INTRODUCCION

El análisis de componentes principales (PCA) es una técnica útil para el análisis exploratorio de datos, que le permite visualizar mejor la variación presente en un conjunto de datos con muchas variables. Es particularmente útil en el caso de conjuntos de datos “amplios”, donde tiene muchas variables para cada muestra. En este tutorial, descubrirá PCA en R.

DESCRIPCION DE LA DATA

CORRELACION

La correlación está íntimamente ligada con la regresión en el sentido de que se centra en el estudio del grado de asociación entre variables. Por lo tanto, una variable independiente que presente un alto grado de correlación con una variable dependiente será muy útil para predecir los valores de ésta última. Cuando la relación entre las variables es lineal, se habla de correlación lineal. Una de las medidas más utilizadas para medir la correlación lineal entre variables es el coeficiente de correlación lineal de Pearson.

Teoría de la Correlación: Estudia el grado de dependencia entre las variables, es decir su objetivo es medir el grado de ajuste existente entre la función teórica (función ajustada) y la nube de puntos.

En esta práctica se mostrará cómo ajustar un modelo de regresión con RStudio, prestando especial atención a los modelos de regresión lineal. Además, enseñaremos como calcular e interpretar algunas medidas de correlación.

#CALCULO DE LOS COMPONENTES PRINCIPALES

  • ESCALADO DE LAS VARIABLES

Identifica las direcciones en las que la varianza es mayor.

  • INFLUENCIA DE LOS OUTLIERS

Se denominan outliers a aquellas observaciones con caracteristicas diferentes de las demas. Este tipo de casos no pueden ser caracterizados categoricamente como beneficos o problematicos sino que deben ser contemplados en el contexto del analisis y debe evaluarse el tipo de informacion que pueden proporcionar.

NUMERO OPTIMO DE COMPONENTES

Partiendo de un set de datos con n observaciones y p variables, el número de componentes principales distintos será de:

\(min(n−1,p)\)

No existe un método objetivo para escoger el número de componentes principales que son suficientes para un análisis, por lo que depende del juicio del analista y del problema en cuestión. Si explican suficiente variabilidad y el objetivo es la visualización de los datos, no se suelen escoger más de tres componentes principales, para así facilitar la representación gráfica y la interpretación. Si este no es el principal objetivo, o si lo que se pretende es determinar el número óptimo de componentes que expliquen un mínimo porcentaje de varianza o que queramos utilizar para un análisis supervisado, como por ejemplo regresión de componentes principales, una manera objetiva de determinar el número de componentes es mediante validación cruzada.

PRUEBAS

#PRUEBAS DE CORRELACION INDIVIDUAL

Una vez calculado el valor del coeficiente de correlación interesa determinar si tal valor obtenido muestra que las variables X e Y están relacionadas en realidad o tan solo presentan dicha relación como consecuencia del azar. En otras palabras, nos preguntamos por la significación de dicho coeficiente de correlación. Un coeficiente de correlación se dice que es significativo si se puede afirmar, con una cierta probabilidad, que es diferente de cero. Más estrictamente, en términos estadísticos, preguntarse por la significación de un cierto coeficiente de correlación no es otra cosa que preguntarse por la probabilidad de que tal coeficiente proceda de una población cuyo valor sea de cero. A este respecto, como siempre, tendremos dos hipótesis posibles: H0: = 0-> r El coeficiente de correlación obtenido procede de una población cuya correlación es cero (p = 0 ). H1 : = 0-> xy r El coeficiente de correlación obtenido procede de una población cuyo coeficiente de correlación es distinto de cero (p=/0 ).

#PRUEBAS DE CORRELACION DE BARTLETT

Se utiliza para probar la Hipótesis Nula que afirma que las variables no están correlacionadas en la población. Es decir, comprueba si la matriz de correlaciones es una matriz de identidad. Se puede dar como válidos aquellos resultados que nos presenten un valor elevado del test y cuya fiabilidad sea menor a 0.05. En este caso se rechaza la Hipótesis Nula y se continúa con el Análisis.

Si las variables no están intercorrelacionadas, entonces el test de esfericidad de Bartlett debe presentar un valor (significancia) superior al límite de 0.05. En nuestro caso (Tabla 1) dicho análisis presentó una significancia muy inferior al límite 0.05, pues fue de 0.000, lo cual nos indica que la matriz de datos es válida para continuar con el proceso de análisis factorial.

