Load Library
library(ggrepel)
library(psych)
library(sjPlot)
library(ppcor)
library(factoextra)
library(corrplot)
library(FactoMineR)
library(dplyr)
Import Data
data <- read.csv("WHR2023.csv")
str(data)
## 'data.frame': 137 obs. of 19 variables:
## $ Country.name : chr "Finland" "Denmark" "Iceland" "Israel" ...
## $ Ladder.score : num 7.8 7.59 7.53 7.47 7.4 ...
## $ Standard.error.of.ladder.score : num 0.036 0.041 0.049 0.032 0.029 0.037 0.044 0.043 0.069 0.038 ...
## $ upperwhisker : num 7.88 7.67 7.62 7.54 7.46 ...
## $ lowerwhisker : num 7.73 7.51 7.43 7.41 7.35 ...
## $ Logged.GDP.per.capita : num 10.8 11 10.9 10.6 10.9 ...
## $ Social.support : num 0.969 0.954 0.983 0.943 0.93 0.939 0.943 0.92 0.879 0.952 ...
## $ Healthy.life.expectancy : num 71.2 71.2 72 72.7 71.5 ...
## $ Freedom.to.make.life.choices : num 0.961 0.934 0.936 0.809 0.887 0.948 0.947 0.891 0.915 0.887 ...
## $ Generosity : num -0.019 0.134 0.211 -0.023 0.213 0.165 0.141 0.027 0.024 0.175 ...
## $ Perceptions.of.corruption : num 0.182 0.196 0.668 0.708 0.379 0.202 0.283 0.266 0.345 0.271 ...
## $ Ladder.score.in.Dystopia : num 1.78 1.78 1.78 1.78 1.78 ...
## $ Explained.by..Log.GDP.per.capita : num 1.89 1.95 1.93 1.83 1.94 ...
## $ Explained.by..Social.support : num 1.58 1.55 1.62 1.52 1.49 ...
## $ Explained.by..Healthy.life.expectancy : num 0.535 0.537 0.559 0.577 0.545 0.562 0.544 0.582 0.549 0.513 ...
## $ Explained.by..Freedom.to.make.life.choices: num 0.772 0.734 0.738 0.569 0.672 0.754 0.752 0.678 0.71 0.672 ...
## $ Explained.by..Generosity : num 0.126 0.208 0.25 0.124 0.251 0.225 0.212 0.151 0.149 0.23 ...
## $ Explained.by..Perceptions.of.corruption : num 0.535 0.525 0.187 0.158 0.394 0.52 0.463 0.475 0.418 0.471 ...
## $ Dystopia...residual : num 2.36 2.08 2.25 2.69 2.11 ...
Ambil Data Numerik
data_num <- data[, sapply(data, is.numeric)]
dim(data_num)
## [1] 137 18
Cleaning Data
colSums(is.na(data_num))
## Ladder.score
## 0
## Standard.error.of.ladder.score
## 0
## upperwhisker
## 0
## lowerwhisker
## 0
## Logged.GDP.per.capita
## 0
## Social.support
## 0
## Healthy.life.expectancy
## 1
## Freedom.to.make.life.choices
## 0
## Generosity
## 0
## Perceptions.of.corruption
## 0
## Ladder.score.in.Dystopia
## 0
## Explained.by..Log.GDP.per.capita
## 0
## Explained.by..Social.support
## 0
## Explained.by..Healthy.life.expectancy
## 1
## Explained.by..Freedom.to.make.life.choices
## 0
## Explained.by..Generosity
## 0
## Explained.by..Perceptions.of.corruption
## 0
## Dystopia...residual
## 1
data_num <- na.omit(data_num)
apply(data_num, 2, sd)
## Ladder.score
## 1.14284053
## Standard.error.of.ladder.score
## 0.02299565
## upperwhisker
## 1.12044167
## lowerwhisker
## 1.16652219
## Logged.GDP.per.capita
## 1.21010663
## Social.support
## 0.12959657
## Healthy.life.expectancy
## 5.75039035
## Freedom.to.make.life.choices
## 0.11249764
## Generosity
## 0.14160355
## Perceptions.of.corruption
## 0.17735282
## Ladder.score.in.Dystopia
## 0.00000000
## Explained.by..Log.GDP.per.capita
## 0.43396909
## Explained.by..Social.support
## 0.32726285
## Explained.by..Healthy.life.expectancy
## 0.15669110
## Explained.by..Freedom.to.make.life.choices
## 0.14967122
## Explained.by..Generosity
## 0.07599332
## Explained.by..Perceptions.of.corruption
## 0.12700872
## Dystopia...residual
## 0.50439005
data_num <- data_num[, apply(data_num, 2, sd) > 0]
Rasio Sampel
n <- nrow(data_num)
p <- ncol(data_num)
n
## [1] 136
p
## [1] 17
n/p
## [1] 8
Matriks Korelasi
mat_corr <- cor(data_num)
round(mat_corr,2)
## Ladder.score
## Ladder.score 1.00
## Standard.error.of.ladder.score -0.51
## upperwhisker 1.00
## lowerwhisker 1.00
## Logged.GDP.per.capita 0.78
## Social.support 0.84
## Healthy.life.expectancy 0.75
## Freedom.to.make.life.choices 0.66
## Generosity 0.04
## Perceptions.of.corruption -0.47
## Explained.by..Log.GDP.per.capita 0.78
## Explained.by..Social.support 0.84
## Explained.by..Healthy.life.expectancy 0.75
## Explained.by..Freedom.to.make.life.choices 0.66
## Explained.by..Generosity 0.04
## Explained.by..Perceptions.of.corruption 0.47
## Dystopia...residual 0.49
## Standard.error.of.ladder.score
## Ladder.score -0.51
## Standard.error.of.ladder.score 1.00
## upperwhisker -0.48
## lowerwhisker -0.54
## Logged.GDP.per.capita -0.58
## Social.support -0.48
## Healthy.life.expectancy -0.62
## Freedom.to.make.life.choices -0.29
## Generosity 0.10
## Perceptions.of.corruption 0.30
## Explained.by..Log.GDP.per.capita -0.58
## Explained.by..Social.support -0.48
## Explained.by..Healthy.life.expectancy -0.62
## Explained.by..Freedom.to.make.life.choices -0.29
## Explained.by..Generosity 0.10
## Explained.by..Perceptions.of.corruption -0.30
## Dystopia...residual -0.01
## upperwhisker lowerwhisker
## Ladder.score 1.00 1.00
## Standard.error.of.ladder.score -0.48 -0.54
## upperwhisker 1.00 1.00
## lowerwhisker 1.00 1.00
## Logged.GDP.per.capita 0.78 0.79
## Social.support 0.84 0.84
## Healthy.life.expectancy 0.74 0.76
## Freedom.to.make.life.choices 0.66 0.66
## Generosity 0.04 0.04
## Perceptions.of.corruption -0.47 -0.47
## Explained.by..Log.GDP.per.capita 0.78 0.79
## Explained.by..Social.support 0.84 0.84
## Explained.by..Healthy.life.expectancy 0.74 0.76
## Explained.by..Freedom.to.make.life.choices 0.66 0.66
## Explained.by..Generosity 0.04 0.03
