library(readxl)
library(MVN)
library(psych)
##
## Attaching package: 'psych'
## The following object is masked from 'package:MVN':
##
## mardia
library(corrplot)
## corrplot 0.95 loaded
library(factoextra)
## Loading required package: ggplot2
##
## Attaching package: 'ggplot2'
## The following objects are masked from 'package:psych':
##
## %+%, alpha
## Welcome to factoextra!
## Want to learn more? See two factoextra-related books at https://www.datanovia.com/en/product/practical-guide-to-principal-component-methods-in-r/
library(GPArotation)
##
## Attaching package: 'GPArotation'
## The following objects are masked from 'package:psych':
##
## equamax, varimin
data <- read_excel("Dry_Bean_Dataset.xlsx")
data <- data[, !(names(data) %in% c("Class", "Solidity", "ShapeFactor4"))]
data_numeric <- data[sapply(data, is.numeric)]
cor(data_numeric)
## Area Perimeter MajorAxisLength MinorAxisLength
## Area 1.00000000 0.96672218 0.93183359 0.951601599
## Perimeter 0.96672218 1.00000000 0.97733775 0.913178555
## MajorAxisLength 0.93183359 0.97733775 1.00000000 0.826051550
## MinorAxisLength 0.95160160 0.91317856 0.82605155 1.000000000
## AspectRation 0.24173480 0.38527565 0.55033477 -0.009161131
## Eccentricity 0.26748137 0.39106554 0.54197162 0.019573875
## ConvexArea 0.99993923 0.96768921 0.93260701 0.951339329
## EquivDiameter 0.98496752 0.99138043 0.96173336 0.948538894
## Extent 0.05434485 -0.02115958 -0.07806191 0.145957056
## roundness -0.35753034 -0.54764667 -0.59635758 -0.210343945
## Compactness -0.26806683 -0.40685686 -0.56837707 -0.015066473
## ShapeFactor1 -0.84795833 -0.86462294 -0.77360867 -0.947204167
## ShapeFactor2 -0.63929075 -0.76759233 -0.85923764 -0.471347004
## ShapeFactor3 -0.27214485 -0.40843530 -0.56818480 -0.019326233
## AspectRation Eccentricity ConvexArea EquivDiameter Extent
## Area 0.241734796 0.26748137 0.99993923 0.98496752 0.05434485
## Perimeter 0.385275645 0.39106554 0.96768921 0.99138043 -0.02115958
## MajorAxisLength 0.550334771 0.54197162 0.93260701 0.96173336 -0.07806191
## MinorAxisLength -0.009161131 0.01957387 0.95133933 0.94853889 0.14595706
## AspectRation 1.000000000 0.92429255 0.24330102 0.30364704 -0.37018356
## Eccentricity 0.924292554 1.00000000 0.26925479 0.31866708 -0.31936188
## ConvexArea 0.243301025 0.26925479 1.00000000 0.98522625 0.05256368
## EquivDiameter 0.303647037 0.31866708 0.98522625 1.00000000 0.02838294
## Extent -0.370183561 -0.31936188 0.05256368 0.02838294 1.00000000
## roundness -0.766979298 -0.72227246 -0.36208262 -0.43594454 0.34441115
## Compactness -0.987687299 -0.97031302 -0.26992245 -0.32764998 0.35421175
## ShapeFactor1 0.024592773 0.01991968 -0.84794973 -0.89274073 -0.14161642
## ShapeFactor2 -0.837841217 -0.86014079 -0.64086162 -0.71306865 0.23795572
## ShapeFactor3 -0.978592275 -0.98105770 -0.27402416 -0.33038937 0.34762441
## roundness Compactness ShapeFactor1 ShapeFactor2 ShapeFactor3
## Area -0.3575303 -0.268066825 -0.847958328 -0.6392907 -0.272144848
## Perimeter -0.5476467 -0.406856863 -0.864622945 -0.7675923 -0.408435296
## MajorAxisLength -0.5963576 -0.568377073 -0.773608665 -0.8592376 -0.568184805
## MinorAxisLength -0.2103439 -0.015066473 -0.947204167 -0.4713470 -0.019326233
## AspectRation -0.7669793 -0.987687299 0.024592773 -0.8378412 -0.978592275
## Eccentricity -0.7222725 -0.970313022 0.019919682 -0.8601408 -0.981057697
## ConvexArea -0.3620826 -0.269922448 -0.847949735 -0.6408616 -0.274024160
## EquivDiameter -0.4359445 -0.327649979 -0.892740731 -0.7130686 -0.330389365
## Extent 0.3444112 0.354211746 -0.141616424 0.2379557 0.347624414
## roundness 1.0000000 0.768086378 0.230272514 0.7828242 0.763125731
## Compactness 0.7680864 1.000000000 -0.009394033 0.8689392 0.998685813
## ShapeFactor1 0.2302725 -0.009394033 1.000000000 0.4691974 -0.008320199
## ShapeFactor2 0.7828242 0.868939199 0.469197371 1.0000000 0.872970779
## ShapeFactor3 0.7631257 0.998685813 -0.008320199 0.8729708 1.000000000
cor(data_numeric)
