0.4898 Mean :10.51 Mean :5.878
## 3rd Qu.:3.280 3rd Qu.:0.5500 3rd Qu.:11.40 3rd Qu.:6.000
## Max. :3.820 Max. :1.0800 Max. :14.20 Max. :9.000
library(psych)
describe(USArrests)
## vars n mean sd median trimmed mad min max
## acidezfija 1 4898 6.85 0.84 6.80 6.82 0.74 3.80 14.20
## acidezvolátil 2 4898 0.28 0.10 0.26 0.27 0.09 0.08 1.10
## ácidocÃtrico 3 4898 0.33 0.12 0.32 0.33 0.09 0.00 1.66
## azúcarresidual 4 4898 6.39 5.07 5.20 5.80 5.34 0.60 65.80
## cloruros 5 4898 0.05 0.02 0.04 0.04 0.01 0.01 0.35
## dióxidodeazufrelibre 6 4898 35.31 17.01 34.00 34.36 16.31 2.00 289.00
## dióxidodeazufretotal 7 4898 138.36 42.50 134.00 136.96 43.00 9.00 440.00
## densidad 8 4898 0.99 0.00 0.99 0.99 0.00 0.99 1.04
## pH 9 4898 3.19 0.15 3.18 3.18 0.15 2.72 3.82
## sulfatos 10 4898 0.49 0.11 0.47 0.48 0.10 0.22 1.08
## alcohol 11 4898 10.51 1.23 10.40 10.43 1.48 8.00 14.20
## calidad 12 4898 5.88 0.89 6.00 5.85 1.48 3.00 9.00
## range skew kurtosis se
## acidezfija 10.40 0.65 2.17 0.01
## acidezvolátil 1.02 1.58 5.08 0.00
## ácidocÃtrico 1.66 1.28 6.16 0.00
## azúcarresidual 65.20 1.08 3.46 0.07
## cloruros 0.34 5.02 37.51 0.00
## dióxidodeazufrelibre 287.00 1.41 11.45 0.24
## dióxidodeazufretotal 431.00 0.39 0.57 0.61
## densidad 0.05 0.98 9.78 0.00
## pH 1.10 0.46 0.53 0.00
## sulfatos 0.86 0.98 1.59 0.00
## alcohol 6.20 0.49 -0.70 0.02
## calidad 6.00 0.16 0.21 0.01
#Obteniendo solo promedios
#obteniendo solo las medias
apply(X = USArrests, MARGIN = 2, FUN = mean)
## acidezfija acidezvolátil ácidocÃtrico
## 6.85478767 0.27824112 0.33419151
## azúcarresidual cloruros dióxidodeazufrelibre
## 6.39141486 0.04577236 35.30808493
## dióxidodeazufretotal densidad pH
## 138.36065741 0.99402738 3.18826664
## sulfatos alcohol calidad
## 0.48984688 10.51426705 5.87790935
#Obteniendo varianzas
#obteniendo solo las varianzas
apply(X = USArrests, MARGIN = 2, FUN = var)
## acidezfija acidezvolátil ácidocÃtrico
## 7.121136e-01 1.015954e-02 1.464579e-02
## azúcarresidual cloruros dióxidodeazufrelibre
## 2.572577e+01 4.773337e-04 2.892427e+02
## dióxidodeazufretotal densidad pH
## 1.806085e+03 8.945524e-06 2.280118e-02
## sulfatos alcohol calidad
## 1.302471e-02 1.514427e+00 7.843557e-01
#Mostrando las correlaciones
corr.test(USArrests) # correlaciones y pruebas de significancia
## Warning in abbreviate(rownames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(rownames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(rownames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(rownames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(colnames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(colnames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(colnames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Warning in abbreviate(colnames(r), minlength = minlength): abreviatura utilizada
## con caracteres no ASCII
## Call:corr.test(x = USArrests)
## Correlation matrix
## acidezfija acidezvolátil ácidocÃtrico azúcarresidual
## acidezfija 1.00 -0.02 0.29 0.09
## acidezvolátil -0.02 1.00 -0.15 0.06
## ácidocÃtrico 0.29 -0.15 