## Explained.by..Perceptions.of.corruption 0.47 0.47
## Dystopia...residual 0.50 0.48
## Logged.GDP.per.capita Social.support
## Ladder.score 0.78 0.84
## Standard.error.of.ladder.score -0.58 -0.48
## upperwhisker 0.78 0.84
## lowerwhisker 0.79 0.84
## Logged.GDP.per.capita 1.00 0.74
## Social.support 0.74 1.00
## Healthy.life.expectancy 0.84 0.73
## Freedom.to.make.life.choices 0.45 0.55
## Generosity -0.16 0.04
## Perceptions.of.corruption -0.44 -0.28
## Explained.by..Log.GDP.per.capita 1.00 0.74
## Explained.by..Social.support 0.74 1.00
## Explained.by..Healthy.life.expectancy 0.84 0.73
## Explained.by..Freedom.to.make.life.choices 0.45 0.55
## Explained.by..Generosity -0.16 0.04
## Explained.by..Perceptions.of.corruption 0.44 0.28
## Dystopia...residual -0.04 0.15
## Healthy.life.expectancy
## Ladder.score 0.75
## Standard.error.of.ladder.score -0.62
## upperwhisker 0.74
## lowerwhisker 0.76
## Logged.GDP.per.capita 0.84
## Social.support 0.73
## Healthy.life.expectancy 1.00
## Freedom.to.make.life.choices 0.42
## Generosity -0.14
## Perceptions.of.corruption -0.40
## Explained.by..Log.GDP.per.capita 0.84
## Explained.by..Social.support 0.73
## Explained.by..Healthy.life.expectancy 1.00
## Explained.by..Freedom.to.make.life.choices 0.42
## Explained.by..Generosity -0.14
## Explained.by..Perceptions.of.corruption 0.40
## Dystopia...residual -0.01
## Freedom.to.make.life.choices
## Ladder.score 0.66
## Standard.error.of.ladder.score -0.29
## upperwhisker 0.66
## lowerwhisker 0.66
## Logged.GDP.per.capita 0.45
## Social.support 0.55
## Healthy.life.expectancy 0.42
## Freedom.to.make.life.choices 1.00
## Generosity 0.16
## Perceptions.of.corruption -0.38
## Explained.by..Log.GDP.per.capita 0.45
## Explained.by..Social.support 0.55
## Explained.by..Healthy.life.expectancy 0.41
## Explained.by..Freedom.to.make.life.choices 1.00
## Explained.by..Generosity 0.16
## Explained.by..Perceptions.of.corruption 0.38
## Dystopia...residual 0.21
## Generosity Perceptions.of.corruption
## Ladder.score 0.04 -0.47
## Standard.error.of.ladder.score 0.10 0.30
## upperwhisker 0.04 -0.47
## lowerwhisker 0.04 -0.47
## Logged.GDP.per.capita -0.16 -0.44
## Social.support 0.04 -0.28
## Healthy.life.expectancy -0.14 -0.40
## Freedom.to.make.life.choices 0.16 -0.38
## Generosity 1.00 -0.12
## Perceptions.of.corruption -0.12 1.00
## Explained.by..Log.GDP.per.capita -0.16 -0.44
## Explained.by..Social.support 0.04 -0.28
## Explained.by..Healthy.life.expectancy -0.14 -0.40
## Explained.by..Freedom.to.make.life.choices 0.16 -0.38
## Explained.by..Generosity 1.00 -0.12
## Explained.by..Perceptions.of.corruption 0.12 -1.00
## Dystopia...residual 0.02 0.00
## Explained.by..Log.GDP.per.capita
## Ladder.score 0.78
## Standard.error.of.ladder.score -0.58
## upperwhisker 0.78
## lowerwhisker 0.79
## Logged.GDP.per.capita 1.00
## Social.support 0.74
## Healthy.life.expectancy 0.84
## Freedom.to.make.life.choices 0.45
## Generosity -0.16
## Perceptions.of.corruption -0.44
## Explained.by..Log.GDP.per.capita 1.00
## Explained.by..Social.support 0.74
## Explained.by..Healthy.life.expectancy 0.84
## Explained.by..Freedom.to.make.life.choices 0.45
## Explained.by..Generosity -0.16
## Explained.by..Perceptions.of.corruption 0.44
## Dystopia...residual -0.04
## Explained.by..Social.support
## Ladder.score 0.84
## Standard.error.of.ladder.score -0.48
## upperwhisker 0.84
## lowerwhisker 0.84
## Logged.GDP.per.capita 0.74
## Social.support 1.00
## Healthy.life.expectancy 0.73
## Freedom.to.make.life.choices 0.55
## Generosity 0.04
## Perceptions.of.corruption -0.28
## Explained.by..Log.GDP.per.capita 0.74
## Explained.by..Social.support 1.00
## Explained.by..Healthy.life.expectancy 0.73
## Explained.by..Freedom.to.make.life.choices 0.55
## Explained.by..Generosity 0.04
## Explained.by..Perceptions.of.corruption 0.28
## Dystopia...residual 0.15
## Explained.by..Healthy.life.expectancy
## Ladder.score 0.75
## Standard.error.of.ladder.score -0.62
## upperwhisker 0.74
## lowerwhisker 0.76
## Logged.GDP.per.capita 0.84
## Social.support 0.73
## Healthy.life.expectancy 1.00
## Freedom.to.make.life.choices 0.41
## Generosity -0.14
## Perceptions.of.corruption -0.40
## Explained.by..Log.GDP.per.capita 0.84
## Explained.by..Social.support 0.73
## Explained.by..Healthy.life.expectancy 1.00
## Explained.by..Freedom.to.make.life.choices 0.41
## Explained.by..Generosity -0.14
## Explained.by..Perceptions.of.corruption 0.40
## Dystopia...residual -0.01
## Explained.by..Freedom.to.make.life.choices
## Ladder.score 0.66
## Standard.error.of.ladder.score -0.29
## upperwhisker 0.66
## lowerwhisker 0.66
## Logged.GDP.per.capita 0.45
## Social.support 0.55
## Healthy.life.expectancy 0.42
## Freedom.to.make.life.choices 1.00
## Generosity 0.16
## Perceptions.of.corruption -0.38
## Explained.by..Log.GDP.per.capita 0.45
## Explained.by..Social.support 0.55
## Explained.by..Healthy.life.expectancy 0.41
## Explained.by..Freedom.to.make.life.choices 1.00
## Explained.by..Generosity 0.16
## Explained.by..Perceptions.of.corruption 0.38
## Dystopia...residual 0.21
## Explained.by..Generosity
## Ladder.score 0.04
## Standard.error.of.ladder.score 0.10
## upperwhisker 0.04
## lowerwhisker 0.03
## Logged.GDP.per.capita -0.16
## Social.support 0.04
## Healthy.life.expectancy -0.14