## Area Perimeter MajorAxisLength MinorAxisLength
## Area 1.00000000 0.96672218 0.93183359 0.951601599
## Perimeter 0.96672218 1.00000000 0.97733775 0.913178555
## MajorAxisLength 0.93183359 0.97733775 1.00000000 0.826051550
## MinorAxisLength 0.95160160 0.91317856 0.82605155 1.000000000
## AspectRation 0.24173480 0.38527565 0.55033477 -0.009161131
## Eccentricity 0.26748137 0.39106554 0.54197162 0.019573875
## ConvexArea 0.99993923 0.96768921 0.93260701 0.951339329
## EquivDiameter 0.98496752 0.99138043 0.96173336 0.948538894
## Extent 0.05434485 -0.02115958 -0.07806191 0.145957056
## roundness -0.35753034 -0.54764667 -0.59635758 -0.210343945
## Compactness -0.26806683 -0.40685686 -0.56837707 -0.015066473
## ShapeFactor1 -0.84795833 -0.86462294 -0.77360867 -0.947204167
## ShapeFactor2 -0.63929075 -0.76759233 -0.85923764 -0.471347004
## ShapeFactor3 -0.27214485 -0.40843530 -0.56818480 -0.019326233
## AspectRation Eccentricity ConvexArea EquivDiameter Extent
## Area 0.241734796 0.26748137 0.99993923 0.98496752 0.05434485
## Perimeter 0.385275645 0.39106554 0.96768921 0.99138043 -0.02115958
## MajorAxisLength 0.550334771 0.54197162 0.93260701 0.96173336 -0.07806191
## MinorAxisLength -0.009161131 0.01957387 0.95133933 0.94853889 0.14595706
## AspectRation 1.000000000 0.92429255 0.24330102 0.30364704 -0.37018356
## Eccentricity 0.924292554 1.00000000 0.26925479 0.31866708 -0.31936188
## ConvexArea 0.243301025 0.26925479 1.00000000 0.98522625 0.05256368
## EquivDiameter 0.303647037 0.31866708 0.98522625 1.00000000 0.02838294
## Extent -0.370183561 -0.31936188 0.05256368 0.02838294 1.00000000
## roundness -0.766979298 -0.72227246 -0.36208262 -0.43594454 0.34441115
## Compactness -0.987687299 -0.97031302 -0.26992245 -0.32764998 0.35421175
## ShapeFactor1 0.024592773 0.01991968 -0.84794973 -0.89274073 -0.14161642
## ShapeFactor2 -0.837841217 -0.86014079 -0.64086162 -0.71306865 0.23795572
## ShapeFactor3 -0.978592275 -0.98105770 -0.27402416 -0.33038937 0.34762441
## roundness Compactness ShapeFactor1 ShapeFactor2 ShapeFactor3
## Area -0.3575303 -0.268066825 -0.847958328 -0.6392907 -0.272144848
## Perimeter -0.5476467 -0.406856863 -0.864622945 -0.7675923 -0.408435296
## MajorAxisLength -0.5963576 -0.568377073 -0.773608665 -0.8592376 -0.568184805
## MinorAxisLength -0.2103439 -0.015066473 -0.947204167 -0.4713470 -0.019326233
## AspectRation -0.7669793 -0.987687299 0.024592773 -0.8378412 -0.978592275
## Eccentricity -0.7222725 -0.970313022 0.019919682 -0.8601408 -0.981057697
## ConvexArea -0.3620826 -0.269922448 -0.847949735 -0.6408616 -0.274024160
## EquivDiameter -0.4359445 -0.327649979 -0.892740731 -0.7130686 -0.330389365
## Extent 0.3444112 0.354211746 -0.141616424 0.2379557 0.347624414
## roundness 1.0000000 0.768086378 0.230272514 0.7828242 0.763125731
## Compactness 0.7680864 1.000000000 -0.009394033 0.8689392 0.998685813
## ShapeFactor1 0.2302725 -0.009394033 1.000000000 0.4691974 -0.008320199
## ShapeFactor2 0.7828242 0.868939199 0.469197371 1.0000000 0.872970779
## ShapeFactor3 0.7631257 0.998685813 -0.008320199 0.8729708 1.000000000
corrplot::corrplot(cor(data_numeric),tl.col = "black",type= "full",tl.srt=40,tl.cex = 0.5)
r <- cor(data_numeric)
KMO(data_numeric)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = data_numeric)
## Overall MSA = 0.68
## MSA for each item =
## Area Perimeter MajorAxisLength MinorAxisLength AspectRation
## 0.78 0.85 0.68 0.57 0.55
## Eccentricity ConvexArea EquivDiameter Extent roundness
## 0.60 0.78 0.61 0.99 0.80
## Compactness ShapeFactor1 ShapeFactor2 ShapeFactor3
## 0.54 0.83 0.87 0.54
bartlett.test(data_numeric)
##
## Bartlett test of homogeneity of variances
##
## data: data_numeric
## Bartlett's K-squared = 3297140, df = 13, p-value < 2.2e-16
data[sapply(data, is.numeric)]
## # A tibble: 13,611 × 14
## Area Perimeter MajorAxisLength MinorAxisLength AspectRation Eccentricity
## <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 28395 610. 208. 174. 1.20 0.550
## 2 28734 638. 201. 183. 1.10 0.412
## 3 29380 624. 213. 176. 1.21 0.563
## 4 30008 646. 211. 183. 1.15 0.499
## 5 30140 620. 202. 190. 1.06 0.334
## 6 30279 635. 213. 182. 1.17 0.520
## 7 30477 670. 211. 184. 1.15 0.489
## 8 30519 630. 213. 183. 1.17 0.514
## 9 30685 636. 214. 183. 1.17 0.514
## 10 30834 632. 217. 181. 1.20 0.554
## # ℹ 13,601 more rows
## # ℹ 8 more variables: ConvexArea <dbl>, EquivDiameter <dbl>, Extent <dbl>,
## # roundness <dbl>, Compactness <dbl>, ShapeFactor1 <dbl>, ShapeFactor2 <dbl>,
## # ShapeFactor3 <dbl>
data_numeric <- na.omit(data_numeric)
