Análisis PCA
Iris Pamela Monroy Romero
Cargar Datos
data <- read_csv2("C:/Users/MIRZ/Downloads/data_pca.csv")## ℹ Using "','" as decimal and "'.'" as grouping mark. Use `read_delim()` for more control.## Rows: 200 Columns: 16
## ── Column specification ────────────────────────────────────────────────────────
## Delimiter: ";"
## dbl (16): x1, x2, x3, x4, x5, x6, x7, x8, x9, x10, x11, x12, x13, x14, x15, y
##
## ℹ Use `spec()` to retrieve the full column specification for this data.
## ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.View(data)Normalizar datos (Quitamos la columna de la variable dependiente)
data1 <- scale(data[,-16])
View(data1)Calcular factor de adecuación muestral de Kaiser-Meyer_Olkin
# Calcular el KMO
psych::KMO(data1)## Kaiser-Meyer-Olkin factor adequacy
## Call: psych::KMO(r = data1)
## Overall MSA = 0.34
## MSA for each item =
## x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15
## 0.36 0.27 0.24 0.46 0.53 0.55 0.45 0.27 0.42 0.26 0.43 0.46 0.28 0.62 0.33Nota: #No se toma en cuenta porque se va a reducir mucho (estan mal los datos)
Análisis de Componentes Principales (PCA)
# Calcular PCA
pca <- princomp(data1)
summary(pca) # Resumen del PCA ## Importance of components:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5
## Standard deviation 1.6220588 1.4501268 1.3332930 1.2434264 1.15529908
## Proportion of Variance 0.1762864 0.1408957 0.1191069 0.1035919 0.08942821
## Cumulative Proportion 0.1762864 0.3171821 0.4362890 0.5398809 0.62930907
## Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## Standard deviation 1.05569426 0.90471763 0.88908929 0.8622762 0.80999883
## Proportion of Variance 0.07467272 0.05484181 0.05296347 0.0498171 0.04395967
## Cumulative Proportion 0.70398179 0.75882360 0.81178707 0.8616042 0.90556384
## Comp.11 Comp.12 Comp.13 Comp.14 Comp.15
## Standard deviation 0.7012045 0.59518243 0.53958339 0.4662240 0.234552581
## Proportion of Variance 0.0329439 0.02373482 0.01950755 0.0145638 0.003686091
## Cumulative Proportion 0.9385077 0.96224255 0.98175010 0.9963139 1.000000000Nota: #Solo considerar los que tienen la proporción de varianza más del 6% porque estamos reduciendo la dimensión. #Hasta el momento se observa que las principales componentes que aportan mayor varianza son de la 1 a 6.
Cargas de las variables
# Cargas de las variables
pca$loadings##
## Loadings:
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9 Comp.10
## x1 0.141 0.320 0.200 0.604 0.137 0.102 0.199 0.109
## x2 -0.419 0.180 -0.248 0.145 0.236 -0.110 -0.570
## x3 -0.274 0.177 0.259 0.483 -0.131 -0.207 0.367
## x4 -0.307 0.447 -0.223 0.129 -0.167 -0.291 -0.399 -0.152
## x5 -0.236 -0.410 -0.354 0.102 -0.163
## x6 0.132 -0.203 -0.628 0.178 -0.112 0.340
## x7 0.112 0.340 -0.464 -0.345 0.151 -0.194 0.136
## x8 0.385 -0.246 0.153 -0.132 -0.268 0.382 0.424 -0.258
## x9 0.142 0.246 -0.284 -0.510 -0.336 0.157 -0.536
## x10 -0.386 0.110 -0.342 -0.331 0.327 0.273 0.383
## x11 0.137 -0.255 0.122 -0.300 0.528 0.574 -0.364
## x12 0.102 0.330 -0.226 0.346 -0.643 -0.434 -0.209
## x13 0.232 -0.223 -0.648 -0.301 0.246
## x14 0.175 0.410 0.305 -0.182 0.158 0.154 -0.256
## x15 0.521 -0.153 0.135 0.173 -0.256 -0.249 0.151
## Comp.11 Comp.12 Comp.13 Comp.14 Comp.15
## x1 0.134 0.135 0.588
## x2 0.203 -0.186 -0.459
## x3 -0.232 -0.412 0.113 -0.382
## x4 0.576
## x5 -0.582 0.204 0.470
## x6 -0.171 -0.566 0.147
## x7 0.662
## x8 -0.385 -0.355
## x9 -0.367
## x10 0.367 -0.367
## x11 0.237
## x12 0.223
## x13 0.136 0.524
## x14 -0.693 -0.248
## x15 0.344 -0.611
##
## Comp.1 Comp.2 Comp.3 Comp.4 Comp.5 Comp.6 Comp.7 Comp.8 Comp.9
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067 0.067
## Cumulative Var 0.067 0.133 0.200 0.267 0.333 0.400 0.467 0.533 0.600
## Comp.10 Comp.11 Comp.12 Comp.13 Comp.14 Comp.15
## SS loadings 1.000 1.000 1.000 1.000 1.000 1.000
## Proportion Var 0.067 0.067 0.067 0.067 0.067 0.067
## Cumulative Var 0.667 0.733 0.800 0.867 0.933 1.000Nota: #La variable x1 tiene una carga fuerte con la componente 14, mientras que la variable x2 esta relacionada negativamente con la componente 10.
