PARCIAL2_MAE118
DEBEE BERENICE PEREZ VIDES
2022-10-26
EJERCICIO 2
Una empresa especializada en el diseño de automoviles de turismo desea estudiar cuales son los desos del publico que comrpa automoviles. Para ello deiseña una encuesta con 10 preguntas donde se le pide a cada uno de los 20 encuestados que valore de 1 a 5 si una caracteristica es o no muy importante. Los encuestados deberan contestar con un 5 si la caracteristica es muy importante, un 4 si es importante, un 3 si tiene regular importancia, un 2 si es poco importante y 1 si no es nada importante. Las 10 caracteristicas (V1 a V10) a valorar son: precio, financiacion, consumo, combustible, seguridad, confort, capacidad, prestaciones, modernidad y aerodinamica. El fichero 6-2.RData recoge los datos a ser utilizados.
REALIZA UN ANALISIS FACTORIAL QUE PERMITA EXTRAER UNOS FACTORES ADECUADOS LOS DATOS QUE RESUMAN CORRECTAMENTE LA INFORMACION QUE CONTIENE. PROPONGA UNA SOLUCION ADECUADA DE LA CANTIDAD DE FACTORES A RETENER Y JUSTIFIQUE SU RESPUESTA, SOBRE LA BASE DE LAS PRUEBAS DE VALIDACION DEL ANALISIS FACTORIAL, ESTUDIADAS EN CLASE E INDIQUE LAS VARIABLES QUE SE AGRUPARIAN EN CADA FACTOR.
load("C:/Users/50379/Downloads/6-2.RData")
colnames(X6_2)<-c("precio","financiacion","consumo","combustible","seguridad","confort","capacidad","prestaciones","modernidad","aerodinamica")
X6_2## precio financiacion consumo combustible seguridad confort capacidad
## 1 4 1 4 3 3 2 4
## 2 5 5 4 4 3 3 4
## 3 2 1 3 1 4 2 1
## 4 1 1 1 1 4 4 2
## 5 1 1 2 1 5 5 4
## 6 5 5 5 5 3 3 4
## 7 4 5 4 4 2 2 5
## 8 3 2 3 1 4 4 2
## 9 4 4 4 3 4 4 3
## 10 5 5 5 5 2 2 3
## 11 2 2 2 1 5 4 4
## 12 4 4 5 5 4 5 5
## 13 3 2 2 1 4 5 4
## 14 5 5 4 4 5 4 4
## 15 4 3 3 1 4 4 5
## 16 5 5 4 4 4 5 4
## 17 4 4 5 2 4 5 5
## 18 5 5 4 4 2 2 1
## 19 3 3 2 2 4 4 5
## 20 5 5 4 4 4 5 4
## prestaciones modernidad aerodinamica
## 1 4 4 4
## 2 1 1 3
## 3 5 4 5
## 4 5 5 4
## 5 3 3 2
## 6 2 2 1
## 7 1 1 1
## 8 5 5 5
## 9 1 1 1
## 10 2 2 2
## 11 3 4 3
## 12 2 1 2
## 13 4 3 3
## 14 1 2 2
## 15 3 4 4
## 16 2 1 1
## 17 4 4 2
## 18 2 2 3
## 19 4 5 4
## 20 3 2 1#Matriz de Covarianza
cov(X6_2)## precio financiacion consumo combustible seguridad
## precio 1.8000000 1.9157895 1.3157895 1.7263158 -0.6210526
## financiacion 1.9157895 2.6736842 1.4210526 2.1368421 -0.6631579
## consumo 1.3157895 1.4210526 1.4210526 1.5263158 -0.5263158
## combustible 1.7263158 2.1368421 1.5263158 2.4842105 -0.8000000
## seguridad -0.6210526 -0.6631579 -0.5263158 -0.8000000 0.8526316
## confort -0.3052632 -0.1368421 -0.3157895 -0.4842105 0.8000000
## capacidad 0.3631579 0.5157895 0.2894737 0.3473684 0.2052632
## prestaciones -1.2052632 -1.7789474 -0.9210526 -1.6105263 0.3736842
## modernidad -1.2736842 -1.8105263 -1.1052632 -1.8315789 0.4631579
## aerodinamica -0.9000000 -1.5368421 -0.8684211 -1.3894737 0.1526316
## confort capacidad prestaciones modernidad