PEMODELAN DAN KLASIFIKASI STATUS AKADEMIK MAHASISWA MENGGUNAKAN ANALISIS DISKRIMINAN DAN REGRESI LOGISTIK MULTINOMIAL
Celine Nurhidayah Santoso (24031554033) | Dista Ishlahul Amalia (24031554063) | Dessy Saputri (24031554190)
2026-04-26
LIBRARY
library(MASS)## Warning: package 'MASS' was built under R version 4.5.3library(nnet)## Warning: package 'nnet' was built under R version 4.5.3library(MVN)## Warning: package 'MVN' was built under R version 4.5.3library(biotools)## Warning: package 'biotools' was built under R version 4.5.3## ---
## biotools version 4.3library(corrplot)## Warning: package 'corrplot' was built under R version 4.5.3## corrplot 0.95 loadedlibrary(ggplot2)
library(dplyr)##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
##
## select## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(GGally)## Warning: package 'GGally' was built under R version 4.5.3library(broom)
library(marginaleffects)## Warning: package 'marginaleffects' was built under R version 4.5.3library(pscl)## Warning: package 'pscl' was built under R version 4.5.3## Classes and Methods for R originally developed in the
## Political Science Computational Laboratory
## Department of Political Science
## Stanford University (2002-2015),
## by and under the direction of Simon Jackman.
## hurdle and zeroinfl functions by Achim Zeileis.IMPORT DATA
data <- read.csv("data.csv", sep=";")