#PRUEBA DEL KMO

El test KMO (Kaiser, Meyer y Olkin) relaciona los coeficientes de correlación, rjh, observados entre las variables Xj y Xh, y ajh son los coeficientes de correlación parcial entre las variables Xj y Xh. Cuanto más cerca de 1 tenga el valor obtenido del test KMO, implica que la relación entres las variables es alta. Si KMO ≥ 0.9, el test es muy bueno; notable para KMO ≥ 0.8; mediano para KMO ≥ 0.7; bajo para KMO ≥ 0.6; y muy bajo para KMO < 0.5.

La prueba de esfericidad de Bartlett evalúa la aplicabilidad del análisis factorial de las variables estudiadas. El modelo es significativo (aceptamos la hipótesis nula, H0) cuando se puede aplicar el análisis factorial

#PRUEBA DE ESFERICIDAD DE BARTLETT:

Si Sig. (p-valor) < 0.05 aceptamos H0 (hipótesis nula) > se puede aplicar el análisis factorial.

Si Sig. (p-valor) > 0.05 rechazamos H0 > no se puede aplicar el análisis factorial.

ANALISIS DE COMPONENTES PRINCIPALES

En estadística, el análisis de componentes principales (en español ACP, en inglés, PCA) es una técnica utilizada para describir un conjunto de datos en términos de nuevas variables (“componentes”) no correlacionadas. Los componentes se ordenan por la cantidad de varianza original que describen, por lo que la técnica es útil para reducir la dimensionalidad de un conjunto de datos.

Técnicamente, el ACP busca la proyección según la cual los datos queden mejor representados en términos de mínimos cuadrados. Esta convierte un conjunto de observaciones de variables posiblemente correlacionadas en un conjunto de valores de variables sin correlación lineal llamadas componentes principales.

El ACP se emplea sobre todo en análisis exploratorio de datos y para construir modelos predictivos. El ACP comporta el cálculo de la descomposición en autovalores de la matriz de covarianza, normalmente tras centrar los datos en la media de cada atributo.

Ejemplo en R

#Carga de Data

cliente=read.csv("https://raw.githubusercontent.com/VictorGuevaraP/Mineria-de-datos-2019-2/master/clientes.csv", sep = ";")

Como primer paso se carga la data y se le asigna un nombre

str(cliente)
## 'data.frame':    850 obs. of  9 variables:
##  $ ID_cliente         : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ edad               : int  41 47 33 29 47 40 38 42 26 47 ...
##  $ educacion          : int  2 1 2 2 1 1 2 3 1 3 ...
##  $ años_empleo        : int  6 26 10 4 31 23 4 0 5 23 ...
##  $ Ingreso            : int  19 100 57 19 253 81 56 64 18 115 ...
##  $ Tarjeta_credito    : num  0.124 4.582 6.111 0.681 9.308 ...
##  $ otra_tarjeta       : num  1.073 8.218 5.802 0.516 8.908 ...
##  $ Direccion          : Factor w/ 32 levels "NBA000","NBA001",..: 2 22 14 10 9 17 14 10 7 12 ...
##  $ Ratio.ingreso.deuda: num  6.3 12.8 20.9 6.3 7.2 10.9 1.6 6.6 15.5 4 ...

Alli podemos observar los tipos de dato de las variables que se tiene en la data.

missing(cliente)
## [1] FALSE

Con este codigo podemos observar si existen datos perdidos dentro de la data siendo false el resultado lo que nos da ah entender que no existen missing

cliente_cor=cliente[c(2:7,9)]

Vamos a seleccionar las variables con la cual nosotros vamos a trabajar.

library(corrplot)
## corrplot 0.84 loaded
cor(cliente_cor)
##                            edad    educacion años_empleo     Ingreso
## edad                1.000000000  0.012982860  0.55424133  0.47621808
## educacion           0.012982860  1.000000000 -0.15111705  0.21821936
## años_empleo         0.554241333 -0.151117051  1.00000000  0.62509257
## Ingreso             0.476218084  0.218219356  0.62509257  1.00000000
## Tarjeta_credito     0.278911779  0.099080615  0.38174363  0.55151036
## otra_tarjeta        0.337839059  0.140937875  0.41442984  0.60335568
## Ratio.ingreso.deuda 0.008240009  0.008053386 -0.03362502 -0.03558488
##                     Tarjeta_credito otra_tarjeta Ratio.ingreso.deuda
## edad                     0.27891178    0.3378391         0.008240009
## educacion                0.09908061    0.1409379         0.008053386
## años_empleo              0.38174363    0.4144298        -0.033625023
## Ingreso                  0.55151036    0.6033557        -0.035584878
## Tarjeta_credito          1.00000000    0.6449553         0.514970534
## otra_tarjeta             0.64495531    1.0000000         0.572545041
## Ratio.ingreso.deuda      0.51497053    0.5725450         1.000000000