## Freedom.to.make.life.choices 0.16
## Generosity 1.00
## Perceptions.of.corruption -0.12
## Explained.by..Log.GDP.per.capita -0.16
## Explained.by..Social.support 0.04
## Explained.by..Healthy.life.expectancy -0.14
## Explained.by..Freedom.to.make.life.choices 0.16
## Explained.by..Generosity 1.00
## Explained.by..Perceptions.of.corruption 0.12
## Dystopia...residual 0.02
## Explained.by..Perceptions.of.corruption
## Ladder.score 0.47
## Standard.error.of.ladder.score -0.30
## upperwhisker 0.47
## lowerwhisker 0.47
## Logged.GDP.per.capita 0.44
## Social.support 0.28
## Healthy.life.expectancy 0.40
## Freedom.to.make.life.choices 0.38
## Generosity 0.12
## Perceptions.of.corruption -1.00
## Explained.by..Log.GDP.per.capita 0.44
## Explained.by..Social.support 0.28
## Explained.by..Healthy.life.expectancy 0.40
## Explained.by..Freedom.to.make.life.choices 0.38
## Explained.by..Generosity 0.12
## Explained.by..Perceptions.of.corruption 1.00
## Dystopia...residual 0.00
## Dystopia...residual
## Ladder.score 0.49
## Standard.error.of.ladder.score -0.01
## upperwhisker 0.50
## lowerwhisker 0.48
## Logged.GDP.per.capita -0.04
## Social.support 0.15
## Healthy.life.expectancy -0.01
## Freedom.to.make.life.choices 0.21
## Generosity 0.02
## Perceptions.of.corruption 0.00
## Explained.by..Log.GDP.per.capita -0.04
## Explained.by..Social.support 0.15
## Explained.by..Healthy.life.expectancy -0.01
## Explained.by..Freedom.to.make.life.choices 0.21
## Explained.by..Generosity 0.02
## Explained.by..Perceptions.of.corruption 0.00
## Dystopia...residual 1.00
corrplot(mat_corr,
method = "square",
type = "full",
order = "hclust",
tl.col = "black",
tl.cex = 0.45)
Uji Bartlett & KMO
cortest.bartlett(mat_corr, n = n)
## $chisq
## [1] 15741.57
##
## $p.value
## [1] 0
##
## $df
## [1] 136
mat_corr = cor(data_num)
KMO(mat_corr)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = mat_corr)
## Overall MSA = 0.79
## MSA for each item =
## Ladder.score
## 0.85
## Standard.error.of.ladder.score
## 0.83
## upperwhisker
## 0.84
## lowerwhisker
## 0.86
## Logged.GDP.per.capita
## 0.81
## Social.support
## 0.94
## Healthy.life.expectancy
## 0.77
## Freedom.to.make.life.choices
## 0.84
## Generosity
## 0.41
## Perceptions.of.corruption
## 0.70
## Explained.by..Log.GDP.per.capita
## 0.88
## Explained.by..Social.support
## 0.79
## Explained.by..Healthy.life.expectancy
## 0.85
## Explained.by..Freedom.to.make.life.choices
## 0.75
## Explained.by..Generosity
## 0.54
## Explained.by..Perceptions.of.corruption
## 0.68
## Dystopia...residual
## 0.27
data_num = data_num[, !names(data_num) %in% "Dystopia...residual"]
mat_corr = cor(data_num)
KMO(mat_corr)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = mat_corr)
## Overall MSA = 0.8
## MSA for each item =
## Ladder.score
## 0.82
## Standard.error.of.ladder.score
## 0.83
## upperwhisker
## 0.84
## lowerwhisker
## 0.85
## Logged.GDP.per.capita
## 0.86
## Social.support
## 0.86
## Healthy.life.expectancy
## 0.83
## Freedom.to.make.life.choices
## 0.78
## Generosity
## 0.48
## Perceptions.of.corruption
## 0.67
## Explained.by..Log.GDP.per.capita
## 0.86
## Explained.by..Social.support
## 0.86
## Explained.by..Healthy.life.expectancy
## 0.83
## Explained.by..Freedom.to.make.life.choices
## 0.78
## Explained.by..Generosity
## 0.48
## Explained.by..Perceptions.of.corruption
## 0.67
data_num = data_num[, !names(data_num) %in% "Generosity"]
mat_corr = cor(data_num)
KMO(mat_corr)
## Kaiser-Meyer-Olkin factor adequacy
## Call: KMO(r = mat_corr)
## Overall MSA = 0.82
## MSA for each item =
## Ladder.score
## 0.82
## Standard.error.of.ladder.score
## 0.83
## upperwhisker
## 0.85
## lowerwhisker
## 0.85
## Logged.GDP.per.capita
## 0.86
## Social.support
## 0.85
## Healthy.life.expectancy
## 0.83
## Freedom.to.make.life.choices
## 0.78
## Perceptions.of.corruption
## 0.71
## Explained.by..Log.GDP.per.capita
## 0.86
## Explained.by..Social.support
## 0.85
## Explained.by..Healthy.life.expectancy
## 0.83
## Explained.by..Freedom.to.make.life.choices
## 0.78
## Explained.by..Generosity
## 0.65
## Explained.by..Perceptions.of.corruption
## 0.71
Partial Correlation
pcor(data_num)$estimate
## [,1] [,2] [,3] [,4] [,5]
## [1,] 1.00000000 -0.0229351958 -0.07815804 -0.03276391 0.23882495
## [2,] -0.02293520 1.0000000000 -0.99847084 0.99844862 -0.11073399
## [3,] -0.07815804 -0.9984708423 1.00000000 0.99384487 -0.09697078
## [4,] -0.03276391 0.9984486216 0.99384487 1.00000000 0.12383876
## [5,] 0.23882495 -0.1107339900 -0.09697078 0.12383876 1.00000000
## [6,] 0.52579625 -0.0020732238 0.02688914 0.03152413 0.17463470
## [7,] 0.11498923 -0.2621562762 -0.25497312 0.26840672 0.46231381
## [8,] 0.40376064 0.0023164385 0.02435819 0.02024965 -0.05730766
## [9,] -0.24265874 0.0363608932 0.02318217 -0.05004196 -0.16457508
## [10,] 0.23349479 -0.1258680786 -0.11234151 0.13866271 -0.99970721
## [11,] 0.52543048 0.0043330607 0.03325458 0.02510073 0.17602140
## [12,] 0.10417890 -0.4032387701 -0.39645515 0.40896753 0.47649268
## [13,] 0.40395714 0.0005247824 0.02258212 0.02205196 -0.05736289
## [14,] 0.03788261 0.0265771535 0.02951985 -0.02498450 -0.23208912
## [15,] 0.24223000 -0.0374376568 -0.02428096 0.05109528 0.16475266
## [,6] [,7] [,8] [,9] [,10]
## [1,] 0.525796247 0.11498923 0.403760639 -0.24265874 0.23349479
## [2,] -0.002073224 -0.26215628 0.002316439 0.03636089 -0.12586808
## [3,] 0.026889138 -0.25497312 0.024358189 0.02318217 -0.11234151
## [4,] 0.031524135 0.26840672 0.020249647 -0.05004196 0.13866271
## [5,] 0.174634702 0.46231381 -0.057307660 -0.16457508 -0.99970721
## [6,] 1.000000000 0.18295559 0.054465727 0.32332794 0.18183066
## [7,] 0.182955589 1.00000000 -0.085851675 -0.08720379 0.45215675
## [8,] 0.054465727 -0.08585167 1.000000000 -0.11999317 -0.05397222
## [9,] 0.323327941 -0.08720379 -0.119993166 1.00000000 -0.16964025
## [10,] 0.181830658 0.45215675 -0.053972220 -0.16964025 1.00000000
## [11,] -0.999974995 0.18487832 0.054510383 0.32387401 0.18336066
## [12,] 0.105882372 -0.96284858 -0.066733287 -0.02142352 0.46826711
## [13,] 0.053998955 -0.08622538 -0.999998254 -0.11963261 -0.05404741
## [14,] 0.159857779 -0.08826317 0.111919200 -0.18905851 -0.24849771
## [15,] -0.323147670 0.08699930 0.119957393 0.99999815 0.16982423
## [,11] [,12] [,13] [,14] [,15]
## [1,] 0.525430483 0.10417890 0.4039571442 0.03788261 0.24223000
## [2,] 0.004333061 -0.40323877 0.0005247824 0.02657715 -0.03743766
## [3,] 0.033254581 -0.39645515 0.0225821190 0.02951985 -0.02428096
## [4,] 0.025100728 0.40896753 0.0220519571 -0.02498450 0.05109528
## [5,] 0.176021401 0.47649268 -0.0573628878 -0.23208912 0.16475266
## [6,] -0.999974995 0.10588237 0.0539989548 0.15985778 -0.32314767
## [7,] 0.184878325 -0.96284858 -0.0862253761 -0.08826317 0.08699930
## [8,] 0.054510383 -0.06673329 -0.9999982536 0.11191920 0.11995739
## [9,] 0.323874013 -0.02142352 -0.1196326130 -0.18905851 0.99999815
## [10,] 0.183360656 0.46826711 -0.0540474114 -0.24849771 0.16982423
## [11,] 1.000000000 0.10806891 0.0540543717 0.16259064 -0.32369142
## [12,] 0.108068907 1.00000000 -0.0674440835 0.13650377 0.02074574
## [13,] 0.054054372 -0.06744408 1.0000000000 0.11226863 0.11959467
## [14,] 0.162590641 0.13650377 0.1122686250 1.00000000 0.19059414
## [15,] -0.323691416 0.02074574 0.1195946654 0.19059414 1.00000000
Standardisasi Data
data_scaled <- scale(data_num)
head(data_scaled)
## Ladder.score Standard.error.of.ladder.score upperwhisker lowerwhisker
## 1 1.977143 -1.2400045 1.967285 1.984519
## 2 1.786390 -1.0225720 1.781644 1.789923
## 3 1.737389 -0.6746801 1.744159 1.728201
## 4 1.687513 -1.4139505 1.663833 1.708485
## 5 1.626263 -1.5444099 1.596895 1.652763
## 6 1.619263 -1.1965180 1.604035 1.632190
## Logged.GDP.per.capita Social.support Healthy.life.expectancy
## 1 1.1047033 1.314600 1.075121
## 2 1.2451868 1.198856 1.092512
## 3 1.1906462 1.422628 1.231632
## 4 0.9782682 1.113977 1.344147
## 5 1.2286593 1.013666 1.144682
## 6 1.1799033 1.083112 1.249023
## Freedom.to.make.life.choices Perceptions.of.corruption
## 1 1.5370910 -3.0593720
## 2 1.2970860 -2.9804333
## 3 1.3148642 -0.3190715
## 4 0.1859516 -0.0935324
## 5 0.8792995 -1.9485917
## 6 1.4215331 -2.9466024
## Explained.by..Log.GDP.per.capita Explained.by..Social.support
## 1 1.1039516 1.313659
## 2 1.2445146 1.200600
## 3 1.1915155 1.420607
## 4 0.9772145 1.118097
## 5 1.2283845 1.017261
## 6 1.1799939 1.084485
## Explained.by..Healthy.life.expectancy
## 1 1.077429
## 2 1.090193
## 3 1.230597
## 4 1.345472
## 5 1.141249
## 6 1.249742
## Explained.by..Freedom.to.make.life.choices Explained.by..Generosity
## 1 1.5439724 -0.3038193
## 2 1.2900826 0.7752229
## 3 1.3168078 1.3279031
## 4 0.1876662 -0.3301374
## 5 0.8758413 1.3410621
## 6 1.4237088 0.9989268
## Explained.by..Perceptions.of.corruption
## 1 3.05901883
## 2 2.98028408
## 3 0.31904943
## 4 0.09071865
## 5 1.94885882
## 6 2.94091670
PCA Manual
pca_cov <- cov(data_scaled)
pc <- eigen(pca_cov)
pc$values
## [1] 9.230900e+00 1.782334e+00 1.469342e+00 8.372929e-01 6.255914e-01
## [6] 4.366978e-01 3.167007e-01 3.011251e-01 5.742928e-06 4.510633e-06
## [11] 2.908879e-06 1.462823e-06 5.020987e-07 1.969544e-07 6.105159e-08
pc$vectors
## [,1] [,2] [,3] [,4] [,5] [,6]
## [1,] 0.311414338 -0.03700666 0.1088730 0.035101137 -0.16778656 0.22964812
## [2,] -0.204954000 -0.18297970 0.1659741 -0.023380846 -0.80540545 -0.48686588
## [3,] 0.309399876 -0.04511375 0.1176289 0.034790543 -0.20343781 0.21461357
## [4,] 0.313006843 -0.02919997 0.1002740 0.035310850 -0.13333275 0.24375091
## [5,] 0.292765066 0.19177171 -0.1237022 -0.011346446 -0.04669026 -0.25006872
## [6,] 0.287049505 0.10851543 0.2265742 0.193799846 -0.17301618 0.17015961
## [7,] 0.285595274 0.22165382 -0.1307235 0.063962210 0.12551045 -0.38379549
## [8,] 0.225447934 -0.35366818 0.3060861 -0.398182599 0.19321472 -0.16466440
## [9,] -0.182102820 0.39980449 0.5164658 -0.006978190 0.10894851 -0.07591536
## [10,] 0.292751377 0.19177230 -0.1237285 -0.011303346 -0.04667551 -0.25024479
## [11,] 0.287071927 0.10848880 0.2264109 0.193638108 -0.17299083 0.17080876
## [12,] 0.285547601 0.22182825 -0.1308504 0.063941509 0.12554230 -0.38404404
## [13,] 0.225466605 -0.35363114 0.3061320 -0.398054795 0.19300615 -0.16483206
## [14,] -0.002127628 -0.44398016 0.2196359 0.771480391 0.26445436 -0.24673841
## [15,] 0.182101403 -0.39965767 -0.5166298 0.006784731 -0.10901024 0.07581136
## [,7] [,8] [,9] [,10] [,11]
## [1,] 0.22724120 -0.29895023 3.911162e-03 -0.0064389798 1.122534e-02
## [2,] -0.03645674 -0.07929691 -9.698183e-04 -0.0033388110 1.489677e-03
## [3,] 0.23023220 -0.30806218 8.819541e-03 0.0440540584 -2.056479e-02
## [4,] 