library(readxl)
library(ggplot2)
library(psych)
##
## Attaching package: 'psych'
## The following objects are masked from 'package:ggplot2':
##
## %+%, alpha
CARAGAMOS LA BASE DE DATOS Y HACEMOS SUMMARY
data1 <- read_excel("C:/Users/estudio/Desktop/MAESTRIA/ANALISIS_MULTIVARIADO/Tabla 1.2.3 ejemplo automotriz.xlsx",range = "B2:P102" )
summary(data1)
## EL UB DP VE TR
## Min. :1.00 Min. :1.00 Min. :1.00 Min. :1.00 Min. :1.00
## 1st Qu.:4.00 1st Qu.:2.75 1st Qu.:2.00 1st Qu.:2.00 1st Qu.:2.00
## Median :5.00 Median :4.00 Median :3.00 Median :4.00 Median :3.00
## Mean :4.87 Mean :3.62 Mean :3.29 Mean :3.79 Mean :3.23
## 3rd Qu.:6.00 3rd Qu.:5.00 3rd Qu.:4.00 3rd Qu.:5.00 3rd Qu.:5.00
## Max. :7.00 Max. :7.00 Max. :6.00 Max. :7.00 Max. :7.00
## FI IM CO DC RB
## Min. :1.00 Min. :1.00 Min. :1.00 Min. :1.00 Min. :1.00
## 1st Qu.:2.75 1st Qu.:3.00 1st Qu.:5.00 1st Qu.:4.00 1st Qu.:3.00
## Median :4.00 Median :4.00 Median :6.00 Median :5.50 Median :4.00
## Mean :3.63 Mean :4.38 Mean :5.54 Mean :5.21 Mean :4.14
## 3rd Qu.:5.00 3rd Qu.:6.00 3rd Qu.:7.00 3rd Qu.:6.00 3rd Qu.:5.00
## Max. :7.00 Max. :7.00 Max. :7.00 Max. :7.00 Max. :7.00
## BG MP AP EA CM
## Min. :1.0 Min. :1.00 Min. :1.00 Min. :1.00 Min. :1.00
## 1st Qu.:3.0 1st Qu.:2.00 1st Qu.:4.00 1st Qu.:4.00 1st Qu.:3.00
## Median :4.0 Median :3.00 Median :4.00 Median :5.50 Median :4.00
## Mean :3.9 Mean :3.35 Mean :4.25 Mean :5.21 Mean :3.94
## 3rd Qu.:5.0 3rd Qu.:5.00 3rd Qu.:5.00 3rd Qu.:6.00 3rd Qu.:5.00
## Max. :7.0 Max. :7.00 Max. :6.00 Max. :7.00 Max. :7.00
# MEDIDAS DE TENDENCIA CENTRAL Y DISPERSIÓN
apply(X = data1, MARGIN = 2, FUN = mean) # MEDIAS DE CADA VARIABLE
## EL UB DP VE TR FI IM CO DC RB BG MP AP EA CM
## 4.87 3.62 3.29 3.79 3.23 3.63 4.38 5.54 5.21 4.14 3.90 3.35 4.25 5.21 3.94
apply(X = data1, MARGIN = 2, FUN = var) # VARIANZA DE CADA VARIABLE
## EL UB DP VE TR FI IM CO
## 3.548586 2.541010 2.127172 2.672626 3.047576 2.457677 2.864242 2.533737
## DC RB BG MP AP EA CM
## 2.389798 1.939798 1.343434 2.573232 1.118687 2.389798 2.420606
CALCULAMOS LA MATRIZ DE VARIANZA - COVARIANZA
## CALCULAMOS LA MATRIZ DE VARIANZA - COVARIANZA
var_cor <- data.frame(cov(data1)) # en la diagonal está la varianza de cada variable
var_cor
## EL UB DP VE TR FI
## EL 3.54858586 -0.43373737 0.9875758 1.3764646 1.3837374 -0.402121212
## UB -0.43373737 2.54101010 -0.1816162 -0.5452525 -0.4268687 2.393333333
## DP 0.98757576 -0.18161616 2.1271717 1.1423232 1.6700000 -0.134040404
## VE 1.37646465 -0.54525253 1.1423232 2.6726263 1.1295960 -0.533030303
## TR 1.38373737 -0.42686869 1.6700000 1.1295960 3.0475758 -0.388787879
## FI -0.40212121 2.39333333 -0.1340404 -0.5330303 -0.3887879 2.457676768
## IM 0.57515152 0.14585859 0.5452525 0.2422222 0.7298990 0.030909091
## CO 0.64666667 -0.43919192 0.3569697 0.5185859 0.3088889 -0.363838384
## DC 1.46191919 -0.75777778 0.2112121 0.8122222 0.5572727 -0.578080808
## RB -0.10282828 -0.04727273 0.2418182 0.3529293 0.5129293 -0.119393939
## BG 0.01717172 0.04242424 0.1202020 0.1909091 0.3161616 -0.007070707
## MP 0.73282828 -0.21919192 1.3015152 0.7207071 2.5550505 -0.202525253
## AP 0.41666667 -0.30808081 0.4823232 0.3661616 0.4671717 -0.138888889
## EA 1.46191919 -0.75777778 0.2112121 0.8122222 0.5572727 -0.578080808
## CM 0.13353535 -0.13414141 0.2296970 0.3004040 0.3270707 0.028080808
## IM CO DC RB BG MP
## EL 0.57515152 0.6466667 1.4619192 -0.10282828 0.017171717 0.7328283
## UB 0.14585859 -0.4391919 -0.7577778 -0.04727273 0.042424242 -0.2191919
## DP 0.54525253 0.3569697 0.2112121 0.24181818 0.120202020 1.3015152
## VE 0.24222222 0.5185859 0.8122222 0.35292929 0.190909091 0.7207071
## TR 0.72989899 0.3088889 0.5572727 0.51292929 0.316161616 2.5550505
## FI 0.03090909 -0.3638384 -0.5780808 -0.11939394 -0.007070707 -0.2025253
## IM 2.86424242 1.2775758 0.3638384 0.33010101 0.240404040 0.7242424
## CO 1.27757576 2.5337374 0.9258586 0.64080808 0.589898990 0.3444444
## DC 0.36383838 0.9258586 2.3897980 0.21272727 0.223232323 0.3904040
## RB 0.33010101 0.6408081 0.2127273 1.93979798 1.115151515 0.4757576
## BG 0.24040404 0.5898990 0.2232323 1.11515152 1.343434343 0.2676768
## MP 0.72424242 0.3444444 0.3904040 0.47575758 0.267676768 2.5732323
## AP 0.40909091 0.6111111 0.8257576 0.17676768 0.035353535 0.3964646
## EA 0.36383838 0.9258586 2.3897980 0.21272727 0.223232323 0.3904040
## CM 0.49777778 0.8408081 0.4369697 1.40242424 1.014141414 0.2939394
## AP EA CM
## EL 0.41666667 1.4619192 0.13353535
## UB -0.30808081 -0.7577778 -0.13414141
## DP 0.48232323 0.2112121 0.22969697
## VE 0.36616162 0.8122222 0.30040404
## TR 0.46717172 0.5572727 0.32707071
## FI -0.13888889 -0.5780808 0.02808081
## IM 0.40909091 0.3638384 0.49777778
## CO 0.61111111 0.9258586 0.84080808
## DC 0.82575758 2.3897980 0.43696970
## RB 0.17676768 0.2127273 1.40242424
## BG 0.03535354 0.2232323 1.01414141
## MP 0.39646465 0.3904040 0.29393939
## AP 1.11868687 0.8257576 0.41919192
## EA 0.82575758 2.3897980 0.43696970
## CM 0.41919192 0.4369697 2.42060606
CALCULAMOS LOS VALORES Y VECTORES PROPIOS
auto <- eigen(cov(data1))
auto$values # valores propios
## [1] 1.104326e+01 5.397022e+00 4.785816e+00 3.959578e+00 2.828401e+00
## [6] 2.176940e+00 1.595934e+00 1.125946e+00 1.111098e+00 7.567603e-01
## [11] 5.339769e-01 4.251314e-01 1.623279e-01 6.578549e-02 -2.220446e-16
auto$vectors # vectores propios