Se puede ver la correlacion de cada una de las variables seleccionadas.

corrplot(cor(cliente_cor))

En esta grafica se puede apreciar la correlacion existente entre las variables representadas por colores siendo las de tono azul las que poseen una correlacion positiva y rojo siendo una correlacion negativa.

#Uso de las librerias utilizadas para el grafico 
library(PerformanceAnalytics)
## Loading required package: xts
## Loading required package: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
## Registered S3 method overwritten by 'xts':
##   method     from
##   as.zoo.xts zoo
## 
## Attaching package: 'PerformanceAnalytics'
## The following object is masked from 'package:graphics':
## 
##     legend
library(psych)

chart.Correlation(cliente_cor)

Con estas librerias se busca observar la correlacion entre las variables mediante graficos.

cortest(cor(cliente_cor))
## Warning in cortest(cor(cliente_cor)): n not specified, 100 used
## Tests of correlation matrices 
## Call:cortest(R1 = cor(cliente_cor))
##  Chi Square value 395  with df =  21   with probability < 1e-70

Se rechaza H0 , por lo cual se acepta H1 lo que da a entender que las correlaciones son distintas.

#PRUEBA DE ESFERICIDAD DE BARLETT
#Utilizando la libreria
library(rela)
cortest.bartlett(cor(cliente_cor),n=850)
## $chisq
## [1] 2782.794
## 
## $p.value
## [1] 0
## 
## $df
## [1] 21

Pvalue es 0 por ello se acepta Ha , lo cual significa que existe correlación entre las variables cuando usas cor(data).

#Prueba KMO
KMO(cliente_cor)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = cliente_cor)
## Overall MSA =  0.62
## MSA for each item = 
##                edad           educacion         años_empleo 
##                0.83                0.33                0.73 
##             Ingreso     Tarjeta_credito        otra_tarjeta 
##                0.57                0.73                0.65 
## Ratio.ingreso.deuda 
##                0.37

Según el resultado se justifica la realizacion del PCA (ya que MSA>0.5).

scree(cliente_cor)

Visualizamos en el grafico de sedimentacion la cantidad optima de componentes que pueden haber en la data en este caso se observa que el numero de componentes son 3.

#Analisis paralelo
fa.parallel(cliente_cor,fa="pc")

## Parallel analysis suggests that the number of factors =  NA  and the number of components =  3

Se utilizara la funcion fa.parallel con lo cual podemos realziar gráficos de pantalla de datos o matrices de correlación en comparación con matrices aleatorias.

componentes_clientes<-prcomp(cliente_cor, scale=TRUE,center = TRUE)
componentes_clientes
## Standard deviations (1, .., p=7):
## [1] 1.7562752 1.2131944 1.0424863 0.7605054 0.5995351 0.5446299 0.3499237
## 
## Rotation (n x k) = (7 x 7):
##                            PC1        PC2          PC3         PC4
## edad                -0.3533771  0.3776825 -0.047835841 -0.80710071
## educacion           -0.0766529 -0.1560156  0.906566561 -0.18204239
## años_empleo         -0.4028106  0.4191734 -0.213041667  0.15006833
## Ingreso             -0.4648857  0.2524987  0.250570469  0.37631427
## Tarjeta_credito     -0.4537238 -0.2724664 -0.044181438  0.25117597
## otra_tarjeta        -0.4810655 -0.2688641 -0.008099897  0.03745223
## Ratio.ingreso.deuda -0.2314834 -0.6686010 -0.256239894 -0.29465919
##                             PC5         PC6         PC7
## edad                 0.19206436  0.20388851 -0.01792971
## educacion           -0.02231146 -0.33484680 -0.04648568
## años_empleo         -0.20342602 -0.74241210 -0.03965078
## Ingreso             -0.05755393  0.38241128  0.60512553
## Tarjeta_credito      0.75947917 -0.03752756 -0.27683652
## otra_tarjeta        -0.57265469  0.30399509 -0.52390209
## Ratio.ingreso.deuda -0.11479056 -0.23467350  0.52787940