0.22409248 -0.28990949 -1.259071e-02 -0.0396637227 9.588166e-03
## [5,] 0.39858064 0.37204649 1.117769e-02 0.0004095776 -1.381612e-04
## [6,] -0.39669033 0.31732928 -1.038658e-01 -0.0637676907 -6.952733e-01
## [7,] -0.26612526 -0.33785853 -1.091798e-01 0.1445666816 -3.512853e-02
## [8,] -0.05445235 0.06662063 -6.899579e-01 -0.0452242544 1.121272e-01
## [9,] 0.13262216 -0.07085599 -3.270192e-02 0.6863925764 -4.886730e-02
## [10,] 0.39885448 0.37185936 -1.104094e-02 -0.0002880759 8.404395e-05
## [11,] -0.39643746 0.31746004 1.032080e-01 0.0641389698 6.953671e-01
## [12,] -0.26627301 -0.33763081 1.090455e-01 -0.1447965623 3.565659e-02
## [13,] -0.05520296 0.06694565 6.899695e-01 0.0453066318 -1.120194e-01
## [14,] 0.16868806 0.01354585 5.968626e-05 0.0001647022 1.647631e-04
## [15,] -0.13247655 0.07033615 -3.286707e-02 0.6864071345 -4.901307e-02
## [,12] [,13] [,14] [,15]
## [1,] -0.0218920131 2.529994e-02 -4.016909e-02 8.147086e-01
## [2,] 0.0056156867 5.512322e-02 -5.304040e-04 -3.343414e-04
## [3,] -0.0595364041 -6.992694e-01 2.705548e-02 -3.951439e-01
## [4,] 0.0845903195 7.019181e-01 1.299111e-02 -4.202122e-01
## [5,] -0.0284563255 1.081362e-02 7.056170e-01 3.368426e-02
## [6,] 0.0396389458 5.734124e-03 2.411958e-03 1.065092e-02
## [7,] -0.6775612288 7.682294e-02 -2.578730e-02 -1.981138e-02
## [8,] 0.0921009126 -2.485890e-02 1.472019e-02 5.235385e-03
## [9,] 0.1568112238 2.561978e-02 5.648939e-03 9.847325e-03
## [10,] 0.0282838134 -1.077184e-02 -7.055109e-01 -3.368360e-02
## [11,] -0.0395242040 -5.693020e-03 -2.681874e-03 -1.069778e-02
## [12,] 0.6773541336 -7.679719e-02 2.586719e-02 1.984933e-02
## [13,] -0.0920346865 2.492295e-02 -1.475384e-02 -5.216547e-03
## [14,] 0.0000617966 -5.334772e-05 8.629219e-05 -3.919250e-06
## [15,] 0.1568610422 2.571642e-02 5.575033e-03 9.876472e-03
sumvar <- sum(pc$values)
propvar <- (pc$values / sumvar) * 100
cumvar <- data.frame(
eigen_value = pc$values,
propvar = propvar,
cum = cumsum(propvar)
)
cumvar
## eigen_value propvar cum
## 1 9.230900e+00 6.153933e+01 61.53933
## 2 1.782334e+00 1.188223e+01 73.42156
## 3 1.469342e+00 9.795615e+00 83.21718
## 4 8.372929e-01 5.581953e+00 88.79913
## 5 6.255914e-01 4.170609e+00 92.96974
## 6 4.366978e-01 2.911319e+00 95.88106
## 7 3.167007e-01 2.111338e+00 97.99240
## 8 3.011251e-01 2.007501e+00 99.99990
## 9 5.742928e-06 3.828619e-05 99.99994
## 10 4.510633e-06 3.007089e-05 99.99997
## 11 2.908879e-06 1.939253e-05 99.99999
## 12 1.462823e-06 9.752157e-06 99.99999
## 13 5.020987e-07 3.347325e-06 100.00000
## 14 1.969544e-07 1.313029e-06 100.00000
## 15 6.105159e-08 4.070106e-07 100.00000
scores_manual <- as.matrix(data_scaled) %*% pc$vectors
head(scores_manual)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7]
## 1 5.924945 -2.2073707 -1.803664 -0.5602149 -0.4375955 1.0643820 -0.37367717
## 2 5.585480 -2.4316638 -1.752973 0.3971005 -0.2795842 0.5097201 -0.08652672
## 3 4.683336 -0.5340145 1.250480 0.8608631 0.1624367 -0.2462469 0.37021355
## 4 3.964661 1.2257097 0.174618 0.3905916 0.1143152 0.7421067 0.27890015
## 5 4.892086 -1.4734952 -1.050070 1.0815719 0.5155043 0.4005753 0.34303627
## 6 5.494840 -2.5223262 -1.748597 0.4296565 0.1485363 0.2477967 -0.20506027
## [,8] [,9] [,10] [,11] [,12]
## 1 -0.11183362 0.004858199 -4.657647e-04 -0.0021067920 0.0013621970
## 2 0.03378413 -0.004933264 5.650661e-05 0.0014292183 -0.0005711069
## 3 -0.30856184 0.001186939 1.704007e-04 -0.0014256270 -0.0003673645
## 4 -0.83935060 0.002179032 -2.206526e-03 0.0025727946 0.0003626193
## 5 -0.13782675 -0.002146446 8.185646e-04 0.0023782849 -0.0017503496
## 6 -0.01553533 0.001867838 -3.743321e-03 0.0006583365 -0.0002907241
## [,13] [,14] [,15]
## 1 -4.869255e-04 0.0002778996 7.113549e-05
## 2 -1.850627e-04 0.0004519019 -3.367879e-04
## 3 4.982133e-04 -0.0005671649 2.577038e-04
## 4 5.175780e-04 0.0007694942 -8.714844e-05
## 5 -8.140741e-05 0.0002080108 -8.012025e-05
## 6 -6.856012e-04 -0.0001673192 -2.835822e-05
PCA dengan psych
pc_psych <- principal(data_scaled, nfactors = 3, rotate = "none")
pc_psych
## Principal Components Analysis
## Call: principal(r = data_scaled, nfactors = 3, rotate = "none")
## Standardized loadings (pattern matrix) based upon correlation matrix
## PC1 PC2 PC3 h2 u2 com
## Ladder.score 0.95 0.05 0.13 0.92 0.085 1.0
## Standard.error.of.ladder.score -0.62 0.24 0.20 0.49 0.512 1.5
## upperwhisker 0.94 0.06 0.14 0.91 0.092 1.1
## lowerwhisker 0.95 0.04 0.12 0.92 0.079 1.0
## Logged.GDP.per.capita 0.89 -0.26 -0.15 0.88 0.121 1.2
## Social.support 0.87 -0.14 0.27 0.86 0.143 1.3
## Healthy.life.expectancy 0.87 -0.30 -0.16 0.87 0.134 1.3
## Freedom.to.make.life.choices 0.68 0.47 0.37 0.83 0.170 2.4
## Perceptions.of.corruption -0.55 -0.53 0.63 0.98 0.017 2.9
## Explained.by..Log.GDP.per.capita 0.89 -0.26 -0.15 0.88 0.121 1.2
## Explained.by..Social.support 0.87 -0.14 0.27 0.86 0.143 1.3
## Explained.by..Healthy.life.expectancy 0.87 -0.30 -0.16 0.87 0.134 1.3
## Explained.by..Freedom.to.make.life.choices 0.69 0.47 0.37 0.83 0.170 2.4
## Explained.by..Generosity -0.01 0.59 0.27 0.42 0.578 1.4
## Explained.by..Perceptions.of.corruption 0.55 0.53 -0.63 0.98 0.017 2.9
##
## PC1 PC2 PC3
## SS loadings 9.23 1.78 1.47
## Proportion Var 0.62 0.12 0.10
## Cumulative Var 0.62 0.73 0.83
## Proportion Explained 0.74 0.14 0.12
## Cumulative Proportion 0.74 0.88 1.00
##
## Mean item complexity = 1.6
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.04