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.38277533 0.084980625 0.2009794 -0.41865660 0.104940975 0.32856154
## [2,] -0.19627184 -0.440678407 -0.1394138 -0.47046683 0.116815354 -0.01299471
## [3,] 0.25910195 -0.271286960 0.2040792 0.05460784 0.008073716 0.19365101
## [4,] 0.30393209 -0.004831676 0.1437609 -0.02832031 0.253581979 0.58497233
## [5,] 0.38074027 -0.361386694 0.2844687 0.15230159 0.029438749 -0.25126463
## [6,] -0.17682394 -0.412145802 -0.1504044 -0.48661434 0.153027925 -0.07483337
## [7,] 0.20318499 -0.207613561 -0.2462993 -0.09565388 -0.721423656 0.12336650
## [8,] 0.24689394 0.052398871 -0.3904180 -0.02320697 -0.360310400 0.16340848
## [9,] 0.31959956 0.312819052 -0.1213701 -0.28244200 0.111698800 -0.32903864
## [10,] 0.13452204 -0.152405810 -0.3812459 0.27341381 0.286901424 0.03242335
## [11,] 0.09751468 -0.102981010 -0.3117268 0.15561340 0.215091431 0.03091499
## [12,] 0.30374117 -0.368857270 0.2053546 0.17209739 -0.045091817 -0.39019123
## [13,] 0.16477225 0.039485501 -0.0846866 -0.06744521 -0.044265568 -0.16518182
## [14,] 0.31959956 0.312819052 -0.1213701 -0.28244200 0.111698800 -0.32903864
## [15,] 0.16024857 -0.107183999 -0.4897921 0.19298205 0.280873622 0.05878295
## [,7] [,8] [,9] [,10] [,11]
## [1,] 0.653778399 0.17528792 0.02507365 0.01237796 0.178544499
## [2,] -0.059423401 -0.08059210 0.09870545 -0.04183261 0.033919180
## [3,] -0.261132077 0.43232854 -0.24725939 -0.56038893 -0.310008962
## [4,] -0.492889447 -0.40164204 0.03849746 0.25282365 0.034362582
## [5,] 0.100802190 -0.03368844 0.09397564 0.11557674 0.024804088
## [6,] -0.126216314 0.07300825 0.00998406 0.09151583 -0.026593473
## [7,] 0.105679134 -0.42020920 -0.32626541 -0.10389710 -0.020409122
## [8,] -0.183563957 0.42752118 0.59759683 0.18685948 -0.020053654
## [9,] -0.129687269 -0.14272715 -0.02600721 -0.10454143 -0.151982873
## [10,] 0.101185699 -0.19736062 0.10188207 -0.33150635 0.524823379
## [11,] 0.152279576 -0.12724909 0.27367266 -0.37545096 -0.268159963
## [12,] -0.007007441 -0.07642855 0.17674174 0.26040978 -0.008526656
## [13,] -0.306546218 0.32547253 -0.32508763 -0.01387051 0.628288892
## [14,] -0.129687269 -0.14272715 -0.02600721 -0.10454143 -0.151982873
## [15,] 0.160848910 0.20268251 -0.48058095 0.46040603 -0.281384616
## [,12] [,13] [,14] [,15]
## [1,] 0.034380565 0.134222332 0.040252106 -3.259264e-16
## [2,] -0.041869693 0.074592776 -0.694768564 -1.992801e-15
## [3,] -0.206830002 0.088909934 -0.003643757 -2.109712e-16
## [4,] 0.089143607 0.023651767 0.017066838 -9.012624e-17
## [5,] 0.073697394 -0.710903495 -0.106780228 1.636071e-15