Revisar varianza y eigenvalores
# Gráficos de varianza y eigenvalores
fviz_eig(pca, choice = "variance")
fviz_eig(pca, choice = "eigenvalue")
Nota: La componente uno y dos aportan la mayor varianza, además estos mismos componentes son los que tienen eigenvalores mayores a 1, lo adecuado es extraer unicamente dos factores.
Gráficos de Puntuaciones y Variables
# Gráfico de puntuaciones de individuos
fviz_pca_ind(pca,
col.ind = "cos2",
gradient.cols = c("red", "yellow", "green"),
repel = FALSE)
> Nota: #Las observaciones en color verde fuerte son
representadas en mejor medida. #las observaciones 21 Y 43 no son tan
bien representadas, pero son la minoria
# Gráfico de variables
fviz_pca_var(pca,
col.var = "contrib",
gradient.cols = c("red", "yellow", "green"),
repel = FALSE)
> Nota: #Las variables x11, x12, x7, x9, x1, x14 están
agrupadas y apuntan en la misma dirección por lo que están positivamente
correlacionadas entre sí.
# Biplot de PCA
fviz_pca_biplot(pca,
col.var = "red",
col.ind = "black")
> Nota: #Las observaciones se encuentran agrupadas
mayormente en el cuadrante 1 y 3
Análisis de Correlaciones
# Matriz de correlaciones
psych::cor.plot(data1)
# Determinante de la matriz de correlaciones
det(cor(data1))## [1] 0.004667778Nota: #Existen diversas variables que estan correlacionadas tanto positiva como negativamente, lo cual es bueno para nuestro análisis de componentes. Esto se confirma con el resultado del determinante que es muy cercano a 0.
PCA utilizando psych::principal (Rotación Varimax)
# Análisis PCA alternativo usando principal() de psych
pca2 <- psych::principal(data1,
nfactors = 6,
residuals = FALSE,
rotate = "varimax",
scores = TRUE,
oblique.scores = FALSE,
method = "regression",
use = "pairwise",
cor = "cor")
pca2## Principal Components Analysis
## Call: psych::principal(r = data1, nfactors = 6, residuals = FALSE,
## rotate = "varimax", scores = TRUE, oblique.scores = FALSE,
## method = "regression", use = "pairwise", cor = "cor")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC4 RC3 RC6 RC5 h2 u2 com
## x1 -0.06 0.57 -0.04 0.06 -0.10 -0.72 0.86 0.14 2.0
## x2 0.80 -0.05 0.07 0.02 0.00 -0.15 0.68 0.32 1.1
## x3 0.22 0.08 -0.84 -0.08 0.06 0.01 0.77 0.23 1.2
## x4 -0.01 0.06 0.07 -0.50 -0.65 0.12 0.69 0.31 2.0
## x5 0.10 -0.85 0.03 -0.03 -0.06 -0.07 0.75 0.25 1.1
## x6 0.12 0.07 0.87 0.00 0.04 0.03 0.78 0.22 1.1
## x7 0.02 0.03 0.05 0.87 0.21 -0.01 0.80 0.20 1.1
## x8 -0.73 -0.13 0.12 0.11 -0.12 0.00 0.59 0.41 1.2
## x9 -0.06 0.10 0.04 0.77 -0.12 0.00 0.63 0.37 1.1
## x10 0.76 -0.07 0.13 0.02 -0.08 0.13 0.62 0.38 1.2
## x11 -0.02 -0.07 0.03 -0.04 0.78 0.02 0.61 0.39 1.0
## x12 0.02 0.41 0.00 -0.01 0.54 0.06 0.46 0.54 1.9
## x13 -0.05 0.31 0.00 -0.01 -0.05 0.88 0.87 0.13 1.3
## x14 0.03 0.80 0.04 0.09 -0.03 0.04 0.66 0.34 1.0
## x15 -0.77 0.15 0.42 -0.03 0.07 0.00 0.80 0.20 1.7
##
## RC1 RC2 RC4 RC3 RC6 RC5
## SS loadings 2.42 2.04 1.69 1.63 1.42 1.35
## Proportion Var 0.16 0.14 0.11 0.11 0.09 0.09
## Cumulative Var 0.16 0.30 0.41 0.52 0.61 0.70
## Proportion Explained 0.23 0.19 0.16 0.15 0.13 0.13
## Cumulative Proportion 0.23 0.42 0.58 0.74 0.87 1.00
##
## Mean item complexity = 1.3
## Test of the hypothesis that 6 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.08
## with the empirical chi square 263.19 with prob < 4.2e-39
##
## Fit based upon off diagonal values = 0.83Nota: #Los valores indican las cargas en cada componente, además, varimax ayuda a simplificar la interpretación de estas.