1.00 0.09
## azúcarresidual 0.09 0.06 0.09 1.00
## cloruros 0.02 0.07 0.11 0.09
## dióxidodeazufrelibre -0.05 -0.10 0.09 0.30
## dióxidodeazufretotal 0.09 0.09 0.12 0.40
## densidad 0.27 0.03 0.15 0.84
## pH -0.43 -0.03 -0.16 -0.19
## sulfatos -0.02 -0.04 0.06 -0.03
## alcohol -0.12 0.07 -0.08 -0.45
## calidad -0.11 -0.19 -0.01 -0.10
## cloruros dióxidodeazufrelibre dióxidodeazufretotal
## acidezfija 0.02 -0.05 0.09
## acidezvolátil 0.07 -0.10 0.09
## ácidocÃtrico 0.11 0.09 0.12
## azúcarresidual 0.09 0.30 0.40
## cloruros 1.00 0.10 0.20
## dióxidodeazufrelibre 0.10 1.00 0.62
## dióxidodeazufretotal 0.20 0.62 1.00
## densidad 0.26 0.29 0.53
## pH -0.09 0.00 0.00
## sulfatos 0.02 0.06 0.13
## alcohol -0.36 -0.25 -0.45
## calidad -0.21 0.01 -0.17
## densidad pH sulfatos alcohol calidad
## acidezfija 0.27 -0.43 -0.02 -0.12 -0.11
## acidezvolátil 0.03 -0.03 -0.04 0.07 -0.19
## ácidocÃtrico 0.15 -0.16 0.06 -0.08 -0.01
## azúcarresidual 0.84 -0.19 -0.03 -0.45 -0.10
## cloruros 0.26 -0.09 0.02 -0.36 -0.21
## dióxidodeazufrelibre 0.29 0.00 0.06 -0.25 0.01
## dióxidodeazufretotal 0.53 0.00 0.13 -0.45 -0.17
## densidad 1.00 -0.09 0.07 -0.78 -0.31
## pH -0.09 1.00 0.16 0.12 0.10
## sulfatos 0.07 0.16 1.00 -0.02 0.05
## alcohol -0.78 0.12 -0.02 1.00 0.44
## calidad -0.31 0.10 0.05 0.44 1.00
## Sample Size
## [1] 4898
## Probability values (Entries above the diagonal are adjusted for multiple tests.)
## acidezfija acidezvolátil ácidocÃtrico azúcarresidual
## acidezfija 0.00 0.96 0.00 0.00
## acidezvolátil 0.11 0.00 0.00 0.00
## ácidocÃtrico 0.00 0.00 0.00 0.00
## azúcarresidual 0.00 0.00 0.00 0.00
## cloruros 0.11 0.00 0.00 0.00
## dióxidodeazufrelibre 0.00 0.00 0.00 0.00
## dióxidodeazufretotal 0.00 0.00 0.00 0.00
## densidad 0.00 0.06 0.00 0.00
## pH 0.00 0.03 0.00 0.00
## sulfatos 0.23 0.01 0.00 0.06
## alcohol 0.00 0.00 0.00 0.00
## calidad 0.00 0.00 0.52 0.00
## cloruros dióxidodeazufrelibre dióxidodeazufretotal
## acidezfija 0.96 0.01 0.00
## acidezvolátil 0.00 0.00 0.00
## ácidocÃtrico 0.00 0.00 0.00
## azúcarresidual 0.00 0.00 0.00
## cloruros 0.00 0.00 0.00
## dióxidodeazufrelibre 0.00 0.00 0.00
## dióxidodeazufretotal 0.00 0.00 0.00
## densidad 0.00 0.00 0.00
## pH 0.00 0.97 0.87
## sulfatos 0.24 0.00 0.00
## alcohol 0.00 0.00 0.00
## calidad 0.00 0.57 0.00
## densidad pH sulfatos alcohol calidad
## acidezfija 0.00 0.00 1.00 0 0
## acidezvolátil 0.64 0.31 0.16 0 0
## ácidocÃtrico 0.00 0.00 0.00 0 1
## azúcarresidual 0.00 0.00 0.64 0 0
## cloruros 0.00 0.00 1.00 0 0
## dióxidodeazufrelibre 0.00 1.00 0.00 0 1
## dióxidodeazufretotal 0.00 1.00 0.00 0 0
## densidad 0.00 0.00 0.00 0 0
## pH 0.00 0.00 0.00 0 0
## sulfatos 0.00 0.00 0.00 1 0
## alcohol 0.00 0.00 0.22 0 0
## calidad 0.00 0.00 0.00 0 0
##
## To see confidence intervals of the correlations, print with the short=FALSE option
cor.plot(cor(USArrests)) # grafico de calor
#Prueba de Bartlett
library(psych)
cortest.bartlett(cor(USArrests),n=dim(USArrests))
## $chisq
## [1] 26470.70416 33.36681
##
## $p.value
## [1] 0.0000000 0.9997282
##
## $df
## [1] 66
#Prueba KMO.