## [6,] 0.004366406 -0.124828835 0.681463457 2.071356e-15
## [7,] 0.030959638 -0.009889070 0.060561178 6.684597e-17
## [8,] -0.107333500 -0.071759266 -0.035020793 1.992742e-16
## [9,] -0.109325629 -0.021539610 -0.021051489 7.071068e-01
## [10,] -0.447859869 -0.003684249 0.098545815 1.886544e-16
## [11,] 0.690781192 0.069192833 0.046465163 4.286322e-17
## [12,] -0.028168771 0.658218384 0.080970065 -1.350587e-15
## [13,] 0.472396779 0.052523623 -0.062323079 -6.572293e-16
## [14,] -0.109325629 -0.021539610 -0.021051489 -7.071068e-01
## [15,] -0.052885000 0.001842352 -0.107174377 -3.953732e-16
VARIANZA TOTAL Y VARIANZA GENERALIZADA
vtotal <- sum(diag(cov(data1))) # varianza total
vtotal
## [1] 35.96798
vgen <- det(cov(data1)) # varianza generalizada
vgen
## [1] 0
PRIMERAS COMPONENTES PRINCIPALES
x1 <- scale(data1[,1], scale = FALSE) # la función scale le resta la media a nuestros datos
x2 <- scale(data1[,2], scale = FALSE)
x3 <- scale(data1[,3], scale = FALSE)
x4 <- scale(data1[,4], scale = FALSE)
x5 <- scale(data1[,5], scale = FALSE)
x6 <- scale(data1[,6], scale = FALSE)
x7 <- scale(data1[,7], scale = FALSE)
x8 <- scale(data1[,8], scale = FALSE)
x9 <- scale(data1[,9], scale = FALSE)
x10 <- scale(data1[,10], scale = FALSE)
x11 <- scale(data1[,11], scale = FALSE)
x12 <- scale(data1[,12], scale = FALSE)
x13 <- scale(data1[,13], scale = FALSE)
x14 <- scale(data1[,14], scale = FALSE)
x15 <- scale(data1[,15], scale = FALSE)
suma1 <- function(x1, x2,x3,x4, x5, x6, x7, x8,x9,x10,x11,x12,x13,x14,x15) {
z1 <- 0.38277533 * (x1) - 0.19627184*(x2) + 0.25910195*(x3) + 0.30393209*(x4) + 0.38074027* (x5)+
-0.17682394* (x6) + 0.20318499*(x7) + 0.24689394* (x8) + 0.31959956* (x9) + 0.13452204 * (x10)
+ 0.09751468* (x11) + 0.30374117* (x12) + 0.16477225*(x13) + 0.31959956*(x14) + 0.16024857*(x15)
return(z1)
}
s1 <- suma1(x1, x2,x3,x4, x5, x6, x7, x8,x9,x10,x11,x12,x13,x14,x15) # valores de la primera componente principal
s1
## EL
## [1,] 2.01698262
## [2,] 0.31588596
## [3,] -1.56940434
## [4,] 1.05842928
## [5,] -0.22854081
## [6,] -3.22557875
## [7,] 4.05718298
## [8,] -0.03875068
## [9,] -4.87662615
## [10,] -1.94243413
## [11,] -3.20274713
## [12,] 4.65256480
## [13,] 1.66240222
## [14,] 2.03292839
## [15,] 3.03543450
## [16,] -0.72798600
## [17,] -2.24601336
## [18,] -3.14498644
## [19,] -4.27399245
## [20,] -2.66800601
## [21,] 0.49956500
## [22,] -2.23354849
## [23,] -0.76516014
## [24,] -3.81699225
## [25,] -1.33034430
## [26,] 1.36951423
## [27,] 3.56290378
## [28,] 3.64374947
## [29,] -1.65376038
## [30,] 0.46022318
## [31,] -1.67668996
## [32,] -1.03989297
## [33,] 1.97504436
## [34,] 0.08229125
## [35,] 