Matriz de Pesos y Puntuaciones
# Pesos de los componentes
pca2$weights## RC1 RC2 RC4 RC3 RC6
## x1 -0.008727579 0.2792604831 -0.007237084 -0.01527418 -0.091588546
## x2 0.347445455 0.0040542499 0.111942053 0.01275760 -0.002653909
## x3 0.025220962 0.0472773165 -0.491534113 -0.02545133 0.035909049
## x4 0.003568835 0.0734721529 0.048916959 -0.22268542 -0.406875705
## x5 0.010811259 -0.4185764561 0.023497517 0.02449604 -0.014296960
## x6 0.125340287 0.0420708386 0.542636482 -0.04827402 0.046513370
## x7 0.021601246 -0.0274162575 -0.003459397 0.53463456 0.015853266
## x8 -0.304573037 -0.0938811312 0.002234392 0.08698561 -0.099920860
## x9 -0.009219345 0.0191129775 -0.019401843 0.52155816 -0.212794964
## x10 0.334173404 0.0004521551 0.136097304 0.03778716 -0.065646513
## x11 -0.015511335 -0.0578383249 0.031514256 -0.14507604 0.588000386
## x12 0.021797373 0.1920790342 0.014156384 -0.10667257 0.387946754
## x13 -0.003859800 0.1578934621 -0.028795850 0.03836012 -0.053144256
## x14 0.048754865 0.3991573828 0.025836092 0.02854465 -0.057791927
## x15 -0.288725458 0.0444343090 0.197316966 -0.06405394 0.066900852
## RC5
## x1 -0.532518411
## x2 -0.106498653
## x3 0.031410906
## x4 0.061999780
## x5 -0.053850311
## x6 -0.001304753
## x7 0.037945017
## x8 -0.002944088
## x9 0.044229464
## x10 0.098142293
## x11 0.005480346
## x12 0.038824028
## x13 0.656302428
## x14 0.034560186
## x15 -0.017402741pca2$weights[1:6,]## RC1 RC2 RC4 RC3 RC6 RC5
## x1 -0.008727579 0.27926048 -0.007237084 -0.01527418 -0.091588546 -0.532518411
## x2 0.347445455 0.00405425 0.111942053 0.01275760 -0.002653909 -0.106498653
## x3 0.025220962 0.04727732 -0.491534113 -0.02545133 0.035909049 0.031410906
## x4 0.003568835 0.07347215 0.048916959 -0.22268542 -0.406875705 0.061999780
## x5 0.010811259 -0.41857646 0.023497517 0.02449604 -0.014296960 -0.053850311
## x6 0.125340287 0.04207084 0.542636482 -0.04827402 0.046513370 -0.001304753Nuevos valores de las variables
pca2$scores## RC1 RC2 RC4 RC3 RC6
## [1,] 1.696675712 -2.95237390 0.18409563 -1.878654143 -0.673987884
## [2,] 0.351284360 1.08835815 -0.06242438 -2.727522318 0.259612560
## [3,] -0.201057151 -0.57101629 0.25247399 1.120188178 -1.026319387
## [4,] 0.170299405 0.47762532 0.51199628 0.207655637 -0.605058470
## [5,] 1.759096644 -0.06691141 -0.30379172 0.102550019 0.253110592
## [6,] -0.652624337 0.68606782 0.42292026 -1.805348449 -0.847561608
## [7,] 2.184837727 -1.11440944 0.89051816 -1.309657745 -0.193225576
## [8,] -2.199632155 -0.14959795 1.00364600 1.335361317 -0.861191559
## [9,] -0.116663140 -0.35762612 -0.34233539 1.587338793 0.695920508
## [10,] -0.641678048 0.46743514 0.66839606 -1.447722199 -0.833514181
## [11,] -0.794145937 0.72021506 0.60547108 -0.698097829 1.193845348
## [12,] -2.133031724 2.40206452 0.16210372 -0.058633355 0.324717899
## [13,] -0.358288317 0.06683173 -0.52418785 -1.310118628 -0.517293133
## [14,] 1.247022136 0.57597071 0.72167660 1.359679490 0.275169109
## [15,] -0.172029438 0.30343334 0.04612618 -0.182531972 0.166891808
## [16,] -0.321610659 0.73767031 -0.68668399 -0.546450535 -1.400197744
## [17,] -0.486137110 2.04836826 0.77157837 0.202395822 0.247323109
## [18,] 0.328502629 -1.95453150 0.74732870 0.031011616 -0.168250895
## [19,] -0.101565209 -0.08614786 -0.45361911 -0.190402586 0.024778837
## [20,] -0.127054189 -0.17151817 -1.04385934 0.869199081 -1.768970472
## [21,] -1.495302935 -1.16482774 0.41847956 -2.812503672 -0.166417309
## [22,] 0.130429000 -0.32955749 0.75790637 0.888626492 2.259695878
## [23,] -0.222172119 -2.03333412 0.67066554 1.564371182 1.990806009
## [24,] -0.124141464 0.50078464 -0.55297139 -0.143367617 -0.913284587
## [25,] -0.317613859 0.19348970 -0.34821277 -0.871013558 1.891105814
## [26,] 1.066631680 -0.80505473 -0.16984415 -0.049852993 0.108642507
## [27,] 1.063888592 1.58131511 1.75535491 -2.035482940 0.804347356
## [28,] 1.681845046 -2.54116441 -0.30714295 0.371240044 -0.637140307
## [29,] 1.587969984 0.64875596 -1.20761357 0.759610526 1.519006824
## [30,] 2.271218931 0.25014974 1.65513179 0.758705225 0.422499257
## [31,] -1.671718572 0.16957039 1.77601105 0.494568919 -0.869365385
## [32,] 0.788681226 1.74566916 -0.99717308 -1.294210547 -0.536393513
## [33,] -0.937492683 -0.69895784 -0.90730283 -1.111724215 0.963315097
## [34,] 1.720424392 1.70801870 -2.18896350 -0.409162457 -0.486994709
## [35,] -1.091063709 0.39245819 1.18054601 1.332961692 1.149350625
## [36,] -1.050123438 -1.64159753 -1.70265790 0.533996289 -0.517763748
## [37,] 1.480970058 -0.26932713 -0.55172918 -0.555579922 0.398837887
## [38,] -0.091238751 0.86694841 0.25117600 1.010178424 2.082154647
## [39,] -0.017076897 0.63255933 0.59080485 -0.375990697 -0.336746935
## [40,] 0.755412513 1.76222834 0.73123544 0.510385354 -0.154442233
## [41,] 1.054846822 0.06971828 0.76612062 -0.557367395 -0.061886082
## [42,] -1.551290406 -0.17776582 -0.15054803 0.189260805 1.093368150
## [43,] 0.589617528 0.60596860 -2.25922471 -0.471881484 0.874935329
## [44,] 0.650816186 -0.23392216 -0.51276673 0.266952260 1.045861140
## [45,] -0.144608772 0.52244077 1.14102578 0.231851155 -1.078075938
## [46,] 1.422827531 0.27078598 -0.04087503 -1.311678293 0.517340417
## [47,] -0.935362476 0.89790839 -0.88260279 0.498910163 1.298518938
## [48,] -1.540437126 -0.75362303 1.62601585 -0.760197357 -1.392789837
## [49,] 0.226352870 -1.68305424 -0.94766294 -1.527224570 1.512421176
## [50,] -0.737796566 0.48921454 -1.63148547 -1.345296502 -1.076331063
## [51,] 0.123113051 -0.20557143 0.39441201 -0.452214836 1.081780159
## [52,] 0.095122007 -0.71774840 -0.05755255 -0.079421316 -0.058850984
## [53,] -1.060952566 1.28747977 -1.69368603 0.555649976 -1.588164134
## [54,] 0.387140469 -0.37233459 -1.35371062 1.075835481 -1.614362384
## [55,] -0.214703924 1.50524981 1.70142068 1.194486157 -0.494534789
## [56,] -1.314498811 -0.23919772 0.98973400 0.347111028 1.895876942
## [57,] -0.083617237 0.85170841 0.46562941 1.708649469 0.475446268
## [58,] 0.663465690 1.17953300 -1.74984656 0.543536565 0.576974093
## [59,] -0.319120490 0.36812946 0.07724003 -0.289612343 0.487029725
## [60,] 1.875828388 2.65913320 -0.70300048 -0.115212123 0.881241038
## [61,] 0.151353320 -0.06276960 0.28553228 1.653840200 -0.804810213
## [62,] -0.157398138 -0.80496203 0.25221464 0.142460894 -0.311081936
## [63,] 0.374723238 -1.98603731 -0.94790686 -1.557130879 0.414883495
## [64,] -0.424054109 0.30036332 0.69070696 0.216233233 0.233455994
## [65,] -0.554787465 0.26588289 -0.17876959 -0.624156460 0.303264326
## [66,] -0.239089346 0.59708165 -0.53491746 0.249678727 0.350468096
## [67,] 0.194697898 -0.22186304 -1.05738345 -0.722344841 -1.581724829
## [68,] 1.637256835 -0.09679031 0.04387329 -0.215262916 1.740468974
## [69,] 0.749962904 -0.45603886 -0.44797323 0.129910254 0.397795268
## [70,] 0.136259901 1.32505746 0.82919286 1.418751018 0.627497270
## [71,] 0.096223037 -0.27201485 -0.47512173 0.528372183 -0.414914581
## [72,] -0.179852743 -0.15448476 -0.47548758 0.374561805 0.953329730
## [73,] -1.230554310 -0.12036741 -0.80791816 0.656793813 -0.923134607
## [74,] -0.135207551 1.49954724 -0.68344829 -0.837968190 -2.246053781
## [75,] 2.361043402 0.81299822 -0.60940414 0.186831504 -1.248609446
## [76,] -1.952353161 -1.30503937 0.31744901 0.850557149 0.095059892
## [77,] -0.780418311 -0.79564126 -1.32697995 -0.015762074 1.488677326
## [78,] -1.231920383 0.41091210 0.23895779 -0.123662948 2.141040431
## [79,] -0.421426079 -0.02550052 -0.55502141 -0.899756764 -0.592987033
## [80,] 0.514164950 0.08331605 1.63948430 0.043456624 -0.645631384
## [81,] -1.260264703 0.94810853 -0.64341283 -0.602658083 -1.498860359
## [82,] 0.267109991 0.21959230 -0.50954000 -0.875003856 1.136918715
## [83,] -1.503091517 0.49939831 1.28088137 0.587045724 1.857589721
## [84,] -0.400932851 0.52943089 0.50536709 0.142969122 0.505343662
## [85,] 0.479924797 0.21742583 -0.89493428 3.610174527 -2.242035341
## [86,] -0.166448097 -0.93990305 2.01926875 -0.364692517 -0.408993707
## [87,] 1.026469011 0.21363230 -0.93111505 0.580351996 1.032307547
## [88,] -1.827349593 -1.40811865 -1.79465254 1.943771431 0.626427848
## [89,] 1.251032037 -0.70168683 -1.12386873 0.979550454 0.952322846
## [90,] -0.235111425 1.48331683 0.08274629 1.188291000 0.439592587
## [91,] 1.077162373 0.53191406 -0.29397435 -0.923175425 0.228050293
## [92,] 0.492626253 -0.75038766 -1.08715981 1.652750732 -1.192661517
## [93,] 0.122230007 1.27651064 -0.38365114 -1.159076300 -1.193543449
## [94,] -0.286641933 -0.42395596 1.05795982 0.830864507 0.696814894
## [95,] -0.903013496 0.73000989 2.05129198 -0.572269243 -2.174491796
## [96,] -0.651524962 -0.83597359 1.77708652 -0.824709500 0.229608552
## [97,] -0.618910206 -0.67369298 0.51388447 1.121065719 -1.754414735
## [98,] 0.665826147 -0.23209892 1.34871623 -0.083452128 0.421533092
## [99,] 0.033297616 0.53375487 0.54032040 0.181922911 -0.036983992
## [100,] -1.300688248 1.32216278 -0.01144614 -1.508107402 0.293199878
## [101,] -0.108034412 0.16403595 -0.54495077 -0.508195499 -1.668931209
## [102,] 1.395216735 -0.16740184 0.14294285 1.397360873 -1.043667387
## [103,] -0.714958241 -2.34203332 -0.70667586 0.582146194 -1.046514968
## [104,] -0.368961474 0.39829728 -0.21207663 0.868602792 -1.476129777
## [105,] 1.356972192 0.89101164 0.55366976 -0.350079866 -0.371591193
## [106,] -1.193265566 -1.63000423 0.34508625 0.841854236 -0.087589127
## [107,] 0.040333085 0.29083220 -1.64281615 -0.162102227 0.643652891
## [108,] -1.061099859 -1.57531486 0.11170241 -1.707182861 -0.145635089
## [109,] 0.515394602 0.26688228 -1.24354092 0.244114395 1.277182027
## [110,] -0.607541194 1.36738227 0.16610553 -0.120100723 -1.018456802
## [111,] -0.102522923 -0.55104521 -0.66085213 0.573670415 -0.191093167
## [112,] 0.904645541 1.79328553 1.27329313 0.828689244 -0.681673456
## [113,] -0.131743965 -1.78932457 0.09197090 -0.331612007 -1.056609203
## [114,] 0.893588709 0.20995112 0.95217888 0.008529476 -0.259290951
## [115,] 0.795907855 -0.96706828 -1.40675338 -1.427078473 -0.033217438
## [116,] 0.845916229 -1.63782878 -1.23411125 -1.227057854 -1.414716092
## [117,] -0.403334784 1.89095626 