# Indicador Kaiser-Meyer-Olkinn KMO y MSA
KMO(USArrests)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = USArrests)
## Overall MSA = 0.4
## MSA for each item =
## acidezfija acidezvolátil ácidocÃtrico
## 0.17 0.30 0.72
## azúcarresidual cloruros dióxidodeazufrelibre
## 0.33 0.70 0.59
## dióxidodeazufretotal densidad pH
## 0.72 0.42 0.16
## sulfatos alcohol calidad
## 0.19 0.41 0.78
pca <- prcomp(USArrests, scale = TRUE)
names(pca)
## [1] "sdev" "rotation" "center" "scale" "x"
head(pca$rotation)
## PC1 PC2 PC3 PC4
## acidezfija -0.15690447 0.56066866 -0.20738436 0.03373494
## acidezvolátil -0.02428722 0.01606694 0.52491466 -0.13119747
## ácidocÃtrico -0.13294430 0.28938115 -0.44635554 0.32953335
## azúcarresidual -0.40605288 -0.03882402 -0.03384313 -0.41615630
## cloruros -0.21754400 0.03691144 0.21471269 0.50961203
## dióxidodeazufrelibre -0.27471931 -0.34554881 -0.31297088 -0.14892788
## PC5 PC6 PC7 PC8 PC9
## acidezfija -0.24413933 0.1058562 0.2235592 0.1304131 -0.63145048
## acidezvolátil -0.70298193 -0.1237047 -0.2236360 -0.2296067 -0.03159628
## ácidocÃtrico -0.06510579 -0.1319587 -0.1203713 -0.6914187 0.24949503
## azúcarresidual 0.01610213 0.2899185 -0.3386086 -0.1132940 0.17730336
## cloruros 0.17829248 -0.4093173 -0.5522550 0.2113973 -0.17916182
## dióxidodeazufrelibre -0.11117214 -0.4880851 0.2240711 0.1288311 0.10184710
## PC10 PC11 PC12
## acidezfija 0.2008712 -0.10411772 0.170792295
## acidezvolátil -0.1417588 -0.27002270 0.013376718
## ácidocÃtrico -0.1063291 -0.05395597 0.009648802
## azúcarresidual 0.3742749 0.17987291 0.493565139
## cloruros 0.2355278 0.09108849 0.025168952
## dióxidodeazufrelibre 0.3273341 -0.49921348 -0.029475198
dim(pca$rotation)
## [1] 12 12
#Obteniendo las medias originales y las estandarizadas
pca$center
## acidezfija acidezvolátil ácidocÃtrico
## 6.85478767 0.27824112 0.33419151
## azúcarresidual cloruros dióxidodeazufrelibre
## 6.39141486 0.04577236 35.30808493
## dióxidodeazufretotal densidad pH
## 138.36065741 0.99402738 3.18826664
## sulfatos alcohol calidad
## 0.48984688 10.51426705 5.87790935
pca$scale
## acidezfija acidezvolátil ácidocÃtrico
## 0.843868228 0.100794548 0.121019804
## azúcarresidual cloruros dióxidodeazufrelibre
## 5.072057784 0.021847968 17.007137325
## dióxidodeazufretotal densidad pH
## 42.498064554 0.002990907 0.151000600
## sulfatos alcohol calidad
## 0.114125834 1.230620568 0.885638575
summary(pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.8294 1.2594 1.1710 1.04157 0.98756 0.96890 0.8771
## Proportion of Variance 0.2789 0.1322 0.1143 0.09041 0.08127 0.07823 0.0641
## Cumulative Proportion 0.2789 0.4111 0.5253 0.61573 0.69701 0.77524 0.8393
## PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.85082 0.74599 0.58561 0.53302 0.14307
## Proportion of Variance 0.06032 0.04638 0.02858 0.02368 0.00171
## Cumulative Proportion 0.89967 0.94604 0.97462 0.99829 1.00000
pca