scale_data <- scale(data_numeric)
pc <- prcomp(scale_data, center = TRUE, scale. = TRUE)
summary(pc)
## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.9018 2.0396 0.90709 0.59481 0.38750 0.28432 0.09118
## Proportion of Variance 0.6015 0.2971 0.05877 0.02527 0.01073 0.00577 0.00059
## Cumulative Proportion 0.6015 0.8986 0.95736 0.98263 0.99336 0.99913 0.99973
## PC8 PC9 PC10 PC11 PC12 PC13
## Standard deviation 0.04269 0.03756 0.01849 0.01240 0.008314 0.003758
## Proportion of Variance 0.00013 0.00010 0.00002 0.00001 0.000000 0.000000
## Cumulative Proportion 0.99986 0.99996 0.99998 0.99999 1.000000 1.000000
## PC14
## Standard deviation 0.001505
## Proportion of Variance 0.000000
## Cumulative Proportion 1.000000
L <- as.matrix(pc$rotation[, 1:3])
L
## PC1 PC2 PC3
## Area 0.29791338 0.2295934 -0.01564508
## Perimeter 0.32426279 0.1624852 -0.03554219
## MajorAxisLength 0.33858492 0.0805077 0.01003636
## MinorAxisLength 0.25179813 0.3326263 -0.06015909
## AspectRation 0.22938815 -0.3514441 0.08597545
## Eccentricity 0.23146973 -0.3393139 0.15183081
## ConvexArea 0.29838419 0.2286491 -0.01709523
## EquivDiameter 0.31242279 0.2058948 -0.02022670
## Extent -0.05513295 0.2249679 0.95704259
## roundness -0.24470800 0.2239782 0.09392582
## Compactness -0.23782129 0.3487827 -0.11339702
## ShapeFactor1 -0.23586442 -0.3230840 0.07826000
## ShapeFactor2 -0.32133463 0.1516088 -0.07023242
## ShapeFactor3 -0.23843733 0.3473458 -0.12230175
lambda <- pc$sdev^2
lambda
## [1] 8.420314e+00 4.159956e+00 8.228101e-01 3.538035e-01 1.501525e-01
## [6] 8.083642e-02 8.313006e-03 1.822189e-03 1.410650e-03 3.417688e-04
## [11] 1.538531e-04 6.912557e-05 1.411931e-05 2.263902e-06
lambda_k <- lambda[1:ncol(L)]
V <- sweep(L, 2, sqrt(lambda_k[1:3]), "/")
V
## PC1 PC2 PC3
## Area 0.10266581 0.11256801 -0.01724757
## Perimeter 0.11174625 0.07966532 -0.03918270
## MajorAxisLength 0.11668189 0.03947235 0.01106437
## MinorAxisLength 0.08677375 0.16308431 -0.06632106
## AspectRation 0.07905090 -0.17231056 0.09478173
## Eccentricity 0.07976825 -0.16636322 0.16738252
## ConvexArea 0.10282806 0.11210505 -0.01884625
## EquivDiameter 0.10766599 0.10094875 -0.02229848
## Extent -0.01899971 0.11030014 1.05507044
## roundness -0.08433037 0.10981494 0.10354644
## Compactness -0.08195710 0.17100567 -0.12501204
## ShapeFactor1 -0.08128273 -0.15840579 0.08627601
## ShapeFactor2 -0.11073716 0.07433271 -0.07742618
## ShapeFactor3 -0.08216940 0.17030119 -0.13482886
scores <- scale_data %*% V
head(scores)
## PC1 PC2 PC3
## [1,] -1.676198 0.9927785 -0.5522655
## [2,] -1.877615 1.6137987 -0.8205392
## [3,] -1.583987 0.9743166 -0.2171171
## [4,] -1.637029 1.2681025 -0.4768893
## [5,] -2.114062 2.1294414 -1.1632550
## [6,] -1.644779 1.2341469 -0.4788713
fa <- principal(scale_data, nfactors = 3, rotate = "none")
fa
## Principal Components Analysis
## Call: principal(r = scale_data, nfactors = 3, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 h2 u2 com
## Area 0.86 0.47 -0.01 0.97 0.0332 1.5
## Perimeter 0.94 0.33 -0.03 1.00 0.0038 1.2
## MajorAxisLength 0.98 0.16 0.01 0.99 0.0077 1.1
## MinorAxisLength 0.73 0.68 -0.05 1.00 0.0029 2.0
## AspectRation 0.67 -0.72 0.08 0.96 0.0370 2.0
## Eccentricity 0.67 -0.69 0.14 0.95 0.0509 2.1
## ConvexArea 0.87 0.47 -0.02 0.97 0.0326 1.5
## EquivDiameter 0.91 0.42 -0.02 1.00 0.0014 1.4
## Extent -0.16 0.46 0.87 0.99 0.0102 1.6
## roundness -0.71 0.46 0.09 0.72 0.2798 1.7
## Compactness -0.69 0.71 -0.10 0.99 0.0071 2.0
## ShapeFactor1 -0.68 -0.66 0.07 0.91 0.0923 2.0
## ShapeFactor2 -0.93 0.31 -0.06 0.97 0.0309 1.2
## ShapeFactor3 -0.69 0.71 -0.11 0.99 0.0071 2.0
##
## PC1 PC2 PC3
## SS loadings 8.42 4.16 0.82
## Proportion Var 0.60 0.30 0.06
## Cumulative Var 0.60 0.90 0.96
## Proportion Explained 0.63 0.31 0.06
## Cumulative Proportion 0.63 0.94 1.00
##
## Mean item complexity = 1.7
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.01
## with the empirical chi square 409.28 with prob < 5.8e-57
##
## Fit based upon off diagonal values = 1
fa$loadings