Con la función prcomp podemos realiza un analisis de PCA en la matriz de datoS para posteriormente pasarla a objeto y mediante la funcion scale se escalan los datos para que todos tengan un valor igualitario y se centra la data para que se distribuya y organize de una mejor manera

summary(componentes_clientes)
## Importance of components:
##                           PC1    PC2    PC3     PC4     PC5     PC6
## Standard deviation     1.7563 1.2132 1.0425 0.76051 0.59954 0.54463
## Proportion of Variance 0.4406 0.2103 0.1552 0.08262 0.05135 0.04237
## Cumulative Proportion  0.4406 0.6509 0.8062 0.88878 0.94013 0.98251
##                            PC7
## Standard deviation     0.34992
## Proportion of Variance 0.01749
## Cumulative Proportion  1.00000

Con esta funcion podemos apreciar algunas caracteristicas de los objetos de la matriz de componentes , de los cuales se puede resaltar “proportion of variance” el cual nos muestra que tan alejada estan los datos de la media

plot(componentes_clientes)

Con esta grafica se peude apreciar el porcentaje de data que tiene cada variable

biplot(componentes_clientes, scale=0.5)

Se usa la funcion “biplot” y se escala a 0.5 para que el grafico esta mas centrado y las variables puedan tener la mayor cantidad datos

componentes_principal<-componentes_clientes$x
componentes_principal<-componentes_principal[,1:3]
head(componentes_principal)
##             PC1         PC2        PC3
## [1,]  0.9273626  0.62187776  0.3306240
## [2,] -3.6059744  1.05601155 -1.1418017
## [3,] -1.8672660 -1.85171269 -0.1929300
## [4,]  1.5335134 -0.09274379  0.4546231
## [5,] -6.6619542  2.26445448 -0.1906138
## [6,] -2.0057321  1.09626357 -0.9815219

Se crea una nueva variable donde se almacenara las varables de los componentes creados anteriormente y se escojen los que pertenecientas a las primera a la tercera variable y posteriormente se visualizan las 5 primeras filas