0.24412672 0.785644682 0.181859146
## [118,] 0.499424574 0.83265462 -0.83131887 0.847105435 -0.476117803
## [119,] -1.046102204 0.40199631 0.91563835 -1.497806530 0.393819169
## [120,] 1.141162155 0.13242365 -1.35142720 -0.715799608 0.894342931
## [121,] 2.251652886 -0.61345727 0.67926473 1.494408499 -0.265117682
## [122,] -1.737994916 0.50490551 -0.75438952 -0.778275013 0.425354968
## [123,] 0.850606687 -1.74170211 1.09156135 0.420678085 0.631528596
## [124,] -0.874453000 -1.06030506 -0.25881442 0.628213482 -0.315813087
## [125,] -0.061917724 0.95480736 2.05705416 0.587101111 1.425715940
## [126,] -0.064222794 -0.95856289 -0.14465248 2.117321435 1.364117555
## [127,] -0.897056260 -0.90905493 0.29749453 -0.689761851 -1.066810166
## [128,] 1.515940562 -0.67259820 2.17558929 -1.897118754 -1.414844525
## [129,] 0.003635467 -0.32946156 1.54600485 -0.182562825 -0.687020244
## [130,] -0.325863772 -0.72165510 -0.09688543 -1.040421709 0.799753738
## [131,] 1.633001817 -0.19587737 1.24164450 1.035504935 -2.725686031
## [132,] -0.365286083 0.75539075 -2.90068670 0.713785329 -0.975224396
## [133,] 0.498579840 -0.70885129 -1.18004054 0.548837597 0.988343630
## [134,] 0.816792170 -0.38012587 -1.03312749 1.025781014 3.105770038
## [135,] -1.250579399 -0.63999682 -1.40480826 0.299722283 0.326364891
## [136,] -0.332557701 -0.14594610 -1.17155713 -0.318800611 -0.683981969
## [137,] 1.933515324 -1.17863201 1.10772371 0.810447835 -0.263410864
## [138,] -1.003358734 1.16882700 0.53248813 0.471010500 -0.204071839
## [139,] 0.676008733 -0.27570595 0.44959580 0.125812386 -0.552074837
## [140,] -1.141207064 -1.97126326 -0.19040145 -0.087881490 1.025016310
## [141,] -0.709101900 -0.16944066 -0.23194030 0.299789033 0.024576034
## [142,] 0.651970973 1.53763202 0.81366081 -0.651398594 1.183212064
## [143,] -1.110547628 -0.13536375 1.36251286 -0.983660473 0.396858964
## [144,] 0.228090539 0.31318007 0.09132920 0.116232845 0.366658985
## [145,] 0.345728619 -0.27042307 -0.35768585 -0.911565333 1.065537927
## [146,] -0.893208235 -1.06239658 -0.17722810 -0.792584946 1.193594851
## [147,] -0.460308844 0.18117082 -0.32339408 -0.566270015 0.461242329
## [148,] 1.703662060 -1.03058709 -0.77145919 -2.488470228 0.563298217
## [149,] 1.058195842 1.07718539 1.06661406 0.993897751 -0.651210599
## [150,] 0.045452973 1.00383363 -0.87039537 1.568665653 1.044709744
## [151,] -0.383350172 -0.72599254 -0.68722225 0.150966974 -0.364108810
## [152,] -0.822628119 -1.66923604 0.06424345 -1.071424150 -0.517397382
## [153,] 0.564506732 0.03240311 -0.33179042 -0.218693542 -0.512908328
## [154,] -1.647663252 -0.24408895 -0.13957119 -1.415824791 -0.096306923
## [155,] -2.088397333 0.35781133 0.56681850 -0.118923700 0.205105603
## [156,] -0.998136881 -0.62820914 -1.45905296 0.888533293 0.797830450
## [157,] -0.531360948 -1.33713196 0.33017818 0.199359950 1.588817787
## [158,] -1.594241137 0.94333956 -0.57808442 1.733346952 0.037285496
## [159,] 0.520402928 -0.64854327 0.97979541 -0.239749543 -0.009981294
## [160,] 0.154469548 1.04296074 -0.85951095 0.409177561 0.531407765
## [161,] 2.458225711 -0.78952926 1.98501496 -0.411984678 1.347626407
## [162,] 0.750790603 -1.49289519 -0.14426713 -0.092645412 -0.770526955
## [163,] 0.487010450 0.15923571 0.36180930 -0.799806181 1.066569599
## [164,] -0.319990083 -0.60655278 1.34330670 0.636576065 0.236781685
## [165,] 