##
## Loadings:
## PC1 PC2 PC3
## Area 0.864 0.468
## Perimeter 0.941 0.331
## MajorAxisLength 0.982 0.164
## MinorAxisLength 0.731 0.678
## AspectRation 0.666 -0.717
## Eccentricity 0.672 -0.692 0.138
## ConvexArea 0.866 0.466
## EquivDiameter 0.907 0.420
## Extent -0.160 0.459 0.868
## roundness -0.710 0.457
## Compactness -0.690 0.711 -0.103
## ShapeFactor1 -0.684 -0.659
## ShapeFactor2 -0.932 0.309
## ShapeFactor3 -0.692 0.708 -0.111
##
## PC1 PC2 PC3
## SS loadings 8.420 4.160 0.823
## Proportion Var 0.601 0.297 0.059
## Cumulative Var 0.601 0.899 0.957
fa.diagram(fa$loadings)
fa_1 <- principal(scale_data, nfactors = 3, rotate = "varimax")
fa_1
## Principal Components Analysis
## Call: principal(r = scale_data, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC3 h2 u2 com
## Area 0.97 -0.18 0.03 0.97 0.0332 1.1
## Perimeter 0.94 -0.33 -0.02 1.00 0.0038 1.2
## MajorAxisLength 0.87 -0.49 -0.02 0.99 0.0077 1.6
## MinorAxisLength 1.00 0.07 0.04 1.00 0.0029 1.0
## AspectRation 0.07 -0.97 -0.11 0.96 0.0370 1.0
## Eccentricity 0.08 -0.97 -0.05 0.95 0.0509 1.0
## ConvexArea 0.97 -0.19 0.03 0.97 0.0326 1.1
## EquivDiameter 0.97 -0.25 0.01 1.00 0.0014 1.1
## Extent 0.09 0.27 0.95 0.99 0.0102 1.2
## roundness -0.28 0.77 0.22 0.72 0.2798 1.4
## Compactness -0.09 0.99 0.09 0.99 0.0071 1.0
## ShapeFactor1 -0.95 -0.08 -0.03 0.91 0.0923 1.0
## ShapeFactor2 -0.53 0.83 0.06 0.97 0.0309 1.7
## ShapeFactor3 -0.09 0.99 0.08 0.99 0.0071 1.0
##
## RC1 RC2 RC3
## SS loadings 6.72 5.69 0.99
## Proportion Var 0.48 0.41 0.07
## Cumulative Var 0.48 0.89 0.96
## Proportion Explained 0.50 0.42 0.07
## Cumulative Proportion 0.50 0.93 1.00
##
## Mean item complexity = 1.2
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.01
## with the empirical chi square 409.28 with prob < 5.8e-57
##
## Fit based upon off diagonal values = 1
fa_1$communality
## Area Perimeter MajorAxisLength MinorAxisLength AspectRation
## 0.9668086 0.9962335 0.9923483 0.9971037 0.9629584
## Eccentricity ConvexArea EquivDiameter Extent roundness
## 0.9490656 0.9674116 0.9985782 0.9897692 0.7201736
## Compactness ShapeFactor1 ShapeFactor2 ShapeFactor3
## 0.9928807 0.9077083 0.9691236 0.9929171
scores <- scale_data %*% solve(cor(scale_data)) %*% as.matrix(fa$loadings)
scores
## PC1 PC2 PC3
## [1,] -1.676198e+00 9.927785e-01 -0.5522655367
## [2,] -1.877615e+00 1.613799e+00 -0.8205391755
## [3,] -1.583987e+00 9.743166e-01 -0.2171171204
## [4,] -1.637029e+00 1.268103e+00 -0.4768892539
## [5,] -2.114062e+00 2.129441e+00 -1.1632549950
## [6,] -1.644779e+00 1.234147e+00 -0.4788713371
## [7,] -1.558767e+00 1.216528e+00 -1.0617292377
## [8,] -1.683048e+00 1.304410e+00 -0.5734210805
## [9,] -1.655710e+00 1.291218e+00 -0.5797629338
## [10,] -1.578166e+00 1.135576e+00 -0.1152038081
## [11,] -1.657370e+00 1.338199e+00 -0.6567624769
## [12,] -1.805145e+00 1.677818e+00 -0.5330288659
## [13,] -1.642961e+00 1.311134e+00 -0.8379066362
## [14,] -1.593699e+00 1.274026e+00 0.0595780340
## [15,] -1.740975e+00 1.551957e+00 -0.5628203360
## [16,] -1.725132e+00 1.475512e+00 -0.8577590873
## [17,] -1.608617e+00 1.290075e+00 -0.4221724541
## [18,] -1.642698e+00 1.315609e+00 -0.7769502231
## [19,] -1.748764e+00 1.550459e+00 -0.7809484188
## [20,] -1.629630e+00 1.289760e+00 -0.4298855442
## [21,] -1.531751e+00 1.084351e+00 -0.3899418989
## [22,] -1.733322e+00 1.539200e+00 -0.7743654282
## [23,] -1.457149e+00 1.112027e+00 -1.0139803654
## [24,] -1.190407e+00 4.578309e-01 -0.2186174626
## [25,] -1.019797e+00 5.977905e-02 -0.3944237245
## [26,] -1.855923e+00 1.854335e+00 -0.9978138560
## [27,] -1.608110e+00 1.385462e+00 -0.6002874602
## [28,] -1.550481e+00 1.192080e+00 -0.3364713737
## [29,] -1.474614e+00 1.081549e+00 -0.2816216109
## [30,] -1.431759e+00 9.392197e-01 -0.1669921958
## [31,] -1.721382e+00 1.598146e+00 -0.8131418898
## [32,] -1.370041e+00 9.130655e-01 -0.3090922854
## [33,] -1.346389e+00 8.477709e-01 0.0416298623
## [34,] -1.686293e+00 1.493056e+00 -0.5045666396
## [35,] -1.786128e+00 1.696878e+00 -0.7857253767
## [36,] -1.817232e+00 1.768531e+00 -0.8016476302
## [37,] -1.785547e+00 1.796398e+00 -0.5981574620
## [38,] -1.752237e+00 1.683391e+00 -1.1441130442
## [39,] -1.214633e+00 5.563241e-01 0.1794984084
## [40,] -1.426068e+00 9.577426e-01 -0.2622517744
## [41,] -1.650629e+00 1.488392e+00 -0.5899939907
## [42,] -1.711420e+00 1.568066e+00 -0.5129651360
## [43,] -1.021914e+00 2.130832e-01 0.3549155114
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## [1968,] -4.313517e-01 9.808813e-01 0.2339549820