4.03920297
## [36,] 1.12546945
## [37,] 5.25260707
## [38,] -2.68540077
## [39,] -1.02835824
## [40,] 4.30334558
## [41,] -2.85718786
## [42,] -1.61911313
## [43,] -0.21981632
## [44,] 1.01156247
## [45,] 3.65165739
## [46,] 2.24213668
## [47,] 0.51077502
## [48,] 1.48204784
## [49,] 0.47743742
## [50,] -5.90681999
## [51,] -1.33034430
## [52,] -2.29704489
## [53,] -3.29349735
## [54,] -2.48082026
## [55,] -3.02724210
## [56,] -5.36471724
## [57,] -1.81638075
## [58,] -0.51325813
## [59,] -3.85678772
## [60,] -3.80943537
## [61,] 3.29083602
## [62,] 0.69939830
## [63,] 0.79956549
## [64,] 0.09332535
## [65,] -6.82579163
## [66,] 1.07423911
## [67,] -0.86544638
## [68,] -0.00759917
## [69,] -1.22627165
## [70,] 4.41567373
## [71,] 2.56024567
## [72,] 0.14378222
## [73,] 0.99166267
## [74,] 0.37604904
## [75,] -0.79600161
## [76,] 1.39594442
## [77,] 1.87965874
## [78,] 2.25153753
## [79,] 3.27686363
## [80,] 0.93923608
## [81,] -3.85997641
## [82,] -0.15598442
## [83,] 1.11470925
## [84,] 1.05868457
## [85,] 0.98780440
## [86,] 0.85204012
## [87,] 1.91993516
## [88,] -0.18349541
## [89,] 2.69547400
## [90,] 3.12944895
## [91,] -1.46260393
## [92,] 1.99751266
## [93,] 1.01248275
## [94,] 1.91458831
## [95,] 2.97683870
## [96,] 0.46493224
## [97,] -1.36688772
## [98,] -0.92135683
## [99,] 2.12759438
## [100,] -0.52231310
## attr(,"scaled:center")
## EL
## 4.87
## de esta misma manera se procede con las componentes Z2 hasta Z15
VARIABILIDAD ExPLICADA
auto_val <- data.frame(auto$values)
auto_val
## auto.values
## 1 1.104326e+01
## 2 5.397022e+00
## 3 4.785816e+00
## 4 3.959578e+00
## 5 2.828401e+00
## 6 2.176940e+00
## 7 1.595934e+00
## 8 1.125946e+00
## 9 1.111098e+00
## 10 7.567603e-01
## 11 5.339769e-01
## 12 4.251314e-01
## 13 1.623279e-01
## 14 6.578549e-02
## 15 -2.220446e-16
l1 <- auto_val[1]/ sum(auto$values) # variabilidad explicada por cada componente
l1
## auto.values
## 1 3.070304e-01
## 2 1.500508e-01
## 3 1.330577e-01
## 4 1.100862e-01
## 5 7.863664e-02
## 6 6.052438e-02
## 7 4.437095e-02
## 8 3.130411e-02
## 9 3.089131e-02
## 10 2.103983e-02
## 11 1.484590e-02
## 12 1.181972e-02
## 13 4.513123e-03
## 14 1.829002e-03
## 15 -6.173397e-18
sum(l1[1:6,]) # tomando las 6 primeras componentes principales se explica un 83.9% de la variabilidad total
## [1] 0.8393861
PCA UTILIZANDO R
pca1 <- prcomp(data1)
pca1