## with the empirical chi square 47.01 with prob < 0.93
##
## Fit based upon off diagonal values = 1
PCA dengan FactoMineR
pca_result <- PCA(data_scaled,
scale.unit = FALSE,
ncp = 4, # ambil 4 PC saja
graph = FALSE)
# Eigenvalues
pca_result$eig
## eigenvalue percentage of variance cumulative percentage of variance
## comp 1 9.163026e+00 6.153933e+01 61.53933
## comp 2 1.769229e+00 1.188223e+01 73.42156
## comp 3 1.458538e+00 9.795615e+00 83.21718
## comp 4 8.311364e-01 5.581953e+00 88.79913
## comp 5 6.209914e-01 4.170609e+00 92.96974
## comp 6 4.334868e-01 2.911319e+00 95.88106
## comp 7 3.143721e-01 2.111338e+00 97.99240
## comp 8 2.989110e-01 2.007501e+00 99.99990
## comp 9 5.700701e-06 3.828619e-05 99.99994
## comp 10 4.477467e-06 3.007089e-05 99.99997
## comp 11 2.887490e-06 1.939253e-05 99.99999
## comp 12 1.452067e-06 9.752157e-06 99.99999
## comp 13 4.984068e-07 3.347325e-06 100.00000
## comp 14 1.955062e-07 1.313029e-06 100.00000
## comp 15 6.060268e-08 4.070106e-07 100.00000
# Loadings (eigenvectors)
pca_result$var$coord
## Dim.1 Dim.2 Dim.3
## Ladder.score 0.942666459 0.04922344 0.1314858
## Standard.error.of.ladder.score -0.620405800 0.24338563 0.2004469
## upperwhisker 0.936568583 0.06000687 0.1420603
## lowerwhisker 0.947487048 0.03883957 0.1211009
## Logged.GDP.per.capita 0.886214197 -0.25508009 -0.1493951
## Social.support 0.868912914 -0.14433894 0.2736336
## Healthy.life.expectancy 0.864510887 -0.29482699 -0.1578748
## Freedom.to.make.life.choices 0.682441942 0.47042243 0.3696600
## Perceptions.of.corruption -0.551234159 -0.53178941 0.6237355
## Explained.by..Log.GDP.per.capita 0.886172762 -0.25508088 -0.1494268
## Explained.by..Social.support 0.868980787 -0.14430352 0.2734363
## Explained.by..Healthy.life.expectancy 0.864366579 -0.29505901 -0.1580279
## Explained.by..Freedom.to.make.life.choices 0.682498459 0.47037315 0.3697155
## Explained.by..Generosity -0.006440435 0.59054852 0.2652542
## Explained.by..Perceptions.of.corruption 0.551229868 0.53159413 -0.6239336
## Dim.4
## Ladder.score 0.032000541
## Standard.error.of.ladder.score -0.021315541
## upperwhisker 0.031717384
## lowerwhisker 0.032191730
## Logged.GDP.per.capita -0.010344178
## Social.support 0.176680888
## Healthy.life.expectancy 0.058312224
## Freedom.to.make.life.choices -0.363009860
## Perceptions.of.corruption -0.006361785
## Explained.by..Log.GDP.per.capita -0.010304885
## Explained.by..Social.support 0.176533437
## Explained.by..Healthy.life.expectancy 0.058293351
## Explained.by..Freedom.to.make.life.choices -0.362893345
## Explained.by..Generosity 0.703333067
## Explained.by..Perceptions.of.corruption 0.006185414
# Skor individu (koordinat observasi)
head(pca_result$ind$coord)
## Dim.1 Dim.2 Dim.3 Dim.4
## 1 5.924945 2.2073707 -1.803664 -0.5602149
## 2 5.585480 2.4316638 -1.752973 0.3971005
## 3 4.683336 0.5340145 1.250480 0.8608631
## 4 3.964661 -1.2257097 0.174618 0.3905916
## 5 4.892086 1.4734952 -1.050070 1.0815719
## 6 5.494840 2.5223262 -1.748597 0.4296565
Visualisasi PCA
# scree plot
fviz_eig(pca_result,
addlabels = TRUE,
ncp = 4,
barfill = "skyblue",
barcolor = "darkblue",
linecolor = "red")
var_names <- rownames(pca_result$var$coord)
alias_map <- setNames(paste0("X", seq_along(var_names)), var_names)
# Rename di semua komponen yang relevan
rownames(pca_result$var$coord) <- alias_map[var_names]
rownames(pca_result$var$cor) <- alias_map[var_names]
rownames(pca_result$var$cos2) <- alias_map[var_names]
rownames(pca_result$var$contrib) <- alias_map[var_names]
library(factoextra)
library(ggplot2)
library(ggrepel)
fviz_pca_biplot(pca_result,
geom.ind = "point",
pointshape = 21,
pointsize = 2,
fill.ind = "white",
col.ind = "gray40",
alpha.ind = 0.7,
col.var = "#E63946",
geom.var = c("arrow", "text"),
addEllipses = TRUE,
ellipse.alpha = 0.05,
label = "var",
repel = TRUE
) +
theme_minimal(base_size = 12) +
theme(
plot.title = element_text(face = "bold", size = 14, hjust = 0.5),
panel.grid.minor = element_blank(),
panel.grid.major = element_line(color = "gray90", linetype = "dashed")
) +
labs(title = "PCA Biplot")
# correlation circle
contrib_circle <- fviz_pca_var(pca_result, col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE) +
ggtitle("Kontribusi Variabel")
plot(contrib_circle)
# variable contribution
contrib_v_PC1 <- fviz_contrib(pca_result, choice = "var", axes = 1, top = 5) + ggtitle("PC1")
plot(contrib_v_PC1)
contrib_v_PC2 <- fviz_contrib(pca_result, choice = "var", axes = 2, top = 5) + ggtitle("PC2")
plot(contrib_v_PC2)
contrib_v_PC3 <- fviz_contrib(pca_result, choice = "var", axes = 3, top = 5) + ggtitle("PC3")
plot(contrib_v_PC3)
Factor Analysis Manual
varcov <- cov(data_scaled)
eig <- eigen(varcov)
L1 <- sqrt(eig$values[1]) * eig$vectors[,1]
L2 <- sqrt(eig$values[2]) * eig$vectors[,2]
L3 <- sqrt(eig$values[3]) * eig$vectors[,3]
L <- cbind(L1, L2, L3)
rownames(L) <- colnames(data_scaled)
colnames(L) <- c("Factor1","Factor2","Factor3")
L