## [1969,] -5.280946e-01 1.178732e+00 -0.9271042399
## [1970,] -8.821133e-02 1.405083e-01 -0.8380737207
## [1971,] -4.796772e-01 1.102257e+00 0.1143377553
## [1972,] -5.699730e-01 1.209340e+00 -0.2098939485
## [1973,] 1.327219e-01 -2.131924e-01 1.1039650367
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## [1975,] -2.646801e-01 5.680121e-01 -0.6928925904
## [1976,] -2.668804e-01 6.520392e-01 -0.4014640519
## [1977,] -4.380327e-01 1.088649e+00 -0.6979306731
## [1978,] -2.810480e-01 6.213992e-01 -0.4681771691
## [1979,] -4.399137e-01 1.015412e+00 -0.1304812267
## [1980,] -7.631078e-01 1.729112e+00 -0.7082209724
## [1981,] -5.689430e-01 1.275044e+00 0.0008515662
## [1982,] -3.289997e-01 8.021393e-01 0.1492167214
## [1983,] -4.395988e-01 9.852679e-01 -0.9834547200
## [1984,] 1.236579e-01 -8.791819e-02 1.3697553117
## [1985,] -2.095138e-01 6.608551e-01 -0.6584440545
## [1986,] -1.664252e-01 6.140960e-01 -0.7664415730
## [1987,] -4.496898e-01 1.075616e+00 -0.0563492650
## [1988,] -3.314815e-01 8.991191e-01 -0.4414202396
## [1989,] -4.336418e-01 1.061504e+00 -0.8352587925
## [1990,] -5.977656e-01 1.461999e+00 -0.7528811438
## [1991,] -1.214555e-01 4.751047e-01 1.0766741650
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## [1993,] -7.339550e-01 1.800479e+00 -1.0003046339
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## [1995,] -2.496606e-01 7.672447e-01 0.8209056984
## [1996,] -8.806558e-01 2.161241e+00 -0.4759706057
## [1997,] -4.299870e-01 1.158993e+00 -0.1918477120
## [1998,] -3.952764e-01 1.086619e+00 -0.6891364130
## [1999,] -2.381209e-01 8.040559e-01 -0.0404258905
## [2000,] -6.395319e-02 3.773090e-01 -0.2267323343
## [2001,] -5.052193e-01 1.357020e+00 0.1426350551
## [2002,] -9.226177e-02 5.086549e-01 0.9602496412
## [2003,] -4.171687e-01 1.169297e+00 -0.5307996294
## [2004,] -6.410359e-01 1.702050e+00 -0.6632003261
## [2005,] -8.024483e-01 2.031917e+00 -0.3669764570
## [2006,] -7.912160e-01 2.006767e+00 -0.5566873979
## [2007,] -6.784676e-01 1.855926e+00 -0.1834544725
## [2008,] 8.390995e-02 1.714934e-01 0.4404538802
## [2009,] 6.949039e-02 2.557822e-01 0.3760340807
## [2010,] 3.331387e-01 -4.041533e-01 -1.5011520122
## [2011,] -7.074245e-01 1.962981e+00 -0.3762133186
## [2012,] 3.209918e-04 3.974047e-01 0.7465544623
## [2013,] -4.890967e-01 1.467386e+00 0.0593957499
## [2014,] 8.582665e-02 1.980447e-01 -0.4271795813
## [2015,] -5.091725e-01 1.514662e+00 -0.5873151564
## [2016,] -4.714559e-01 1.483866e+00 -0.7726088622
## [2017,] 2.226418e-01 -9.322490e-03 0.6362615845
## [2018,] 1.918888e-01 1.546140e-01 0.8998154111
## [2019,] -3.381266e-01 1.409605e+00 -0.9482004165
## [2020,] -4.998965e-02 6.239486e-01 -1.0831751369
## [2021,] -1.049090e-01 8.301278e-01 0.5020216803
## [2022,] -1.850718e-01 1.267160e+00 -0.4042820364
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## [5708,] 4.804102e-01 -1.572838e+00 1.9648007955
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## [5712,] 6.817201e-01 -2.036067e+00 1.0377102998
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## [5714,] 4.119923e-01 -1.145695e+00 2.7922005533
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## [5718,] 5.795206e-01 -1.767308e+00 2.2978076268
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## [5720,] 7.492369e-01 -2.213484e+00 0.9863507645
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## [5725,] 4.416506e-01 -1.428056e+00 0.5231247195
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## [5730,] 6.914873e-01 -2.082459e+00 0.4217593536
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## [5732,] 2.140281e-01 -1.032125e+00 -1.0534755366
## [5733,] 8.566668e-01 -2.231789e+00 2.3780758942
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## [5744,] 3.558475e-01 -1.227546e+00 1.7205778588