aerodinamica
## precio -0.30526316 0.3631579 -1.2052632 -1.27368421 -0.9000000
## financiacion -0.13684211 0.5157895 -1.7789474 -1.81052632 -1.5368421
## consumo -0.31578947 0.2894737 -0.9210526 -1.10526316 -0.8684211
## combustible -0.48421053 0.3473684 -1.6105263 -1.83157895 -1.3894737
## seguridad 0.80000000 0.2052632 0.3736842 0.46315789 0.1526316
## confort 1.37894737 0.6263158 0.2157895 0.09473684 -0.3736842
## capacidad 0.62631579 1.6078947 -0.5289474 -0.33684211 -0.7078947
## prestaciones 0.21578947 -0.5289474 1.9236842 1.81052632 1.3657895
## modernidad 0.09473684 -0.3368421 1.8105263 2.16842105 1.5578947
## aerodinamica -0.37368421 -0.7078947 1.3657895 1.55789474 1.8184211#Matriz R
cor(X6_2)## precio financiacion consumo combustible seguridad
## precio 1.0000000 0.87328595 0.8227068 0.8163752 -0.5013159
## financiacion 0.8732860 1.00000000 0.7290378 0.8291310 -0.4392191
## consumo 0.8227068 0.72903777 1.0000000 0.8123536 -0.4781461
## combustible 0.8163752 0.82913105 0.8123536 1.0000000 -0.5496865
## seguridad -0.5013159 -0.43921906 -0.4781461 -0.5496865 1.0000000
## confort -0.1937601 -0.07126739 -0.2255894 -0.2616171 0.7377945
## capacidad 0.2134668 0.24876462 0.1915028 0.1738070 0.1753079
## prestaciones -0.6477072 -0.78440645 -0.5570735 -0.7367273 0.2917811
## modernidad -0.6446941 -0.75193098 -0.6296349 -0.7891501 0.3406250
## aerodinamica -0.4974610 -0.69699068 -0.5402292 -0.6537458 0.1225791
## confort capacidad prestaciones modernidad aerodinamica
## precio -0.19376008 0.2134668 -0.6477072 -0.64469411 -0.4974610
## financiacion -0.07126739 0.2487646 -0.7844064 -0.75193098 -0.6969907
## consumo -0.22558942 0.1915028 -0.5570735 -0.62963492 -0.5402292
## combustible -0.26161713 0.1738070 -0.7367273 -0.78915014 -0.6537458
## seguridad 0.73779454 0.1753079 0.2917811 0.34062503 0.1225791
## confort 1.00000000 0.4206208 0.1324920 0.05478646 -0.2359846
## capacidad 0.42062076 1.0000000 -0.3007577 -0.18039552 -0.4139927
## prestaciones 0.13249196 -0.3007577 1.0000000 0.88647429 0.7302468
## modernidad 0.05478646 -0.1803955 0.8864743 1.00000000 0.7845472
## aerodinamica -0.23598461 -0.4139927 0.7302468 0.78454720 1.0000000library(corrplot)## corrplot 0.92 loadedlibrary(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:base':
##
## format.pval, unitsMat_R<-rcorr(as.matrix(X6_2))
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))
library(kableExtra)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:kableExtra':
##
## group_rows## The following objects are masked from 'package:Hmisc':
##
## src, summarize## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(Hmisc)
Rx<-X6_2 %>% as.matrix() %>% rcorr()
Rx$r %>% kable(caption="Matriz R(X)",
align = "c",
digits = 2) %>%
kable_material(html_font = "sans-serif") %>%