## Standard deviations (1, .., p=15):
## [1] 3.323141e+00 2.323149e+00 2.187651e+00 1.989869e+00 1.681785e+00
## [6] 1.475446e+00 1.263303e+00 1.061106e+00 1.054086e+00 8.699197e-01
## [11] 7.307373e-01 6.520210e-01 4.028994e-01 2.564868e-01 3.021308e-16
##
## Rotation (n x k) = (15 x 15):
## PC1 PC2 PC3 PC4 PC5 PC6
## EL -0.38277533 -0.084980625 -0.2009794 0.41865660 0.104940975 -0.32856154
## UB 0.19627184 0.440678407 0.1394138 0.47046683 0.116815354 0.01299471
## DP -0.25910195 0.271286960 -0.2040792 -0.05460784 0.008073716 -0.19365101
## VE -0.30393209 0.004831676 -0.1437609 0.02832031 0.253581979 -0.58497233
## TR -0.38074027 0.361386694 -0.2844687 -0.15230159 0.029438749 0.25126463
## FI 0.17682394 0.412145802 0.1504044 0.48661434 0.153027925 0.07483337
## IM -0.20318499 0.207613561 0.2462993 0.09565388 -0.721423656 -0.12336650
## CO -0.24689394 -0.052398871 0.3904180 0.02320697 -0.360310400 -0.16340848
## DC -0.31959956 -0.312819052 0.1213701 0.28244200 0.111698800 0.32903864
## RB -0.13452204 0.152405810 0.3812459 -0.27341381 0.286901424 -0.03242335
## BG -0.09751468 0.102981010 0.3117268 -0.15561340 0.215091431 -0.03091499
## MP -0.30374117 0.368857270 -0.2053546 -0.17209739 -0.045091817 0.39019123
## AP -0.16477225 -0.039485501 0.0846866 0.06744521 -0.044265568 0.16518182
## EA -0.31959956 -0.312819052 0.1213701 0.28244200 0.111698800 0.32903864
## CM -0.16024857 0.107183999 0.4897921 -0.19298205 0.280873622 -0.05878295
## PC7 PC8 PC9 PC10 PC11 PC12
## EL -0.653778399 -0.17528792 0.02507365 -0.01237796 -0.178544499 -0.034380565
## UB 0.059423401 0.08059210 0.09870545 0.04183261 -0.033919180 0.041869693
## DP 0.261132077 -0.43232854 -0.24725939 0.56038893 0.310008962 0.206830002
## VE 0.492889447 0.40164204 0.03849746 -0.25282365 -0.034362582 -0.089143607
## TR -0.100802190 0.03368844 0.09397564 -0.11557674 -0.024804088 -0.073697394
## FI 0.126216314 -0.07300825 0.00998406 -0.09151583 0.026593473 -0.004366406
## IM -0.105679134 0.42020920 -0.32626541 0.10389710 0.020409122 -0.030959638
## CO 0.183563957 -0.42752118 0.59759683 -0.18685948 0.020053654 0.107333500
## DC 0.129687269 0.14272715 -0.02600721 0.10454143 0.151982873 0.109325629
## RB -0.101185699 0.19736062 0.10188207 0.33150635 -0.524823379 0.447859869
## BG -0.152279576 0.12724909 0.27367266 0.37545096 0.268159963 -0.690781192
## MP 0.007007441 0.07642855 0.17674174 -0.26040978 0.008526656 0.028168771
## AP 0.306546218 -0.32547253 -0.32508763 0.01387051 -0.628288892 -0.472396779
## EA 0.129687269 0.14272715 -0.02600721 0.10454143 0.151982873 0.109325629
## CM -0.160848910 -0.20268251 -0.48058095 -0.46040603 0.281384616 0.052885000
## PC13 PC14 PC15
## EL -0.134222332 -0.040252106 1.197502e-16
## UB -0.074592776 0.694768564 -1.271662e-16
## DP -0.088909934 0.003643757 3.746338e-17
## VE -0.023651767 -0.017066838 1.449390e-18
## TR 0.710903495 0.106780228 2.068647e-16
## FI 0.124828835 -0.681463457 -6.172902e-17