## Standard deviations (1, .., p=12):
## [1] 1.8293903 1.2594008 1.1709706 1.0415668 0.9875644 0.9688978 0.8770680
## [8] 0.8508195 0.7459900 0.5856051 0.5330248 0.1430703
##
## Rotation (n x k) = (12 x 12):
## PC1 PC2 PC3 PC4
## acidezfija -0.15690447 0.56066866 -0.20738436 0.03373494
## acidezvolátil -0.02428722 0.01606694 0.52491466 -0.13119747
## ácidocÃtrico -0.13294430 0.28938115 -0.44635554 0.32953335
## azúcarresidual -0.40605288 -0.03882402 -0.03384313 -0.41615630
## cloruros -0.21754400 0.03691144 0.21471269 0.50961203
## dióxidodeazufrelibre -0.27471931 -0.34554881 -0.31297088 -0.14892788
## dióxidodeazufretotal -0.39044148 -0.27232605 -0.12479447 -0.02161841
## densidad -0.50129557 -0.01773344 0.03196758 -0.10386393
## pH 0.13003701 -0.56714503 0.06848384 0.20410995
## sulfatos -0.03364168 -0.24826266 -0.22699505 0.51924489
## alcohol 0.44279498 0.01698188 -0.15887556 -0.13438871
## calidad 0.22713722 -0.14603134 -0.48884718 -0.27820033
## PC5 PC6 PC7 PC8
## acidezfija -0.24413933 0.105856235 0.22355921 0.13041311
## acidezvolátil -0.70298193 -0.123704688 -0.22363601 -0.22960669
## ácidocÃtrico -0.06510579 -0.131958661 -0.12037133 -0.69141866
## azúcarresidual 0.01610213 0.289918546 -0.33860858 -0.11329401
## cloruros 0.17829248 -0.409317266 -0.55225504 0.21139734
## dióxidodeazufrelibre -0.11117214 -0.488085145 0.22407108 0.12883115
## dióxidodeazufretotal -0.27144774 -0.272493820 0.20375343 0.01290262
## densidad 0.07834373 0.326008106 -0.12313568 -0.08667076
## pH 0.11270171 0.192688838 0.07704001 -0.47796137
## sulfatos -0.45623099 0.479811894 -0.04462167 0.33642752
## alcohol -0.30855451 -0.135443327 -0.09801169 -0.08899029
## calidad -0.04112191 -0.005524396 -0.58434519 0.14444197
## PC9 PC10 PC11 PC12
## acidezfija -0.63145048 0.20087123 -0.10411772 0.170792295
## acidezvolátil -0.03159628 -0.14175876 -0.27002270 0.013376718
## ácidocÃtrico 0.24949503 -0.10632912 -0.05395597 0.009648802
## azúcarresidual 0.17730336 0.37427490 0.17987291 0.493565139
## cloruros -0.17916182 0.23552782 0.09108849 0.025168952
## dióxidodeazufrelibre 0.10184710 0.32733415 -0.49921348 -0.029475198
## dióxidodeazufretotal -0.17800832 -0.34735757 0.64355326 0.035060193
## densidad -0.12538636 0.04349161 -0.06686042 -0.761184485
## pH -0.52031593 0.18375599 -0.07911267 0.141842640
## sulfatos 0.23662489 0.05519364 -0.04102077 0.042787387
## alcohol 0.01278298 0.57530003 0.41895440 -0.350156811
## calidad -0.29970621 -0.36771605 -0.14620225 -0.016069252
head(pca$x)