kable_styling(bootstrap_options = c("striped", "hover"))| precio | financiacion | consumo | combustible | seguridad | confort | capacidad | prestaciones | modernidad | aerodinamica | |
|---|---|---|---|---|---|---|---|---|---|---|
| precio | 1.00 | 0.87 | 0.82 | 0.82 | -0.50 | -0.19 | 0.21 | -0.65 | -0.64 | -0.50 |
| financiacion | 0.87 | 1.00 | 0.73 | 0.83 | -0.44 | -0.07 | 0.25 | -0.78 | -0.75 | -0.70 |
| consumo | 0.82 | 0.73 | 1.00 | 0.81 | -0.48 | -0.23 | 0.19 | -0.56 | -0.63 | -0.54 |
| combustible | 0.82 | 0.83 | 0.81 | 1.00 | -0.55 | -0.26 | 0.17 | -0.74 | -0.79 | -0.65 |
| seguridad | -0.50 | -0.44 | -0.48 | -0.55 | 1.00 | 0.74 | 0.18 | 0.29 | 0.34 | 0.12 |
| confort | -0.19 | -0.07 | -0.23 | -0.26 | 0.74 | 1.00 | 0.42 | 0.13 | 0.05 | -0.24 |
| capacidad | 0.21 | 0.25 | 0.19 | 0.17 | 0.18 | 0.42 | 1.00 | -0.30 | -0.18 | -0.41 |
| prestaciones | -0.65 | -0.78 | -0.56 | -0.74 | 0.29 | 0.13 | -0.30 | 1.00 | 0.89 | 0.73 |
| modernidad | -0.64 | -0.75 | -0.63 | -0.79 | 0.34 | 0.05 | -0.18 | 0.89 | 1.00 | 0.78 |
| aerodinamica | -0.50 | -0.70 | -0.54 | -0.65 | 0.12 | -0.24 | -0.41 | 0.73 | 0.78 | 1.00 |
Rx$P %>% kable(caption="p-values de R(X)",
align = "c",
digits = 2) %>%
kable_classic_2(html_font = "sans-serif") %>%
kable_styling(bootstrap_options = c("striped", "hover"))| precio | financiacion | consumo | combustible | seguridad | confort | capacidad | prestaciones | modernidad | aerodinamica | |
|---|---|---|---|---|---|---|---|---|---|---|
| precio | NA | 0.00 | 0.00 | 0.00 | 0.02 | 0.41 | 0.37 | 0.00 | 0.00 | 0.03 |
| financiacion | 0.00 | NA | 0.00 | 0.00 | 0.05 | 0.77 | 0.29 | 0.00 | 0.00 | 0.00 |
| consumo | 0.00 | 0.00 | NA | 0.00 | 0.03 | 0.34 | 0.42 | 0.01 | 0.00 | 0.01 |
| combustible | 0.00 | 0.00 | 0.00 | NA | 0.01 | 0.27 | 0.46 | 0.00 | 0.00 | 0.00 |
| seguridad | 0.02 | 0.05 | 0.03 | 0.01 | NA | 0.00 | 0.46 | 0.21 | 0.14 | 0.61 |
| confort | 0.41 | 0.77 | 0.34 | 0.27 | 0.00 | NA | 0.06 | 0.58 | 0.82 | 0.32 |
| capacidad | 0.37 | 0.29 | 0.42 | 0.46 | 0.46 | 0.06 | NA | 0.20 | 0.45 | 0.07 |
| prestaciones | 0.00 | 0.00 | 0.01 | 0.00 | 0.21 | 0.58 | 0.20 | NA | 0.00 | 0.00 |
| modernidad | 0.00 | 0.00 | 0.00 | 0.00 | 0.14 | 0.82 | 0.45 | 0.00 | NA | 0.00 |
| aerodinamica | 0.03 | 0.00 | 0.01 | 0.00 | 0.61 | 0.32 | 0.07 | 0.00 | 0.00 | NA |
library(stargazer)##
## Please cite as:## Hlavac, Marek (2022). stargazer: Well-Formatted Regression and Summary Statistics Tables.## R package version 5.2.3. https://CRAN.R-project.org/package=stargazerdescomposicion<-eigen(Rx$r)
t(descomposicion$values) %>% kable(caption="Autovalores de R(X)",
align = "c",
digits = 2) %>%
kable_classic_2(html_font = "sans-serif") %>%
kable_styling(bootstrap_options = c("striped", "hover"))| 5.7 | 2.07 | 0.72 | 0.55 | 0.32 | 0.27 | 0.15 | 0.13 | 0.07 | 0.03 |
library(dplyr)
library(factoextra)## Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBalibrary(kableExtra)
library(stargazer)
library(ggplot2)
options(scipen = 99999)