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## [5754,] 5.625210e-01 -1.605096e+00 1.6724762481
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## [5761,] 7.388289e-01 -2.130769e+00 0.1179786771
## [5762,] 5.302054e-01 -1.483204e+00 1.5589158645
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## [5765,] 5.474433e-01 -1.499129e+00 1.9098498006
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## [5774,] 3.694641e-01 -1.234623e+00 1.0894986972
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## [5873,] 4.940193e-01 -1.226478e+00 1.3654862310
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## [5882,] 5.684175e-01 -1.400141e+00 1.4948653742
## [5883,] 5.842749e-01 -1.416503e+00 1.5362188453
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## [5890,] 6.536073e-01 -1.594932e+00 1.9019100628
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## [5894,] 4.405758e-01 -1.120618e+00 1.3879581040
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## [5898,] 5.552057e-01 -1.489962e+00 -1.1086209773
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## [5900,] 5.108761e-01 -1.366143e+00 -0.1054560931
## [5901,] 3.686101e-01 -8.893353e-01 1.7867390270
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## [5992,] 7.510519e-01 -1.628186e+00 2.3531753802
## [5993,] 6.227244e-01 -1.371845e+00 1.6161881416
## [5994,] 5.968492e-01 -1.319233e+00 1.5228101551
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## [5999,] 8.125008e-01 -1.794770e+00 1.2800536311
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## [6018,] 8.186789e-01 -1.861066e+00 0.3176405566
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## [6031,] 4.690800e-01 -9.874081e-01 1.9223833680
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## [6034,] 6.351303e-01 -1.430084e+00 0.9381883996
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## [6040,] 4.789034e-01 -1.012161e+00 2.2035002271
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## [6051,] 8.690893e-01 -1.685367e+00 3.1949276957
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## [6248,] 8.582739e-01 -1.608888e+00 2.2376068502
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## [6255,] 7.128934e-01 -1.309239e+00 0.7869952589
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## [6259,] 6.168687e-01 -1.069170e+00 2.2515368865
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## [6262,] 7.400518e-01 -1.078217e+00 1.9722484281
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## [6348,] 9.611982e-01 -1.723481e+00 2.4799037822
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## [6479,] 1.002539e+00 -1.777612e+00 1.2471275730
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## [6507,] 9.345048e-01 -1.517109e+00 1.4219999407
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## [6510,] 5.489494e-01 -6.085762e-01 0.2536109601
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## [6514,] 8.559250e-01 -1.292445e+00 2.1853916528
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## [6517,] 8.040748e-01 -1.258426e+00 1.9449047673
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## [6520,] 6.831437e-01 -1.000978e+00 1.9954715501
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## [6525,] 7.936324e-01 -1.153870e+00 1.2904882796
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## [6531,] 6.808808e-01 -1.016271e+00 0.7431994243
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## [6544,] 8.368517e-01 -1.288581e+00 0.2000445772
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## [6547,] 7.288887e-01 -1.062833e+00 1.9150359833
## [6548,] 7.900272e-01 -1.139441e+00 2.2266624045
## [6549,] 1.001471e+00 -1.551460e+00 2.8259777529
## [6550,] 8.084774e-01 -1.309628e+00 0.3000654521
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## [6600,] 5.888854e-01 -6.578415e-01 2.3138903561
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## [6628,] 9.582538e-01 -1.469904e+00 1.9941668777
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## [6684,] 5.841293e-01 -6.505545e-01 1.7845381692
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## [6692,] 8.369916e-01 -1.373830e+00 -0.8184429752