## PC1 PC2 PC3 PC4 PC5 PC6
## [1,] -3.5429563 0.3550511 -0.3257996 -1.7352335 0.4008275 0.8916788
## [2,] 0.6127372 -0.2893815 0.8163511 0.8486472 0.5273716 0.4664336
## [3,] -0.1423793 1.1679020 -0.1530525 0.1909000 0.3061774 0.4934076
## [4,] -1.3793842 -0.1995669 -0.3244634 -0.4087818 0.5199860 -0.7688398
## [5,] -1.3793842 -0.1995669 -0.3244634 -0.4087818 0.5199860 -0.7688398
## [6,] -0.1423793 1.1679020 -0.1530525 0.1909000 0.3061774 0.4934076
## PC7 PC8 PC9 PC10 PC11 PC12
## [1,] -0.9368043 0.06998381 0.5938390 -0.000134629 0.04482358 -0.04961423
## [2,] -0.2156768 -0.45274357 -0.3100269 -1.233863444 -0.04319005 -0.14142681
## [3,] -0.1841590 -0.56598395 -1.1131973 0.389541143 -0.82737924 0.17831140
## [4,] 0.0848360 0.16698331 -0.7344227 -0.070773454 0.36389391 0.04092464
## [5,] 0.0848360 0.16698331 -0.7344227 -0.070773454 0.36389391 0.04092464
## [6,] -0.1841590 -0.56598395 -1.1131973 0.389541143 -0.82737924 0.17831140
#vemos componentes para casos:
dim(pca$x)
## [1] 4898 12
pca$center
## acidezfija acidezvolátil ácidocÃtrico
## 6.85478767 0.27824112 0.33419151
## azúcarresidual cloruros dióxidodeazufrelibre
## 6.39141486 0.04577236 35.30808493
## dióxidodeazufretotal densidad pH
## 138.36065741 0.99402738 3.18826664
## sulfatos alcohol calidad
## 0.48984688 10.51426705 5.87790935
pca$scale
## acidezfija acidezvolátil ácidocÃtrico
## 0.843868228 0.100794548 0.121019804
## azúcarresidual cloruros dióxidodeazufrelibre
## 5.072057784 0.021847968 17.007137325
## dióxidodeazufretotal densidad pH
## 42.498064554 0.002990907 0.151000600
## sulfatos alcohol calidad
## 0.114125834 1.230620568 0.885638575
summary(pca)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 1.8294 1.2594 1.1710 1.04157 0.98756 0.96890 0.8771
## Proportion of Variance 0.2789 0.1322 0.1143 0.09041 0.08127 0.07823 0.0641
## Cumulative Proportion 0.2789 0.4111 0.5253 0.61573 0.69701 0.77524 0.8393
## PC8 PC9 PC10 PC11 PC12
## Standard deviation 0.85082 0.74599 0.58561 0.53302 0.14307
## Proportion of Variance 0.06032 0.04638 0.02858 0.02368 0.00171
## Cumulative Proportion 0.89967 0.94604 0.97462 0.99829 1.00000
pca
## Standard deviations (1, .., p=12):
## [1] 1.8293903 1.2594008 1.1709706 1.0415668 0.9875644 0.9688978 0.8770680
## [8] 0.8508195 0.7459900 0.5856051 0.5330248 0.1430703
##
## Rotation (n x k) = (12 x 12):
## PC1 PC2 PC3 PC4
## acidezfija -0.15690447 0.56066866 -0.20738436 0.03373494
## acidezvolátil -0.02428722 0.01606694 0.52491466 -0.13119747
## ácidocÃtrico -0.13294430 0.28938115 -0.44635554 0.32953335
## azúcarresidual -0.40605288 -0.03882402 -0.03384313 -0.41615630
## cloruros -0.21754400 0.03691144 0.21471269 0.50961203
## dióxidodeazufrelibre -0.27471931 -0.34554881 -0.31297088 -0.14892788