0.223519662 0.31729811 0.54127398 0.779929965 0.816210102
## [166,] -1.574405150 0.77181785 0.72186663 -0.930615381 0.064249745
## [167,] -0.443436275 0.58193702 1.75193535 -0.273629551 -0.568844104
## [168,] -0.416907945 0.48428709 -0.63955217 1.014777716 -0.060831376
## [169,] 1.369452023 0.38806880 0.02901107 -0.249081097 1.246388825
## [170,] -0.841203055 -0.17423390 0.11385954 0.295478566 -1.999699389
## [171,] 1.266515701 1.04241454 -0.12445019 -0.462934435 1.187770968
## [172,] 0.958390288 1.09581932 -0.60603104 -0.838625356 -1.828224249
## [173,] 0.275331958 -1.39432214 1.15543190 0.020933953 -0.299523809
## [174,] -1.304445427 -0.70557199 -2.34559754 -1.880933838 0.828448954
## [175,] -1.512786956 -0.09057302 -0.04406826 0.166203000 -0.150662115
## [176,] -0.367702423 0.79104026 1.22665307 -1.628652593 -0.005482783
## [177,] 0.532893020 -0.53188456 1.13923303 3.289787079 -0.631972408
## [178,] -1.780325162 -0.86079831 -0.26784422 0.891530417 -0.555479306
## [179,] -0.166951676 1.66271031 0.61379428 -1.773724723 -0.056624062
## [180,] 1.987921396 -0.80864502 -1.94182133 0.781808454 0.014914693
## [181,] 0.360362584 0.70111545 -1.18053766 0.973171616 0.581189979
## [182,] -0.499525759 0.59896755 -0.24113982 0.336015248 -0.406010382
## [183,] -1.498433331 -0.37678544 0.15441921 0.417299656 -1.603641681
## [184,] -0.562845831 0.87203526 0.33427304 -0.261167127 1.265040762
## [185,] 0.332168945 -0.03411607 -0.10930311 0.541250960 -0.404019238
## [186,] 0.126076092 -0.55478070 -1.77713429 0.428373291 -0.442500420
## [187,] -0.331408243 0.10062822 -0.56811582 0.904157241 -0.772162228
## [188,] 0.024483676 0.45599323 -1.45499732 -1.219884224 -0.685919771
## [189,] -0.493795505 2.30620450 0.55732282 0.135573736 0.875242835
## [190,] -0.677472139 0.46919472 0.52958004 -0.396427758 -0.140128163
## [191,] -0.358006865 0.54568378 -0.72586886 0.498403992 -0.545466508
## [192,] 1.044949190 -1.08767947 1.98077485 0.937090198 -1.430972969
## [193,] 0.913766287 -1.15662080 1.99390502 -0.551381753 -0.044276092
## [194,] -0.812079297 -0.48722203 -1.03663818 -1.179698933 -1.584698277
## [195,] -0.120187813 1.04914374 0.27287413 -0.486070069 0.130688848
## [196,] 1.332279261 1.89059570 -0.28807161 -0.710926532 -1.020090812
## [197,] 0.404530235 -0.61540093 1.67727477 -0.438818732 -0.249558679
## [198,] -0.639071082 -2.16282843 1.22484860 0.770510194 0.689480438
## [199,] 1.897545903 -0.09765963 -1.21421292 -0.076610665 -1.494448116
## [200,] -0.153797277 -0.65979437 0.20350938 -0.560309904 0.947876710
## RC5
## [1,] 0.18450606
## [2,] -1.21332546
## [3,] 0.88046683
## [4,] 0.49093050
## [5,] 0.48789498
## [6,] 0.56793420
## [7,] -0.52900120
## [8,] 0.42154716
## [9,] -1.17394391
## [10,] 3.34970341
## [11,] -0.23608932
## [12,] -0.76244539
## [13,] 0.41267501
## [14,] -0.21688449
## [15,] -2.50215158
## [16,] -1.72856464
## [17,] -1.24685526
## [18,] 0.67456599
## [19,] 0.01617382
## [20,] 0.24508923
## [21,] 1.00380132
## [22,] 0.51191458
## [23,] -0.34468581
## [24,] 0.65055110
## [25,] 0.83599140
## [26,] -0.53269239
## [27,] -0.82956540
## [28,] 1.08045389
## [29,] 1.24080116
## [30,] 1.51713338
## [31,] -0.17173407
## [32,] -0.22286824
## [33,] 0.78600738
## [34,] 1.00285654
## [35,] -1.18796629
## [36,] 0.05708163
## [37,] -0.24445621
## [38,] 1.33531188
## [39,] -0.68416562
## [40,] 0.48238834
## [41,] 0.63028353