componentes_principal
##                  PC1           PC2          PC3
##   [1,]   0.927362635  0.6218777562  0.330624007
##   [2,]  -3.605974390  1.0560115522 -1.141801672
##   [3,]  -1.867266018 -1.8517126890 -0.192929989
##   [4,]   1.533513408 -0.0927437927  0.454623127
##   [5,]  -6.661954151  2.2644544797 -0.190613787
##   [6,]  -2.005732053  1.0962635704 -0.981521908
##   [7,]   0.913438165  1.0755483466  0.825969271
##   [8,]   0.164694248  0.1475101473  1.761439212
##   [9,]   1.165807135 -1.0464296619 -0.895274762
##  [10,]  -2.027593726  2.3494823933  1.431687277
##  [11,]  -0.833239181  0.8523845760  1.670342384
##  [12,]   1.026171987  1.1156715017  0.590448947
##  [13,]   1.677843052  0.0094812907 -0.598269524
##  [14,]  -0.402420189 -0.4137720352 -1.069139026
##  [15,]   1.430379158 -0.7655143588  1.395467511
##  [16,]   1.947161126 -0.6505817717 -0.520090152
##  [17,]   2.098193135  0.3428951483 -0.284363576
##  [18,]   0.417870417 -0.5035000253  2.282296030
##  [19,]  -1.452476135  0.9424087854 -1.002291094
##  [20,]  -0.034327494  0.5992599605 -1.035173640
##  [21,]   1.442336973  0.2955450330  0.512964014
##  [22,]  -0.375502013 -0.4317572039  1.086427863
##  [23,]  -0.926331901 -2.2255675669  0.932702712
##  [24,]  -1.613007999  1.4290147519 -0.834591828
##  [25,]  -3.983906630 -1.7989304881  2.338406457
##  [26,]  -0.721236905  0.6551201698 -0.594267162
##  [27,]   2.073180764  0.3018940209 -0.326406237
##  [28,]  -0.798073196  0.3820365421 -1.237137981
##  [29,]   0.243666273  1.5327314123  0.531464520
##  [30,]   0.066840118 -0.0427543947  0.275818558
##  [31,]  -0.952815349  1.8877802884  1.579868734
##  [32,]  -1.378558524 -0.2660467080 -0.022778481
##  [33,]   1.753448391 -0.2839114425  0.849818675
##  [34,]   0.403326541 -0.1469815274  1.237771393
##  [35,]   0.417466044  0.3172650761 -0.679362869
##  [36,]   0.713352836 -0.1023116906  0.425376521
##  [37,]   0.835510898  0.2317578890  1.515901128
##  [38,]   1.062838363 -0.5927900230 -0.721852177
##  [39,]   2.266422608 -0.2041804326 -0.312090422
##  [40,]  -2.104855240  0.9835043306  1.640742864
##  [41,]   1.966532201 -0.7075375733 -0.622683001
##  [42,]  -3.430393471  0.3738769425  1.224799004
##  [43,]  -0.415519210 -2.3849611744 -0.201613917
##  [44,]  -2.578542496  0.4210412427  4.197844514
##  [45,]  -0.469101320 -0.9298531226 -1.148241742
##  [46,]  -1.998480821 -0.2559863659  1.308353090
##  [47,]   1.453647668 -1.4772835446 -0.935070392
##  [48,]   1.742411566  0.4728150815 -0.399261366
##  [49,]   1.884655541  0.2391823402 -0.392508362
##  [50,]   0.299504075  0.3531892166  0.534576219
##  [51,]  -1.485310861  2.2215860696 -0.784729712
##  [52,]  -1.569584436 -2.4605745773 -1.725741523
##  [53,]   0.736317361 -2.3275185959 -1.172212551
##  [54,]  -1.076146430  2.7918520883 -0.740040906
##  [55,]  -1.673787036 -2.3478513776  1.136999848
##  [56,]   0.957204760 -0.5501910918 -0.693293333
##  [57,]   1.762060377  0.2232938931 -0.375057044
##  [58,]   1.529221576 -0.4335445603  1.561843555
##  [59,]  -0.153786303  0.9214222548 -0.473215113
##  [60,]   0.037686875  1.7056954913 -0.703833337
##  [61,]  -1.466565526  0.2389869635 -1.055544789
##  [62,]  -0.603722169 -0.0202632372 -1.277537385
##  [63,]  -1.492064802  0.3740522599 -0.978009257
##  [64,]  -2.375876246  0.2532513649 -0.079300208
##  [65,]   1.921093544 -0.0086548883  0.597674074
##  [66,]   0.526856488  0.1765619012 -0.587106520
##  [67,]  -0.314822463  1.4673062843 -0.475733972
##  [68,]   1.146183715 -0.6484341557 -0.649674619
##  [69,]   0.622458877 -0.5535165851 -0.846919713
##  [70,]   1.457090129 -1.3204611552 -0.872960110
##  [71,]   0.720312820  0.6228493450  1.707784315
##  [72,]   