## dióxidodeazufretotal -0.39044148 -0.27232605 -0.12479447 -0.02161841
## densidad -0.50129557 -0.01773344 0.03196758 -0.10386393
## pH 0.13003701 -0.56714503 0.06848384 0.20410995
## sulfatos -0.03364168 -0.24826266 -0.22699505 0.51924489
## alcohol 0.44279498 0.01698188 -0.15887556 -0.13438871
## calidad 0.22713722 -0.14603134 -0.48884718 -0.27820033
## PC5 PC6 PC7 PC8
## acidezfija -0.24413933 0.105856235 0.22355921 0.13041311
## acidezvolátil -0.70298193 -0.123704688 -0.22363601 -0.22960669
## ácidocÃtrico -0.06510579 -0.131958661 -0.12037133 -0.69141866
## azúcarresidual 0.01610213 0.289918546 -0.33860858 -0.11329401
## cloruros 0.17829248 -0.409317266 -0.55225504 0.21139734
## dióxidodeazufrelibre -0.11117214 -0.488085145 0.22407108 0.12883115
## dióxidodeazufretotal -0.27144774 -0.272493820 0.20375343 0.01290262
## densidad 0.07834373 0.326008106 -0.12313568 -0.08667076
## pH 0.11270171 0.192688838 0.07704001 -0.47796137
## sulfatos -0.45623099 0.479811894 -0.04462167 0.33642752
## alcohol -0.30855451 -0.135443327 -0.09801169 -0.08899029
## calidad -0.04112191 -0.005524396 -0.58434519 0.14444197
## PC9 PC10 PC11 PC12
## acidezfija -0.63145048 0.20087123 -0.10411772 0.170792295
## acidezvolátil -0.03159628 -0.14175876 -0.27002270 0.013376718
## ácidocÃtrico 0.24949503 -0.10632912 -0.05395597 0.009648802
## azúcarresidual 0.17730336 0.37427490 0.17987291 0.493565139
## cloruros -0.17916182 0.23552782 0.09108849 0.025168952
## dióxidodeazufrelibre 0.10184710 0.32733415 -0.49921348 -0.029475198
## dióxidodeazufretotal -0.17800832 -0.34735757 0.64355326 0.035060193
## densidad -0.12538636 0.04349161 -0.06686042 -0.761184485
## pH -0.52031593 0.18375599 -0.07911267 0.141842640
## sulfatos 0.23662489 0.05519364 -0.04102077 0.042787387
## alcohol 0.01278298 0.57530003 0.41895440 -0.350156811
## calidad -0.29970621 -0.36771605 -0.14620225 -0.016069252
head(pca$x)
## PC1 PC2 PC3 PC4 PC5 PC6
## [1,] -3.5429563 0.3550511 -0.3257996 -1.7352335 0.4008275 0.8916788
## [2,] 0.6127372 -0.2893815 0.8163511 0.8486472 0.5273716 0.4664336
## [3,] -0.1423793 1.1679020 -0.1530525 0.1909000 0.3061774 0.4934076
## [4,] -1.3793842 -0.1995669 -0.3244634 -0.4087818 0.5199860 -0.7688398
## [5,] -1.3793842 -0.1995669 -0.3244634 -0.4087818 0.5199860 -0.7688398
## [6,] -0.1423793 1.1679020 -0.1530525 0.1909000 0.3061774 0.4934076
## PC7 PC8 PC9 PC10 PC11 PC12
## [1,] -0.9368043 0.06998381 0.5938390 -0.000134629 0.04482358 -0.04961423
## [2,] -0.2156768 -0.45274357 -0.3100269 -1.233863444 -0.04319005 -0.14142681
## [3,] -0.1841590 -0.56598395 -1.1131973 0.389541143 -0.82737924 0.17831140
## [4,] 0.0848360 0.16698331 -0.7344227 -0.070773454 0.36389391 0.04092464
## [5,] 0.0848360 0.16698331 -0.7344227 -0.070773454 0.36389391 0.04092464
## [6,] -0.1841590 -0.56598395 -1.1131973 0.389541143 -0.82737924 0.17831140
dim(pca$x)