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## [6699,] 4.533505e-01 -2.786937e-01 1.3259320030
## [6700,] 7.460763e-01 -1.070716e+00 0.0944076470
## [6701,] 6.885338e-01 -8.916844e-01 1.0663524036
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## [6704,] 9.196391e-01 -1.412425e+00 0.8880685250
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## [6711,] 8.997227e-01 -1.389553e+00 1.2996461206
## [6712,] 9.559349e-01 -1.406851e+00 2.1144496086
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## [6729,] 8.548461e-01 -1.241031e+00 0.1507559834
## [6730,] 8.900666e-01 -1.234423e+00 0.7026853822
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## [6740,] 1.088742e+00 -1.579945e+00 2.9878265665
## [6741,] 6.953412e-01 -8.724273e-01 0.1525290412
## [6742,] 6.910803e-01 -7.987999e-01 1.7500442059
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## [6746,] 9.821182e-01 -1.440942e+00 2.1986025268
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## [6749,] 7.421346e-01 -9.297200e-01 0.2430570696
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## [6752,] 8.802757e-01 -1.184479e+00 1.0212289965
## [6753,] 7.823549e-01 -9.702055e-01 0.7905916769
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## [6756,] 1.125294e+00 -1.724944e+00 1.3586631222
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## [6758,] 7.734132e-01 -1.038260e+00 1.0352095653
## [6759,] 8.168416e-01 -1.053288e+00 1.3157901756
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## [6761,] 7.747545e-01 -9.225475e-01 1.1113491642
## [6762,] 1.144335e+00 -1.779034e+00 1.9217943617
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## [6766,] 1.060244e+00 -1.685022e+00 -0.3312944783
## [6767,] 7.602384e-01 -1.016077e+00 0.1903846883
## [6768,] 9.897976e-01 -1.424998e+00 1.8050065146
## [6769,] 8.792953e-01 -1.382183e+00 -1.7525269559
## [6770,] 8.314675e-01 -1.106094e+00 1.8172549876
## [6771,] 8.851179e-01 -1.163892e+00 1.7977293553
## [6772,] 9.894961e-01 -1.544951e+00 0.6100078073
## [6773,] 7.525725e-01 -1.044221e+00 0.0261667325
## [6774,] 8.526792e-01 -1.198378e+00 1.0164873158
## [6775,] 9.002528e-01 -1.329896e+00 0.4809893419
## [6776,] 5.864678e-01 -5.158060e-01 1.8926832766
## [6777,] 1.029015e+00 -1.586663e+00 0.7020522503
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## [6779,] 1.131921e+00 -1.990416e+00 -2.4287034301
## [6780,] 8.875492e-01 -1.200792e+00 2.1203381422
## [6781,] 9.948468e-01 -1.482763e+00 -0.3425670379
## [6782,] 9.171308e-01 -1.420381e+00 -1.9400362562
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## [6784,] 1.336947e+00 -2.398324e+00 -2.7648557193
## [6785,] 1.067634e+00 -1.806753e+00 -2.2229406006
## [6786,] 1.099040e+00 -1.778659e+00 -2.0026044100
## [6787,] 1.084618e+00 -1.606600e+00 1.4429402251
## [6788,] 9.619124e-01 -1.555677e+00 -2.1764718055
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## [6790,] 8.254262e-01 -1.094411e+00 0.6215950432
## [6791,] 8.966800e-01 -1.103159e+00 1.6602403691
## [6792,] 9.568575e-01 -1.303737e+00 2.2780056631
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## [6794,] 8.617859e-01 -1.254409e+00 -1.6007063584
## [6795,] 1.006569e+00 -1.442527e+00 0.7711580302
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## [6797,] 1.312963e+00 -1.877679e+00 -1.2595698165
## [6798,] 7.064625e-01 -8.196369e-01 1.3219698068
## [6799,] 8.478719e-01 -1.098464e+00 1.2875212110
## [6800,] 1.020410e+00 -1.392017e+00 1.8065167769
## [6801,] 7.482503e-01 -8.581251e-01 1.5417079323
## [6802,] 9.798540e-01 -1.572869e+00 -1.3615550021
## [6803,] 9.387206e-01 -1.263494e+00 1.5501097004
## [6804,] 9.387206e-01 -1.263494e+00 1.5501097004
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## [6806,] 9.042725e-01 -1.464827e+00 -2.2186452114
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## [6808,] 9.723543e-01 -1.587262e+00 -2.0105890735