0.254654491  0.9260459179  2.839570371
##  [73,]  -0.961060570  0.3028929652  0.621045694
##  [74,]   0.110476875 -1.5355379773  0.183611025
##  [75,]   1.146085729  0.5943542361 -0.532613056
##  [76,]   0.984529485 -0.4420481370 -0.844195408
##  [77,]   0.512463900  1.4265811840 -0.448700042
##  [78,]   1.325861060 -0.1638641975  0.469835622
##  [79,]  -4.245306216  0.3304917179  0.356702992
##  [80,]  -0.568591445  1.9125184302  0.221848186
##  [81,]  -0.700414370  0.1114097429 -0.678062890
##  [82,]  -2.510708608 -4.0786996464  0.855860085
##  [83,]  -3.026703550  1.1409784720  1.741468396
##  [84,]   0.638409510 -0.0333010602 -0.449121484
##  [85,]  -1.350504354  0.1197729646 -0.020945909
##  [86,]   2.140921879 -0.2044273539 -0.364267773
##  [87,]   1.317478198 -1.7392911647  2.370948952
##  [88,]   1.493334494 -0.6800363709  0.341232584
##  [89,]   0.880869244 -0.1489625944  0.322274460
##  [90,]   0.622208139 -2.4548641563  2.179695873
##  [91,]  -0.011704616  1.2507624904  0.655325096
##  [92,]   1.242324035  0.7408309791  0.623269056
##  [93,]   1.937479773  0.4480089215 -0.273163000
##  [94,]   1.009576002 -1.5215349253 -0.894712802
##  [95,]   1.222954143  0.6948134957  1.527740928
##  [96,]   0.526108316  1.7527959210  0.663865573
##  [97,]   0.830890973  0.1637213955 -0.666111683
##  [98,]   1.016868612  1.5689738224 -0.458889448
##  [99,]   0.386224718 -1.0037913520  0.097492695
## [100,]   2.108874803 -0.6282975960  1.675751392
## [101,]  -0.484713897 -2.0929868001 -1.286127645
## [102,]  -3.879799629 -1.0960494957  2.320047520
## [103,]  -0.422002210  1.5718289059 -0.777963787
## [104,]  -0.079961055  0.4528016662 -0.588761586
## [105,]   1.076789447 -1.0084955478  0.211378292
## [106,]  -3.400255631 -1.5348503023 -1.886043141
## [107,]   0.952694780  1.2991846326 -0.462171535
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## [675,]   1.449601861 -0.8608186117  0.528094827
## [676,]  -1.578775425  2.3202044055  0.609412857
## [677,]   1.200592600  0.3198026554 -0.369946892
## [678,]  -0.323457177  1.1565306800 -0.742512124
## [679,]   0.185141707 -1.0263328806 -1.063123125
## [680,]   0.309289560  0.1119460802 -0.895704645
## [681,]  -0.714195676 -0.2566347030 -1.034491597
## [682,]   1.574707899 -0.2841773449 -0.603951592
## [683,]  -0.423289431 -1.3287097108 -0.993467556
## [684,]  -2.201565712  2.2638907926  1.144080408
## [685,]   1.828563880 -1.0495203456  1.579840535
## [686,]   0.190703322  1.4260845560  2.368230998
## [687,]   1.238688990 -1.9820497423  0.096324184
## [688,]  -0.570388038  0.9834124306  0.503440874
## [689,]   0.824533251  0.6725908706  0.525139158
## [690,]   1.210725249  0.2563629728 -0.640728592
## [691,]   2.247736984 -0.4640620470 -0.389739843
## [692,]   1.036794603  1.2941346391 -0.373739125
## [693,]   0.692890346 -0.0068498934  0.355968573
## [694,]  -2.138752536  0.3715535685 -1.066560557
## [695,]   1.829252690 -0.1743784484 -0.418441830
## [696,]   0.985300519  0.3397349085 -0.387587339
## [697,]  -1.174158274 -1.7870772420  0.179741728
## [698,]   0.329967324  0.8947777387 -0.885240251
## [699,]   1.335524234 -1.0644623771  0.357544497
## [700,]   1.792429971 -0.8570240745 -0.620424480
## [701,]   0.781220043 -0.4149783853  3.248912477
## [702,]  -0.197370206 -0.7534597026 -0.927086413
## [703,]   1.514068958 -0.1142199703  0.612498407
## [704,]   2.123953714 -0.3638844744  0.648102466
## [705,]   1.864263700 -0.7109873781 -0.572387441
## [706,]  -0.808056692  0.3756043916 -0.667914045
## [707,]   0.837019117 -1.2481717236 -0.862339949
## [708,]   1.484018630  1.1441105556 -0.404937230
## [709,]  -2.347068859  0.3354821446 -1.179855838
## [710,]   0.409899650 -0.3296644968 -0.857838152