## [1] 4898 12
par(mfrow=c(1,1))
biplot(x = pca, scale = 0, cex = 0.8, col = c("blue4", "brown3"))
pca$rotation <- -pca$rotation
pca$x <- -pca$x
biplot(x = pca, scale = 0, cex = 0.8, col = c("blue4", "brown3"))
library(ggplot2)
## Warning: package 'ggplot2' was built under R version 4.0.2
##
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
##
## %+%, alpha
pca$sdev^2
## [1] 3.34666886 1.58609030 1.37117206 1.08486150 0.97528337 0.93876295
## [7] 0.76924825 0.72389378 0.55650103 0.34293339 0.28411542 0.02046911
prop_varianza <- pca$sdev^2/sum(pca$sdev^2)
prop_varianza
## [1] 0.278889072 0.132174191 0.114264338 0.090405125 0.081273614 0.078230246
## [7] 0.064104021 0.060324481 0.046375086 0.028577782 0.023676285 0.001705759
ggplot(data = data.frame(prop_varianza, pc = 1:12),aes(x = pc, y =
prop_varianza)) +
geom_col(width = 0.3) +
scale_y_continuous(limits = c(0, 1)) +
theme_bw() +
labs(x = "Componente principal", y = "Proporcion de varianza explicada")
prop_varianza_acum <- cumsum(prop_varianza)
prop_varianza_acum
## [1] 0.2788891 0.4110633 0.5253276 0.6157327 0.6970063 0.7752366 0.8393406
## [8] 0.8996651 0.9460402 0.9746180 0.9982942 1.0000000
ggplot(data = data.frame(prop_varianza_acum, pc = 1:12),
aes(x = pc, y = prop_varianza_acum, group = 1)) +
geom_point() +
geom_line() +
geom_label(aes(label=round(prop_varianza_acum,2)))+
theme_bw() +
labs(x = "Componente principal", y = "Proporcion de varianza explicada a cumulada")
library(psych)
facto=principal(r=USArrests,nfactors=4,rotate="none")
facto$values
## [1] 3.34666886 1.58609030 1.37117206 1.08486150 0.97528337 0.93876295
## [7] 0.76924825 0.72389378 0.55650103 0.34293339 0.28411542 0.02046911
# Grafico de sedimentacion:
plot(facto$values,type="h") # Grafica de Valores propios
facto$communality # Comunalidades
## acidezfija acidezvolátil ácidocÃtrico
## 0.6411845 0.3988635 0.5829618
## azúcarresidual cloruros dióxidodeazufrelibre
## 0.7436393 0.5054999 0.6003300
## dióxidodeazufretotal densidad pH
## 0.6496694 0.8546119 0.6183895
## sulfatos alcohol calidad
## 0.4646925 0.7108334 0.6181171
facto$loadings # Cargas Factoriales, Componentes
##
## Loadings:
## PC1 PC2 PC3 PC4
## acidezfija 0.287 -0.706 0.243
## acidezvolátil -0.615 -0.137
## ácidocÃtrico 0.243 -0.364 0.523 0.343
## azúcarresidual 0.743 -0.433
## cloruros 0.398 -0.251 0.531
## dióxidodeazufrelibre 0.503 0.435 0.366 -0.155
## dióxidodeazufretotal 0.714 0.343 0.146
## densidad 0.917 -0.108
## pH -0.238 0.714 0.213
## sulfatos 0.313 0.266 0.541
## alcohol -0.810 0.186 -0.140
## calidad -0.416 0.184 0.572 -0.290
##
## PC1 PC2 PC3 PC4
## SS loadings 3.347 1.586 1.371 1.085
## Proportion Var 0.279 0.132 0.114 0.090
## Cumulative Var 0.279 0.411 0.525 0.616
# guardando scores
head(facto$scores)