## Factor1 Factor2 Factor3
## Ladder.score 0.946151374 -0.04940541 0.1319719
## Standard.error.of.ladder.score -0.622699360 -0.24428540 0.2011879
## upperwhisker 0.940030955 -0.06022871 0.1425855
## lowerwhisker 0.950989785 -0.03898316 0.1215485
## Logged.GDP.per.capita 0.889490416 0.25602308 -0.1499474
## Social.support 0.872125172 0.14487254 0.2746452
## Healthy.life.expectancy 0.867706871 0.29591693 -0.1584584
## Freedom.to.make.life.choices 0.684964841 -0.47216152 0.3710266
## Perceptions.of.corruption -0.553272000 0.53375537 0.6260414
## Explained.by..Log.GDP.per.capita 0.889448828 0.25602388 -0.1499792
## Explained.by..Social.support 0.872193296 0.14483700 0.2744472
## Explained.by..Healthy.life.expectancy 0.867562030 0.29614980 -0.1586121
## Explained.by..Freedom.to.make.life.choices 0.685021567 -0.47211206 0.3710823
## Explained.by..Generosity -0.006464244 -0.59273170 0.2662348
## Explained.by..Perceptions.of.corruption 0.553267693 -0.53355937 -0.6262402
rot <- varimax(L)
rot$loadings
##
## Loadings:
## Factor1 Factor2 Factor3
## Ladder.score 0.808 -0.472 -0.200
## Standard.error.of.ladder.score -0.664 0.209
## upperwhisker 0.797 -0.484 -0.196
## lowerwhisker 0.817 -0.460 -0.204
## Logged.GDP.per.capita 0.904 -0.241
## Social.support 0.835 -0.397
## Healthy.life.expectancy 0.904 -0.219
## Freedom.to.make.life.choices 0.376 -0.813 -0.164
## Perceptions.of.corruption -0.232 0.192 0.945
## Explained.by..Log.GDP.per.capita 0.904 -0.241
## Explained.by..Social.support 0.835 -0.397
## Explained.by..Healthy.life.expectancy 0.904 -0.219
## Explained.by..Freedom.to.make.life.choices 0.376 -0.813 -0.164
## Explained.by..Generosity -0.289 -0.572 -0.109
## Explained.by..Perceptions.of.corruption 0.232 -0.192 -0.945
##
## Factor1 Factor2 Factor3
## SS loadings 7.533 2.721 2.229
## Proportion Var 0.502 0.181 0.149
## Cumulative Var 0.502 0.684 0.832
Factor Analysis dengan psych
fa_model <- principal(data_scaled, nfactors = 3, rotate = "varimax")
fa_model
## Principal Components Analysis
## Call: principal(r = data_scaled, nfactors = 3, rotate = "varimax")
## Standardized loadings (pattern matrix) based upon correlation matrix
## RC1 RC2 RC3 h2 u2 com
## Ladder.score 0.81 0.47 0.20 0.92 0.085 1.8
## Standard.error.of.ladder.score -0.66 0.06 -0.21 0.49 0.512 1.2
## upperwhisker 0.80 0.48 0.20 0.91 0.092 1.8
## lowerwhisker 0.82 0.46 0.20 0.92 0.079 1.7
## Logged.GDP.per.capita 0.90 0.07 0.24 0.88 0.121 1.2
## Social.support 0.84 0.40 -0.04 0.86 0.143 1.4
## Healthy.life.expectancy 0.90 0.02 0.22 0.87 0.134 1.1
## Freedom.to.make.life.choices 0.38 0.81 0.16 0.83 0.170 1.5
## Perceptions.of.corruption -0.23 -0.19 -0.94 0.98 0.017 1.2
## Explained.by..Log.GDP.per.capita 0.90 0.07 0.24 0.88 0.121 1.2
## Explained.by..Social.support 0.84 0.40 -0.04 0.86 0.143 1.4
## Explained.by..Healthy.life.expectancy 0.90 0.02 0.22 0.87 0.134 1.1
## Explained.by..Freedom.to.make.life.choices 0.38 0.81 0.16 0.83 0.170 1.5
## Explained.by..Generosity -0.29 0.57 0.11 0.42 0.578 1.6
## Explained.by..Perceptions.of.corruption 0.23 0.19 0.94 0.98 0.017 1.2
##
## RC1 RC2 RC3
## SS loadings 7.53 2.72 2.23
## Proportion Var 0.50 0.18 0.15
## Cumulative Var 0.50 0.68 0.83
## Proportion Explained 0.60 0.22 0.18
## Cumulative Proportion 0.60 0.82 1.00
##
## Mean item complexity = 1.4
## Test of the hypothesis that 3 components are sufficient.
##
## The root mean square of the residuals (RMSR) is 0.04
## with the empirical chi square 47.01 with prob < 0.93
##
## Fit based upon off diagonal values = 1
fa_model$loadings
##
## Loadings:
## RC1 RC2 RC3
## Ladder.score 0.808 0.472 0.200
## Standard.error.of.ladder.score -0.664 -0.209
## upperwhisker 0.797 0.484 0.196
## lowerwhisker 0.817 0.460 0.204
## Logged.GDP.per.capita 0.904 0.241
## Social.support 0.835 0.397
## Healthy.life.expectancy 0.904 0.219
## Freedom.to.make.life.choices 0.376 0.813 0.164
## Perceptions.of.corruption -0.232 -0.192 -0.945
## Explained.by..Log.GDP.per.capita 0.904 0.241
## Explained.by..Social.support 0.835 0.397
## Explained.by..Healthy.life.expectancy 0.904 0.219
## Explained.by..Freedom.to.make.life.choices 0.376 0.813 0.164
## Explained.by..Generosity -0.289 0.572 0.109
## Explained.by..Perceptions.of.corruption 0.232 0.192 0.945
##
## RC1 RC2 RC3
## SS loadings 7.533 2.721 2.229
## Proportion Var 0.502 0.181 0.149
## Cumulative Var 0.502 0.684 0.832
FA <- fa(data_scaled,
covar = TRUE,
nfactors = 3,
rotate = "none",
fm = "pa")
FA$loadings
##
## Loadings:
## PA1 PA2 PA3
## Ladder.score 0.944 0.137
## Standard.error.of.ladder.score -0.586 -0.122 0.186
## upperwhisker 0.937 0.149
## lowerwhisker 0.950 0.125
## Logged.GDP.per.capita 0.884 0.191 -0.236
## Social.support 0.861 0.231 0.157
## Healthy.life.expectancy 0.861 0.227 -0.264
## Freedom.to.make.life.choices 0.680 -0.304 0.545
## Perceptions.of.corruption -0.559 0.733 0.375
## Explained.by..Log.GDP.per.capita 0.884 0.191 -0.236
## Explained.by..Social.support 0.861 0.231 0.157
## Explained.by..Healthy.life.expectancy 0.861 0.227 -0.264
## Explained.by..Freedom.to.make.life.choices 0.680 -0.304 0.546
## Explained.by..Generosity -0.259 0.239
## Explained.by..Perceptions.of.corruption 0.559 -0.733 -0.375
##
## PA1 PA2 PA3
## SS loadings 9.091 1.624 1.324
## Proportion Var 0.606 0.108 0.088
## Cumulative Var 0.606 0.714 0.803
FA$scores