## [42,] -1.78112436
## [43,] 0.42271600
## [44,] 0.77882093
## [45,] -0.45699243
## [46,] 1.17971801
## [47,] -0.03157979
## [48,] 0.11300140
## [49,] 1.45972536
## [50,] 0.35284137
## [51,] -0.78385186
## [52,] 1.34464849
## [53,] -0.45639551
## [54,] -1.83422715
## [55,] -1.35572915
## [56,] 1.29851585
## [57,] -1.40775848
## [58,] -0.08509117
## [59,] -0.56898764
## [60,] -0.45524301
## [61,] -0.27244546
## [62,] 0.50486675
## [63,] -2.17121305
## [64,] 1.05836764
## [65,] -0.72818121
## [66,] -0.65424004
## [67,] -0.22574058
## [68,] -1.35842404
## [69,] 0.60651112
## [70,] 0.17999082
## [71,] -0.49777078
## [72,] -0.23714411
## [73,] -0.50334948
## [74,] -0.70732947
## [75,] -0.44328299
## [76,] -1.68142971
## [77,] 0.21419820
## [78,] -1.75142751
## [79,] 0.84075289
## [80,] -1.10680647
## [81,] -0.03041947
## [82,] -0.71265039
## [83,] 0.20084083
## [84,] -1.58422448
## [85,] -1.42056561
## [86,] 1.53607711
## [87,] 1.64723159
## [88,] -0.07293742
## [89,] -0.10097355
## [90,] 1.07972036
## [91,] -1.18928304
## [92,] -0.98652962
## [93,] 0.63976145
## [94,] 0.70976302
## [95,] 1.12215043
## [96,] -0.57291764
## [97,] 0.09714357
## [98,] -0.09665338
## [99,] -0.90542168
## [100,] 0.38917576
## [101,] -0.40921235
## [102,] 0.81316497
## [103,] -1.28430964
## [104,] -0.75364877
## [105,] -0.91420749
## [106,] 1.89361193
## [107,] 0.14265574
## [108,] 0.41664273
## [109,] 0.84792265
## [110,] 0.27643566
## [111,] -0.15100376
## [112,] 1.49860009
## [113,] -0.42632878
## [114,] -1.10126070
## [115,] 0.18891519
## [116,] -1.97844085
## [117,] -0.58803890
## [118,] 0.13291022
## [119,] 0.63204044
## [120,] -1.00743377
## [121,] -2.22885052
## [122,] 0.16788370
## [123,] 0.09447279
## [124,] -0.58771803
## [125,] -1.34310504
## [126,] -0.96682231
## [127,] -0.46903127
## [128,] 0.44576335
## [129,] 0.28450761
## [130,] 0.31327082
## [131,] 0.91555065
## [132,] 0.43083091
## [133,] -0.34636574
## [134,] -0.66481246
## [135,] 1.67750468
## [136,] 0.63554845
## [137,] 1.41164321
## [138,] 2.07601253
## [139,] 1.36428590
## [140,] -0.86850241
## [141,] 2.20810646
## [142,] -0.17086796
## [143,] -0.31430454
## [144,] 0.78676931
## [145,] 0.77052423
## [146,] -0.09942650
## [147,] -0.27686970
## [148,] 0.74491319
## [149,] 2.00059055
## [150,] -0.42466513
## [151,] -0.07086902
## [152,] -0.83659784
## [153,] -0.29654627
## [154,] 0.48158246
## [155,] 1.04204742
## [156,] 1.55546856
## [157,] -0.49446136
## [158,] 0.58490937
## [159,] -0.21264804
## [160,] -0.25088131
## [161,] -2.64103639
## [162,] -0.70074005
## [163,] 0.15986564
## [164,] 1.66123902
## [165,] 2.25539458
## [166,] -0.58252615
## [167,] -0.50673962
## [168,] -0.92631826
## [169,] 0.61055724
## [170,] 1.01097423
## [171,] 0.55777114
## [172,] -0.85802724
## [173,] -0.61581291
## [174,] -0.83589532
## [175,] -0.13304706
## [176,] 0.66250589
## [177,] 0.62481638
## [178,] -0.35789982
## [179,] -0.87637655
## [180,] 1.82040776
## [181,] 0.53504259
## [182,] 1.26812290
## [183,] -0.47238575
## [184,] 1.11810978
## [185,] 1.31059584
## [186,] 0.10947770
## [187,] 1.02619920
## [188,] 0.62663289
## [189,] -0.21015861
## [190,] -0.51013437
## [191,] -0.32891441
## [192,] -0.08255375
## [193,] 0.19166064
## [194,] -0.96087132
## [195,] -0.67274474
## [196,] -2.42308327
## [197,] 0.40197792
## [198,] -1.82406267
## [199,] 0.48995249
## [200,] -0.80669620