## [711,]  -2.257663664 -0.7610009159  0.371605780
## [712,]   0.876556778  0.3403531413  2.368285947
## [713,]  -1.973873103 -1.6964407461 -0.080238199
## [714,]  -5.007992073  0.1201473151  0.881663133
## [715,]   0.732909923  1.0127641414  0.604999467
## [716,]  -0.434453714 -2.3851978290 -1.566632026
## [717,]   0.868328554  0.8681536638 -0.564260947
## [718,]  -1.837448980  1.5893737535  1.787495000
## [719,]   0.252135691  2.0902823890 -0.591228628
## [720,]  -3.026602354 -1.2276728936  2.054375622
## [721,]   0.956084750 -0.8552076200 -0.762427348
## [722,]   0.522417574 -0.3720041644 -0.758367784
## [723,]   0.400182585  0.3692256720 -0.824520630
## [724,]  -0.105022930 -0.4911597600 -1.035586204
## [725,]   0.216228210 -1.7394984565  1.429242613
## [726,]  -4.009189989  2.2532457629  0.245533096
## [727,]   1.355495680  0.6162235093 -0.196411095
## [728,]   0.397677299 -0.1261304772 -0.785431678
## [729,]   1.718668445  0.7747148861 -0.362416112
## [730,]  -0.022703066 -0.1563235650  1.157382467
## [731,]  -1.265449458  0.0368396347  0.316843230
## [732,]  -1.303401731  0.3283162048 -0.797702030
## [733,]   1.197020213 -0.6094064739  0.693349797
## [734,]   0.841497757  1.5327491470  0.640171037
## [735,]  -3.589181232  3.2050112015 -0.809298349
## [736,]   0.257687771  0.8290505003 -0.352196257
## [737,]   0.533950188 -0.2043812784 -0.822646789
## [738,]   0.417573330 -0.0211196865  0.604636585
## [739,]   0.278660298 -1.0405152471  1.313853846
## [740,]   0.083370075  0.4274824882  1.301271880
## [741,]  -0.628445446 -0.6268441623 -1.149919361
## [742,]  -0.774325048  1.8541778861  1.474682447
## [743,]   1.968695188 -0.3426150815 -0.418535526
## [744,]  -0.476865301 -2.0821654255 -0.239984602
## [745,]   0.501267879 -0.0020908875  2.409357382
## [746,]  -0.636753167  2.3485222878 -0.933185571
## [747,]  -1.371795311  2.3604183913  0.814362978
## [748,]  -0.732268300 -0.5542631981 -1.138861129
## [749,]   1.629232867 -1.8494232981  0.182862639
## [750,]   0.704464580 -1.0804955392  1.416152419
## [751,]   0.760780099 -0.1148428163 -0.893513488
## [752,]   1.182257333 -0.1562469275 -0.668224419
## [753,]   0.858555523  0.5591942604 -0.627282501
## [754,]   0.262788304 -1.5961740441 -0.027375591
## [755,]   1.113894722 -1.3943086134 -0.826651058
## [756,]   0.426343714  0.4669344715 -0.733732529
## [757,]   1.399245279 -0.1763742027  0.453366744
## [758,]   2.004671924 -0.2430466299 -0.421867737
## [759,]  -1.657494743  1.6485756902 -0.827552962
## [760,]   0.000268712 -2.5776220223 -1.196896499
## [761,]  -3.436375234  0.1181386741 -1.062452390
## [762,]  -1.518793617 -1.2260330360 -0.095303578
## [763,]   1.545453185 -0.7534499447 -0.628167965
## [764,]  -0.180098727  1.7797186605  0.483643665
## [765,]   2.043957471 -0.6596326144  0.564596180
## [766,]   0.329621730 -0.9996970622  2.785502414
## [767,]   0.430463943  1.0829280800  0.724008364
## [768,]   0.158991255  0.2237794631 -0.748572603
## [769,]   0.846595482  0.4930391419 -0.515100803
## [770,]  -0.807013336  1.3386985512 -0.545733039
## [771,]   1.689101971  0.1693829272 -0.602155815
## [772,]   1.616408548 -0.5357192536 -0.567038250
## [773,]   1.115437852 -1.2584179803  0.268046935
## [774,]   0.677401405  1.8625166863 -0.507198494
## [775,]  -0.592805640 -0.5767033097  1.004052554
## [776,]  -0.934665593  1.0195047560 -0.801486265
## [777,]  -3.886391674 -3.6303800036 -0.727870824
## [778,]   0.411498170  0.1384075894  0.202624272
## [779,]  -0.771370688  1.1799673637 -0.042363262
## [780,]  -0.584935604 -1.3313347796 -1.097998635
## [781,]   1.169499842  0.9190738688  0.661417028
## [782,]   0.610468834  0.6230744547 -0.508712133
## [783,]   0.663391534  0.8605607362 -0.587815861
## [784,]  -0.073607257  0.7349426841 -0.868091845
## [785,]  -3.584595155 -0.7944530658 -1.448785774
## [786,]   1.565763222 -0.1876495713  1.673235072
## [787,]   0.166341231  1.8613869149  0.284189352
## [788,]   0.191105477  0.0844677188 -0.935880936
## [789,]   0.628481058 -0.1153181984  0.202430886
## [790,]   0.823719105  0.1016026775 -0.398834553
## [791,]   0.081647143  0.8223828731  0.528814926
## [792,]  -8.363672052  2.9124824321  0.210885275
## [793,]  -1.376321950 -0.1366304252 -0.923604529
## [794,]  -1.658365604 -1.4906428713  1.342626064
## [795,]   2.020818682  0.1770225740 -0.310923410
## [796,]   1.197051124  0.4375900319  1.555240916
## [797,]   1.214195199 -1.5886420409  2.348812850
## [798,]   1.623157756  0.5039484202  0.693628060
## [799,]   0.364922973 -1.5542143583  0.127425761
## [800,]   1.261321386  0.2935871022 -0.628081087
## [801,]   1.806165606  0.5307082094 -0.383679795
## [802,]  -2.587812578  2.6277494100 -0.958010417
## [803,]   2.052708157 -0.4347976786 -0.449876823
## [804,]   0.508124684 -0.7982074586 -0.937453758
## [805,]   0.540704327  0.3869025533 -0.735747880
## [806,]   1.415199891  0.6926381530 -0.418203802
## [807,]  -0.368000512  0.1343719776  1.199507150
## [808,]   0.795234106 -0.6358456571  1.657031047
## [809,]  -1.951068964  0.3197421110 -1.130143673
## [810,]   0.806490273 -2.2366704940 -1.151317634
## [811,]   0.745866114  0.6433557166 -0.830047453
## [812,]   1.868627014 -1.1253579365  0.424259887
## [813,]   1.622575224  1.0550086100 -0.400091996
## [814,]  -0.004763933 -0.0218914976 -0.717055810
## [815,]   1.196164465  0.4442816627 -0.624491508
## [816,]   1.054832610  0.6665753398  0.664912309
## [817,]   1.092867889  0.5982747960  0.474557359
## [818,]   1.670762803  0.1628767545  0.660827690
## [819,]   0.537218560 -0.8926004633  0.377250612
## [820,]   0.288946762  0.1007631279 -0.684447210
## [821,]   0.638006762 -0.4642098796 -0.839300026
## [822,]  -0.925442049 -0.9169786611 -1.370992263
## [823,]   1.256464346  1.2792313504 -0.407140587
## [824,]   1.068014314 -1.5605626996  2.323165432
## [825,]  -0.116736610 -1.1059269328 -0.086800336
## [826,]  -1.230044253  0.6455463604  0.764333965
## [827,]  -3.372493380 -2.1004347878 -1.784987245
## [828,]   0.070550758 -0.1308489181 -0.840254178
## [829,]   1.107104405  0.5253370815  1.574516796
## [830,]   1.244258565  0.2239317756  0.675422075
## [831,]  -1.553721932 -1.3376983151 -1.247616734
## [832,]   1.089199239 -0.5640828739  0.123640741
## [833,]  -0.464695491 -0.8523919180  0.078552103
## [834,]   0.222285104 -1.3172628120  2.020992832
## [835,]   1.105176537 -0.4546922887  0.515752282
## [836,]   0.236682617 -2.6738059840  1.197501300
## [837,]   1.760992619 -0.4222242469  0.555875200
## [838,]   1.095228817 -0.9713304522 -0.878283181
## [839,]   1.164714068  0.1888972274 -0.697631697
## [840,]   1.223710804  0.3899255388 -0.650821210
## [841,]   0.460851502  0.8159541892  1.162891862
## [842,]   0.456282934  0.1184155315  1.650612875
## [843,]   0.895771960  1.3805476315 -0.587131269
## [844,]   0.852050308  0.6727797208  0.572571968
## [845,]   0.587182390  1.1152178155 -0.461603183
## [846,]   1.471679010  0.0007882011 -0.514515882
## [847,]   1.049838444 -0.0033471608  0.440203543
## [848,]   0.026246757 -4.0523323492  1.467971348
## [849,]   1.112546251  1.1665155575 -0.592330279
## [850,]  -1.424558907  1.5648851989 -0.863739290

mediante este condigo se puede observar todas las observaciones pertenecientes a la data con los 3 componentes anteriormete seleccionados

write.csv(componentes_principal, file = "componentes_clientes.csv")
getwd()
## [1] "C:/Users/Usuario/Desktop"

Se migran los datos a excel