## IM 0.009889070 -0.060561178 1.048803e-16
## CO 0.071759266 0.035020793 -8.150091e-18
## DC 0.021539610 0.021051489 -7.071068e-01
## RB 0.003684249 -0.098545815 -4.210912e-17
## BG -0.069192833 -0.046465163 -9.331311e-17
## MP -0.658218384 -0.080970065 -1.871306e-16
## AP -0.052523623 0.062323079 1.497522e-16
## EA 0.021539610 0.021051489 7.071068e-01
## CM -0.001842352 0.107174377 3.855327e-17
VARIABILIDAD EXPLICADA FORMA GRAFICA 1
prop_varianza1 <- pca1$sdev^2 / sum(pca1$sdev^2)
prop_varianza1
## [1] 3.070304e-01 1.500508e-01 1.330577e-01 1.100862e-01 7.863664e-02
## [6] 6.052438e-02 4.437095e-02 3.130411e-02 3.089131e-02 2.103983e-02
## [11] 1.484590e-02 1.181972e-02 4.513123e-03 1.829002e-03 2.537897e-33
ggplot(data = data.frame(prop_varianza1, pc = 1:15),
aes(x = pc, y = prop_varianza1)) +
geom_col(width = 0.3) +
scale_y_continuous(limits = c(0,1)) +
theme_bw() +
labs(x = "Componente principal",
y = "Prop. de varianza explicada")
REPRESENTACÓN PERPENDICULAR DE LAS COMPONENTES
biplot(x = pca1, scale = 0, cex = 1, col = c("blue4", "brown3"))
PRUEBA DE ESFERICIDAD DE BARTLETT
correl1=cor(data1,use="pairwise.complete.obs") # matriz de correlacion
correl1 # HAY CORRELACIONES > 0.3
## EL UB DP VE TR FI
## EL 1.000000000 -0.14444283 0.35945248 0.44695962 0.4207739 -0.136165455
## UB -0.144442831 1.00000000 -0.07811780 -0.20923068 -0.1533959 0.957717916
## DP 0.359452482 -0.07811780 1.00000000 0.47909167 0.6559005 -0.058623544
## VE 0.446959618 -0.20923068 0.47909167 1.00000000 0.3958009 -0.207979439
## TR 0.420773865 -0.15339593 0.65590047 0.39580088 1.0000000 -0.142060415
## FI -0.136165455 0.95771792 -0.05862354 -0.20797944 -0.1420604 1.000000000
## IM 0.180405479 0.05406596 0.22089787 0.08754674 0.2470476 0.011649813
## CO 0.215661200 -0.17308935 0.15376209 0.19928323 0.1111589 -0.145802622
## DC 0.502013174 -0.30750917 0.09367786 0.32138467 0.2064952 -0.238531409
## RB -0.039192834 -0.02129263 0.11904452 0.15500308 0.2109609 -0.054681655
## BG 0.007864622 0.02296163 0.07110535 0.10075098 0.1562513 -0.003891278
## MP 0.242513023 -0.08571994 0.55629922 0.27482116 0.9123947 -0.080533635
## AP 0.209125422 -0.18272887 0.31266742 0.21176268 0.2530143 -0.083762735
## EA 0.502013174 -0.30750917 0.09367786 0.32138467 0.2064952 -0.238531409
## CM 0.045562395 -0.05408759 0.10122597 0.11810672 0.1204210 0.011512911
## IM CO DC RB BG MP
## EL 0.18040548 0.2156612 0.50201317 -0.03919283 0.007864622 0.24251302
## UB 0.05406596 -0.1730893 -0.30750917 -0.02129263 0.022961628 -0.08571994
## DP 0.22089787 0.1537621 0.09367786 0.11904452 0.071105348 0.55629922
## VE 0.08754674 0.1992832 0.32138467 0.15500308 