## [6809,] 8.389433e-01 -1.193426e+00 -2.0041779475
## [6810,] 9.656587e-01 -1.422836e+00 0.5696469518
## [6811,] 8.810062e-01 -1.275079e+00 -0.8211603249
## [6812,] 1.174166e+00 -1.843655e+00 0.8127245001
## [6813,] 1.110618e+00 -1.803765e+00 -1.3168717687
## [6814,] 1.142280e+00 -2.022340e+00 -2.8657599667
## [6815,] 9.360585e-01 -1.506164e+00 -1.6658256068
## [6816,] 1.105863e+00 -1.672100e+00 0.9267869421
## [6817,] 1.107281e+00 -1.893741e+00 -2.2418980439
## [6818,] 8.631879e-01 -1.237014e+00 -0.4306303078
## [6819,] 7.358549e-01 -7.407539e-01 1.8196959058
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## [6823,] 5.044931e-01 -3.924780e-01 0.2019950543
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## [6826,] 1.006268e+00 -1.667531e+00 -2.1729401297
## [6827,] 7.392160e-01 -8.384070e-01 1.5178253467
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## [6830,] 1.001080e+00 -1.433271e+00 0.5375303876
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## [6835,] 1.019209e+00 -1.511545e+00 -0.6188645731
## [6836,] 1.012251e+00 -1.273746e+00 2.3146171921
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## [6844,] 7.318329e-01 -7.934146e-01 0.9830410368
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## [6851,] 6.062136e-01 -6.061706e-01 0.2407105577
## [6852,] 7.994338e-01 -8.791508e-01 0.2338332235
## [6853,] 7.964774e-01 -9.237465e-01 2.0576886299
## [6854,] 1.145266e+00 -1.900612e+00 -1.7024408562
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## [6856,] 1.108183e+00 -1.619437e+00 2.0246025770
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## [6859,] 9.297022e-01 -1.215905e+00 1.7809679234
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## [6868,] 9.499595e-01 -1.252181e+00 1.2921603427
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## [6872,] 8.266245e-01 -9.897188e-01 1.3412713697
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## [6879,] 8.401636e-01 -1.162894e+00 0.0238616884
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## [6881,] 9.531891e-01 -1.220639e+00 2.2037107767
## [6882,] 1.052165e+00 -1.538381e+00 0.4752604462
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## [6884,] 6.262065e-01 -5.150010e-01 1.1028690595
## [6885,] 8.068239e-01 -1.075951e+00 -1.6714875821
## [6886,] 9.652058e-01 -1.277989e+00 1.7706959827
## [6887,] 9.421816e-01 -1.251180e+00 1.7874256542
## [6888,] 9.123656e-01 -1.146729e+00 1.6936983497
## [6889,] 1.109999e+00 -1.669281e+00 0.1112611613
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## [6891,] 1.021931e+00 -1.284097e+00 1.2958852101
## [6892,] 1.021931e+00 -1.284097e+00 1.2958852101
## [6893,] 1.074283e+00 -1.517108e+00 1.1064172264
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## [6898,] 8.665408e-01 -1.041216e+00 1.5495958567
## [6899,] 1.018211e+00 -1.338976e+00 2.0407149514
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## [6902,] 7.334100e-01 -7.952390e-01 1.0549840743
## [6903,] 1.145032e+00 -1.607243e+00 2.2942341443
## [6904,] 8.570267e-01 -9.903576e-01 1.9835203131
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## [6914,] 9.134923e-01 -1.138359e+00 1.6062612114
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## [6919,] 9.133994e-01 -1.144801e+00 1.7521774338
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## [6922,] 7.149087e-01 -7.296222e-01 1.0901564452
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## [6925,] 1.026407e+00 -1.544556e+00 -1.3066524893
## [6926,] 9.093786e-01 -1.117120e+00 1.3964088524
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## [6928,] 1.044505e+00 -1.547580e+00 -0.0090213289
## [6929,] 1.050592e+00 -1.346412e+00 1.5030752714
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## [6932,] 1.032893e+00 -1.300435e+00 2.3106160573
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## [6934,] 9.595246e-01 -1.118426e+00 1.5572854205
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## [6937,] 9.485578e-01 -1.163693e+00 2.1624048293
## [6938,] 8.197375e-01 -9.027809e-01 1.6828363373
## [6939,] 7.657070e-01 -8.448030e-01 1.1712670088
## [6940,] 8.085245e-01 -8.720481e-01 1.2912861870
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## [6942,] 7.713156e-01 -7.290831e-01 1.5303072274
## [6943,] 8.317023e-01 -9.012168e-01 2.2490339603
## [6944,] 1.124753e+00 -1.493578e+00 2.0272213987
## [6945,] 1.081980e+00 -1.621459e+00 -1.2330975644
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