PC<-princomp(x = X6_2,cor = TRUE,fix_sign = FALSE)
factoextra::get_eig(PC) %>% kable(caption="Resumen de PCA",
align = "c",
digits = 2) %>%
kable_material(html_font = "sans-serif") %>%
kable_styling(bootstrap_options = c("hover"))| eigenvalue | variance.percent | cumulative.variance.percent | |
|---|---|---|---|
| Dim.1 | 5.70 | 57.01 | 57.01 |
| Dim.2 | 2.07 | 20.69 | 77.70 |
| Dim.3 | 0.72 | 7.20 | 84.91 |
| Dim.4 | 0.55 | 5.48 | 90.39 |
| Dim.5 | 0.32 | 3.16 | 93.54 |
| Dim.6 | 0.27 | 2.71 | 96.25 |
| Dim.7 | 0.15 | 1.46 | 97.72 |
| Dim.8 | 0.13 | 1.28 | 99.00 |
| Dim.9 | 0.07 | 0.68 | 99.68 |
| Dim.10 | 0.03 | 0.32 | 100.00 |
fviz_eig(PC,
choice = "eigenvalue",
barcolor = "red",
barfill = "red",
addlabels = TRUE,
)+labs(title = "Gráfico de Sedimentación",subtitle = "Usando princomp, con Autovalores")+
xlab(label = "Componentes")+
ylab(label = "Autovalores")+geom_hline(yintercept = 1)
2 factores a retener
library(dplyr)
library(factoextra)
library(kableExtra)
variables_pca<-get_pca_var(PC)
variables_pca$coord%>%
kable(caption="Correlación de X con las componentes, usando factoextra",
align = "c",
digits = 2) %>%
kable_material(html_font = "sans-serif") %>%
kable_styling(bootstrap_options = c("striped", "hover"))| Dim.1 | Dim.2 | Dim.3 | Dim.4 | Dim.5 | Dim.6 | Dim.7 | Dim.8 | Dim.9 | Dim.10 | |
|---|---|---|---|---|---|---|---|---|---|---|
| precio | -0.88 | -0.10 | -0.27 | -0.25 | 0.21 | -0.07 | 0.02 | 0.05 | 0.18 | -0.02 |
| financiacion | -0.92 | 0.06 | -0.03 | -0.14 | 0.16 | -0.24 | -0.13 | -0.02 | -0.13 | 0.07 |
| consumo | -0.84 | -0.12 | -0.27 | -0.27 | -0.17 | 0.29 | -0.04 | 0.12 | -0.08 | -0.02 |
| combustible | -0.93 | -0.11 | -0.02 | -0.06 | -0.08 | 0.06 | 0.10 | -0.30 | -0.01 | -0.02 |
| seguridad | 0.53 | 0.72 | 0.15 | -0.22 | 0.19 | 0.26 | -0.10 | -0.08 | 0.03 | 0.05 |
| confort | 0.20 | 0.90 | 0.00 | -0.29 | -0.07 | -0.17 | 0.15 | 0.03 | -0.05 | -0.06 |
| capacidad | -0.28 | 0.67 | -0.54 | 0.42 | 0.02 | 0.04 | 0.03 | -0.01 | 0.00 | 0.03 |
| prestaciones | 0.86 | -0.16 | -0.28 | -0.25 | -0.26 | -0.09 | 0.04 | -0.04 | 0.05 | 0.10 |
| modernidad | 0.88 | -0.14 | -0.37 | -0.07 | 0.02 | -0.07 | -0.21 | -0.10 | -0.02 | -0.09 |
| aerodinamica | 0.77 | -0.45 | -0.23 | -0.08 | 0.31 | 0.08 | 0.19 | 0.00 | -0.09 | 0.01 |
library(corrplot)
corrplot(variables_pca$coord,is.corr = FALSE,method = "square",addCoef.col="black",number.cex = 0.75)
library(psych)##
## Attaching package: 'psych'## The following object is masked from 'package:Hmisc':
##
## describe## The following objects are masked from 'package:ggplot2':
##
## %+%, alphalibrary(corrplot)
library(dplyr)
#Modelo de 2 Factores (sin rotar)
numero_de_factores<-2
modelo_2_factores<-principal(r = Rx$r,
nfactors = numero_de_factores,
covar = FALSE,
rotate = "none")
modelo_2_factores## Principal Components Analysis