0.100750978 0.27482116
## TR 0.24704759 0.1111589 0.20649519 0.21096091 0.156251309 0.91239466
## FI 0.01164981 -0.1458026 -0.23853141 -0.05468165 -0.003891278 -0.08053363
## IM 1.00000000 0.4742431 0.13906666 0.14004374 0.122554328 0.26677159
## CO 0.47424305 1.0000000 0.37625585 0.28904731 0.319733860 0.13489594
## DC 0.13906666 0.3762559 1.00000000 0.09880168 0.124585718 0.15743243
## RB 0.14004374 0.2890473 0.09880168 1.00000000 0.690792167 0.21294525
## BG 0.12255433 0.3197339 0.12458572 0.69079217 1.000000000 0.14396700
## MP 0.26677159 0.1348959 0.15743243 0.21294525 0.143967001 1.00000000
## AP 0.22853918 0.3629820 0.50503061 0.11999698 0.028838347 0.23367416
## EA 0.13906666 0.3762559 1.00000000 0.09880168 0.124585718 0.15743243
## CM 0.18904646 0.3395111 0.18168065 0.64720088 0.562377889 0.11777585
## AP EA CM
## EL 0.20912542 0.50201317 0.04556239
## UB -0.18272887 -0.30750917 -0.05408759
## DP 0.31266742 0.09367786 0.10122597
## VE 0.21176268 0.32138467 0.11810672
## TR 0.25301427 0.20649519 0.12042103
## FI -0.08376274 -0.23853141 0.01151291
## IM 0.22853918 0.13906666 0.18904646
## CO 0.36298202 0.37625585 0.33951113
## DC 0.50503061 1.00000000 0.18168065
## RB 0.11999698 0.09880168 0.64720088
## BG 0.02883835 0.12458572 0.56237789
## MP 0.23367416 0.15743243 0.11777585
## AP 1.00000000 0.50503061 0.25473967
## EA 0.50503061 1.00000000 0.18168065
## CM 0.25473967 0.18168065 1.00000000
det(correl1) # determinate de la matriz de correlación
## [1] 0
ep <- -(100-1-(1/6)*(2*15+5))*log(0) # estadistico de prueba
(15^2-15)/2 #grados de libertad
## [1] 105
x_2_0_05 <- 124.3421 # valor aproximado de una chi cuadrado con 105 grados de libertad y significacia 0.05
## como ep > x_2_0_05 se rechaza ho, por tanto se debe aplicar PCA
cortest.bartlett(data1) # prueba de hipotesis
## R was not square, finding R from data
## $chisq
## [1] Inf
##
## $p.value
## [1] 0
##
## $df
## [1] 105
# dado que el valor p < 0.05 se rechaza ho. Por tanto se debe apicar PCA.
NÚMERO DE COMPONENTES A RETENER EN EL PCA
h_10 <- (sum(l1[6:15,])) / (15-5)
h_10
## [1] 0.02211383
sumlog <- log(6.052438e-02)+ log(4.437095e-02)+ log(3.089131e-02)+ log(2.103983e-02)+
log(1.484590e-02)+ log(1.181972e-02)+ log(4.513123e-03)+ log(1.829002e-03)+
log(6.173397e-18)
sumlog
## [1] -73.23755
log(h_10)
## [1] -3.811552
(100-((2*15+11)/6))* ((15-5)*log(h_10)-sumlog) # estadistico de prueba
## [1] 3272.202
((15-5+2)*(15-5+1))/2 # grados de libertad
## [1] 66
x2_0_05 <- 90.5313 # valor aproximado de una chi cuadrado con 66 grados de libertad y significacia 0.05
## como ep > x2_0_05 se rechaza ho, por tanto con 6 componentes está bien