## PA1 PA2 PA3
## 1 -0.78525633 -4.33371639 2.08255903
## 2 0.23609892 -2.80364605 -0.63527101
## 3 4.82573023 2.17083166 -0.97318662
## 4 4.46560364 3.29680207 -3.08931031
## 5 0.64532062 -1.58587540 -0.11961562
## 6 -2.31364919 -4.95707604 2.69826722
## 7 -0.24104859 -2.59536042 -0.14903909
## 8 4.96418449 0.67313219 -4.05243703
## 9 2.56639237 -0.73881552 -1.44696839
## 10 -3.45257898 -5.12432717 3.19196760
## 11 -3.87709431 -4.06287013 3.75570496
## 12 6.67206347 2.61485532 -3.50871026
## 13 8.58033025 3.71370697 -5.62079686
## 14 7.75670769 2.74539480 -5.14105976
## 15 0.78665920 0.62334372 -0.44416475
## 16 -6.08202650 -5.96833248 5.46734381
## 17 2.36350310 1.03274745 -2.75125654
## 18 1.46161672 1.65091311 0.41291943
## 19 7.89754276 3.44198924 -5.35069021
## 20 1.53783444 2.04211783 -1.34634174
## 21 9.26258142 5.77287206 -8.64960322
## 22 -0.39000995 -0.18792611 1.84708679
## 23 4.83371958 2.74410812 -1.45397903
## 24 5.57833387 4.89339690 -3.48902788
## 25 4.26179500 -0.65284845 -3.65405534
## 26 -5.30519234 -4.95019125 5.67909300
## 27 5.68386119 4.40988192 -6.06122645
## 28 7.09675778 3.25148215 -3.79909774
## 29 3.38052969 3.67868811 -2.28972051
## 30 7.36318188 4.04071656 -3.76819763
## 31 -0.10150936 -1.83438069 -0.13186028
## 32 0.81437559 1.20050307 -1.76197657
## 33 -4.39546218 -2.20522975 4.61941455
## 34 0.51559512 0.53109365 1.93962631
## 35 -1.73139234 -0.67623405 2.79174503
## 36 1.22151390 0.49694215 0.98987195
## 37 1.54232499 1.04206937 -0.24909887
## 38 -7.74027434 -4.75521307 8.53232976
## 39 -2.45131626 -1.26563814 1.91709287
## 40 -4.09444674 -4.45339764 5.80698379
## 41 2.31830689 2.36932183 -1.41026278
## 42 0.01953982 -0.40778397 1.28337095
## 43 -2.44054268 -1.03649826 2.15703101
## 44 -6.39519791 -4.35171788 5.82315820
## 45 -6.17039978 -4.19513131 7.19036162
## 46 -2.35419999 -0.34145775 1.69953868
## 47 4.24057490 2.77630683 -3.70446256
## 48 -3.24226661 -0.58819994 2.81755998
## 49 -0.35626267 -0.52451371 1.67421985
## 50 -0.74344923 -2.40250396 3.04084184
## 51 -0.72363826 0.56235091 0.78165788
## 52 -0.96941541 -0.54591892 2.56331225
## 53 5.46895892 3.51657661 -2.36542113
## 54 0.07527028 -0.62185604 0.08031658
## 55 0.14915972 0.53172400 -0.57575830
## 56 0.74661270 1.35250839 0.33715344
## 57 -6.64348832 -4.00817892 4.67818911
## 58 6.22778336 5.86286442 -7.09311428
## 59 3.85253398 3.01825642 -2.92943729
## 60 -5.75739580 -2.80843334 5.66406901
## 61 1.35553906 1.97703783 -1.31077406
## 62 1.98764347 1.93841476 0.03666098
## 63 -5.04057253 -2.07142962 3.71940140
## 64 -5.17899038 -3.83960289 5.29687340
## 65 2.15193401 1.44116823 -1.59744439
## 66 4.63472381 3.54618786 -2.53165874
## 67 1.88737631 2.09485903 -1.10692912
## 68 6.27133951 4.63181671 -3.36452223
## 69 -5.99936106 -3.31126109 4.75524845
## 70 -5.13685521 -2.52873328 3.74138206
## 71 2.98673617 3.11214432 -1.37716904
## 72 6.73113373 5.69478031 -6.39560064
## 73 0.04826215 -0.57314044 0.40675989
## 74 4.08568417 3.40599227 -3.21668410
## 75 -1.59528980 -0.01295142 1.48348688
## 76 -9.12498551 -6.78499269 8.65209300
## 77 -3.92371872 -1.31003119 3.64141437
## 78 0.50628539 0.93437950 -1.47601716
## 79 6.27940696 3.95136493 -4.43933578
## 80 -4.91279827 -5.49838802 5.57262283
## 81 -3.86078326 -1.57913874 1.10404022
## 82 -0.58341021 -1.08309108 -2.83518373
## 83 2.91552087 2.98049924 -2.51736820
## 84 -0.60594202 -0.27586160 2.58268914
## 85 2.67487004 2.60334781 -0.97379728
## 86 -6.68039038 -4.72734651 5.14841922
## 87 2.13489173 2.19425015 -0.56799390
## 88 -3.26707677 -2.02294988 3.48707080
## 89 0.79179868 -0.82136093 1.50123053
## 90 3.07004337 2.13149560 -4.37736671
## 91 -1.21646434 -0.47484519 0.09172572
## 92 0.40685144 1.82883528 -1.12307069
## 93 -5.05420790 -3.79000578 4.32598724
## 94 3.19021424 2.62347999 -2.80232737
## 95 6.89959216 5.27373712 -4.68786611
## 96 -2.80507532 -1.08886538 1.56886172
## 97 -0.90708047 -1.88550516 1.37142575
## 98 2.31251278 3.11558385 -3.37937090
## 100 -2.64254309 -1.43371029 1.62974603
## 101 -3.05036065 -1.03045070 0.53171171
## 102 -6.38743380 -3.97092532 5.18059513
## 103 4.28528539 2.86903395 -5.28273055
## 104 3.62790910 2.36976819 -2.98224984
## 105 1.20776460 1.86940567 -2.22426424
## 106 -6.75093433 -2.95381475 3.64586225
## 107 -4.59664094 -2.50333288 3.67453346
## 108 -7.46066989 -4.50871104 4.42289033
## 109 4.92913455 3.21519810 -5.37286225
## 110 -1.66367993 0.86752283 -0.53310302
## 111 -3.55294115 -1.85612285 3.19878501
## 112 7.40115373 5.35153550 -5.40685293
## 113 -3.81890169 -1.04855889 1.04035604
## 114 2.67526606 1.83308609 -1.93807613
## 115 7.80535353 5.79792532 -6.49042811
## 116 -4.68689159 -4.31851631 2.31762378
## 117 -0.86581326 -0.40329929 -1.38913906
## 118 -6.29722148 -4.68389909 4.55616230
## 119 4.25618039 4.75251224 -6.63472538
## 120 -2.69511864 -1.56781213 2.48851393
## 121 -4.19732720 -2.84430031 0.48756387
## 122 -5.00556369 -2.65617151 1.05884952
## 123 -6.11240114 -4.47799166 5.06972968
## 124 -2.15997535 -1.43003650 2.24960847
## 125 -6.55081091 -3.58982159 3.41875513
## 126 7.03099999 4.58668516 -5.81822599
## 127 -0.94524758 0.12302109 -1.65384691
## 128 -5.74848386 -3.74624544 4.42780748
## 129 5.97958722 2.14325788 -4.52412404
## 130 2.46688298 3.10886349 -6.98770416
## 131 5.43244315 4.08176521 -7.05469821
## 132 -4.36516226 -2.04310025 2.30155412
## 133 -9.16341566 -5.54982770 6.22222360
## 134 0.86942327 0.61294705 -1.28054787
## 135 -7.10557100 -4.37061213 5.29082819
## 136 -4.20412327 -0.18176964 -1.07529102
## 137 3.97510610 4.71240350 -8.47938229