## Call: principal(r = Rx$r, nfactors = numero_de_factores, rotate = "none",
## covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 h2 u2 com
## precio 0.88 -0.10 0.78 0.22 1.0
## financiacion 0.92 0.06 0.86 0.14 1.0
## consumo 0.84 -0.12 0.72 0.28 1.0
## combustible 0.93 -0.11 0.88 0.12 1.0
## seguridad -0.53 0.72 0.80 0.20 1.8
## confort -0.20 0.90 0.85 0.15 1.1
## capacidad 0.28 0.67 0.53 0.47 1.3
## prestaciones -0.86 -0.16 0.77 0.23 1.1
## modernidad -0.88 -0.14 0.79 0.21 1.0
## aerodinamica -0.77 -0.45 0.79 0.21 1.6
##
## PC1 PC2
## SS loadings 5.70 2.07
## Proportion Var 0.57 0.21
## Cumulative Var 0.57 0.78
## Proportion Explained 0.73 0.27
## Cumulative Proportion 0.73 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.07
##
## Fit based upon off diagonal values = 0.98correlaciones_modelo<-variables_pca$coord
corrplot(correlaciones_modelo[,1:numero_de_factores],
is.corr = FALSE,
method = "square",addCoef.col="black",number.cex = 0.75)
library(psych)
library(corrplot)
library(dplyr)
#Modelo de 2 Factores (Rotado)
numero_de_factores<-2
modelo_2_factores<-principal(r = Rx$r,
nfactors = numero_de_factores,
covar = FALSE,
rotate = "varimax")
modelo_2_factores## Principal Components Analysis
## Call: principal(r = Rx$r, nfactors = numero_de_factores, rotate = "varimax",
## covar = FALSE)
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 h2 u2 com
## precio 0.87 -0.18 0.78 0.22 1.1
## financiacion 0.93 -0.02 0.86 0.14 1.0
## consumo 0.83 -0.19 0.72 0.28 1.1
## combustible 0.92 -0.20 0.88 0.12 1.1
## seguridad -0.46 0.77 0.80 0.20 1.6
## confort -0.11 0.91 0.85 0.15 1.0
## capacidad 0.34 0.64 0.53 0.47 1.5
## prestaciones -0.87 -0.07 0.77 0.23 1.0
## modernidad -0.89 -0.05 0.79 0.21 1.0
## aerodinamica -0.80 -0.38 0.79 0.21 1.4
##
## RC1 RC2
## SS loadings 5.67 2.10
## Proportion Var 0.57 0.21
## Cumulative Var 0.57 0.78
## Proportion Explained 0.73 0.27
## Cumulative Proportion 0.73 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 2 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.07
##
## Fit based upon off diagonal values = 0.98correlaciones_modelo<-variables_pca$coord
correlaciones_modelo_rotada<-varimax(correlaciones_modelo[,1:numero_de_factores])$loadings
corrplot(correlaciones_modelo_rotada[,1:numero_de_factores],
is.corr = FALSE,
method = "square",
addCoef.col="black",
number.cex = 0.75)
library(psych)
Barlett<-cortest.bartlett(X6_2)## R was not square, finding R from dataprint(Barlett)## $chisq
## [1] 163.4656
##
## $p.value
## [1] 0.000000000000002362835
##
## $df
## [1] 45KMO<-KMO(X6_2)
print(KMO)## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = X6_2)
## Overall MSA = 0.7
## MSA for each item =
## precio financiacion consumo combustible seguridad confort
## 0.82 0.74 0.84 0.93 0.55 0.32
## capacidad prestaciones modernidad aerodinamica
## 0.37 0.62 0.68 0.84library(rela)
KMO<-paf(as.matrix(X6_2))$KMO
print(KMO)## [1] 0.70012