## PC1 PC2 PC3 PC4
## [1,] 1.93668696 -0.2819206 0.2782304 -1.6659838
## [2,] -0.33494068 0.2297772 -0.6971576 0.8147794
## [3,] 0.07782881 -0.9273473 0.1307057 0.1832816
## [4,] 0.75401310 0.1584618 0.2770893 -0.3924682
## [5,] 0.75401310 0.1584618 0.2770893 -0.3924682
## [6,] 0.07782881 -0.9273473 0.1307057 0.1832816
puntosFact <-cbind(USArrests,facto$scores)
head(puntosFact)
## acidezfija acidezvolátil ácidocÃtrico azúcarresidual cloruros
## 1 7.0 0.27 0.36 20.7 0.045
## 2 6.3 0.30 0.34 1.6 0.049
## 3 8.1 0.28 0.40 6.9 0.050
## 4 7.2 0.23 0.32 8.5 0.058
## 5 7.2 0.23 0.32 8.5 0.058
## 6 8.1 0.28 0.40 6.9 0.050
## dióxidodeazufrelibre dióxidodeazufretotal densidad pH sulfatos alcohol
## 1 45 170 1.0010 3.00 0.45 8.8
## 2 14 132 0.9940 3.30 0.49 9.5
## 3 30 97 0.9951 3.26 0.44 10.1
## 4 47 186 0.9956 3.19 0.40 9.9
## 5 47 186 0.9956 3.19 0.40 9.9
## 6 30 97 0.9951 3.26 0.44 10.1
## calidad PC1 PC2 PC3 PC4
## 1 6 1.93668696 -0.2819206 0.2782304 -1.6659838
## 2 6 -0.33494068 0.2297772 -0.6971576 0.8147794
## 3 6 0.07782881 -0.9273473 0.1307057 0.1832816
## 4 6 0.75401310 0.1584618 0.2770893 -0.3924682
## 5 6 0.75401310 0.1584618 0.2770893 -0.3924682
## 6 6 0.07782881 -0.9273473 0.1307057 0.1832816
write.csv(puntosFact,"fiscoquimicosScores.csv")
# utilizando rotacion
facto=principal(r=USArrests,nfactors=4,rotate="varimax")
facto$values
## [1] 3.34666886 1.58609030 1.37117206 1.08486150 0.97528337 0.93876295
## [7] 0.76924825 0.72389378 0.55650103 0.34293339 0.28411542 0.02046911
facto$communality
## acidezfija acidezvolátil ácidocÃtrico
## 0.6411845 0.3988635 0.5829618
## azúcarresidual cloruros dióxidodeazufrelibre
## 0.7436393 0.5054999 0.6003300
## dióxidodeazufretotal densidad pH
## 0.6496694 0.8546119 0.6183895
## sulfatos alcohol calidad
## 0.4646925 0.7108334 0.6181171
facto$loadings
##
## Loadings:
## RC1 RC2 RC4 RC3
## acidezfija 0.782 0.100 0.136
## acidezvolátil -0.104 0.298 -0.546
## ácidocÃtrico 0.482 0.584
## azúcarresidual 0.807 0.217 -0.214
## cloruros 0.681 0.178
## dióxidodeazufrelibre 0.701 -0.159 -0.155 0.245
## dióxidodeazufretotal 0.764 0.170 0.169
## densidad 0.822 0.223 0.355
## pH -0.770 0.152
## sulfatos -0.281 0.183 0.593
## alcohol -0.619 -0.125 -0.559
## calidad -0.739 0.234
##
## RC1 RC2 RC4 RC3
## SS loadings 2.812 1.682 1.640 1.255
## Proportion Var 0.234 0.140 0.137 0.105
## Cumulative Var 0.234 0.375 0.511 0.616
library(FactoMineR)
# observando los resultados de 2 componentes
result<- PCA(USArrests,scale.unit = TRUE, ncp=4,graph = TRUE)
fa.diagram(facto)