head(data)## Marital.status Application.mode Application.order Course
## 1 1 17 5 171
## 2 1 15 1 9254
## 3 1 1 5 9070
## 4 1 17 2 9773
## 5 2 39 1 8014
## 6 2 39 1 9991
## Daytime.evening.attendance. Previous.qualification
## 1 1 1
## 2 1 1
## 3 1 1
## 4 1 1
## 5 0 1
## 6 0 19
## Previous.qualification..grade. Nacionality Mother.s.qualification
## 1 122.0 1 19
## 2 160.0 1 1
## 3 122.0 1 37
## 4 122.0 1 38
## 5 100.0 1 37
## 6 133.1 1 37
## Father.s.qualification Mother.s.occupation Father.s.occupation
## 1 12 5 9
## 2 3 3 3
## 3 37 9 9
## 4 37 5 3
## 5 38 9 9
## 6 37 9 7
## Admission.grade Displaced Educational.special.needs Debtor
## 1 127.3 1 0 0
## 2 142.5 1 0 0
## 3 124.8 1 0 0
## 4 119.6 1 0 0
## 5 141.5 0 0 0
## 6 114.8 0 0 1
## Tuition.fees.up.to.date Gender Scholarship.holder Age.at.enrollment
## 1 1 1 0 20
## 2 0 1 0 19
## 3 0 1 0 19
## 4 1 0 0 20
## 5 1 0 0 45
## 6 1 1 0 50
## International Curricular.units.1st.sem..credited.
## 1 0 0
## 2 0 0
## 3 0 0
## 4 0 0
## 5 0 0
## 6 0 0
## Curricular.units.1st.sem..enrolled. Curricular.units.1st.sem..evaluations.
## 1 0 0
## 2 6 6
## 3 6 0
## 4 6 8
## 5 6 9
## 6 5 10
## Curricular.units.1st.sem..approved. Curricular.units.1st.sem..grade.
## 1 0 0.00000
## 2 6 14.00000
## 3 0 0.00000
## 4 6 13.42857
## 5 5 12.33333
## 6 5 11.85714
## Curricular.units.1st.sem..without.evaluations.
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 0
## Curricular.units.2nd.sem..credited. Curricular.units.2nd.sem..enrolled.
## 1 0 0
## 2 0 6
## 3 0 6
## 4 0 6
## 5 0 6
## 6 0 5
## Curricular.units.2nd.sem..evaluations. Curricular.units.2nd.sem..approved.
## 1 0 0
## 2 6 6
## 3 0 0
## 4 10 5
## 5 6 6
## 6 17 5
## Curricular.units.2nd.sem..grade.
## 1 0.00000
## 2 13.66667
## 3 0.00000
## 4 12.40000
## 5 13.00000
## 6 11.50000
## Curricular.units.2nd.sem..without.evaluations. Unemployment.rate
## 1 0 10.8
## 2 0 13.9
## 3 0 10.8
## 4 0 9.4
## 5 0 13.9
## 6 5 16.2
## Inflation.rate GDP Target
## 1 1.4 1.74 Dropout
## 2 -0.3 0.79 Graduate
## 3 1.4 1.74 Dropout
## 4 -0.8 -3.12 Graduate
## 5 -0.3 0.79 Graduate
## 6 0.3 -0.92 Graduatestr(data)## 'data.frame': 4424 obs. of 37 variables:
## $ Marital.status : int 1 1 1 1 2 2 1 1 1 1 ...
## $ Application.mode : int 17 15 1 17 39 39 1 18 1 1 ...
## $ Application.order : int 5 1 5 2 1 1 1 4 3 1 ...
## $ Course : int 171 9254 9070 9773 8014 9991 9500 9254 9238 9238 ...
## $ Daytime.evening.attendance. : int 1 1 1 1 0 0 1 1 1 1 ...
## $ Previous.qualification : int 1 1 1 1 1 19 1 1 1 1 ...
## $ Previous.qualification..grade. : num 122 160 122 122 100 ...
## $ Nacionality : int 1 1 1 1 1 1 1 1 62 1 ...
## $ Mother.s.qualification : int 19 1 37 38 37 37 19 37 1 1 ...
## $ Father.s.qualification : int 12 3 37 37 38 37 38 37 1 19 ...
## $ Mother.s.occupation : int 5 3 9 5 9 9 7 9 9 4 ...
## $ Father.s.occupation : int 9 3 9 3 9 7 10 9 9 7 ...
## $ Admission.grade : num 127 142 125 120 142 ...
## $ Displaced : int 1 1 1 1 0 0 1 1 0 1 ...
## $ Educational.special.needs : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Debtor : int 0 0 0 0 0 1 0 0 0 1 ...
## $ Tuition.fees.up.to.date : int 1 0 0 1 1 1 1 0 1 0 ...
## $ Gender : int 1 1 1 0 0 1 0 1 0 0 ...
## $ Scholarship.holder : int 0 0 0 0 0 0 1 0 1 0 ...
## $ Age.at.enrollment : int 20 19 19 20 45 50 18 22 21 18 ...
## $ International : int 0 0 0 0 0 0 0 0 1 0 ...
## $ Curricular.units.1st.sem..credited. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Curricular.units.1st.sem..enrolled. : int 0 6 6 6 6 5 7 5 6 6 ...
## $ Curricular.units.1st.sem..evaluations. : int 0 6 0 8 9 10 9 5 8 9 ...
## $ Curricular.units.1st.sem..approved. : int 0 6 0 6 5 5 7 0 6 5 ...
## $ Curricular.units.1st.sem..grade. : num 0 14 0 13.4 12.3 ...
## $ Curricular.units.1st.sem..without.evaluations.: int 0 0 0 0 0 0 0 0 0 0 ...
## $ Curricular.units.2nd.sem..credited. : int 0 0 0 0 0 0 0 0 0 0 ...
## $ Curricular.units.2nd.sem..enrolled. : int 0 6 6 6 6 5 8 5 6 6 ...
## $ Curricular.units.2nd.sem..evaluations. : int 0 6 0 10 6 17 8 5 7 14 ...
## $ Curricular.units.2nd.sem..approved. : int 0 6 0 5 6 5 8 0 6 2 ...
## $ Curricular.units.2nd.sem..grade. : num 0 13.7 0 12.4 13 ...
## $ Curricular.units.2nd.sem..without.evaluations.: int 0 0 0 0 0 5 0 0 0 0 ...
## $ Unemployment.rate : num 10.8 13.9 10.8 9.4 13.9 16.2 15.5 15.5 16.2 8.9 ...
## $ Inflation.rate : num 1.4 -0.3 1.4 -0.8 -0.3 0.3 2.8 2.8 0.3 1.4 ...
## $ GDP : num 1.74 0.79 1.74 -3.12 0.79 -0.92 -4.06 -4.06 -0.92 3.51 ...
## $ Target : chr "Dropout" "Graduate" "Dropout" "Graduate" ...names(data)## [1] "Marital.status"
## [2] "Application.mode"
## [3] "Application.order"
## [4] "Course"
## [5] "Daytime.evening.attendance."
## [6] "Previous.qualification"
## [7] "Previous.qualification..grade."
## [8] "Nacionality"
## [9] "Mother.s.qualification"
## [10] "Father.s.qualification"
## [11] "Mother.s.occupation"
## [12] "Father.s.occupation"
## [13] "Admission.grade"
## [14] "Displaced"
## [15] "Educational.special.needs"
## [16] "Debtor"
## [17] "Tuition.fees.up.to.date"
## [18] "Gender"
## [19] "Scholarship.holder"
## [20] "Age.at.enrollment"
## [21] "International"
## [22] "Curricular.units.1st.sem..credited."
## [23] "Curricular.units.1st.sem..enrolled."
## [24] "Curricular.units.1st.sem..evaluations."
## [25] "Curricular.units.1st.sem..approved."
## [26] "Curricular.units.1st.sem..grade."
## [27] "Curricular.units.1st.sem..without.evaluations."
## [28] "Curricular.units.2nd.sem..credited."
## [29] "Curricular.units.2nd.sem..enrolled."
## [30] "Curricular.units.2nd.sem..evaluations."
## [31] "Curricular.units.2nd.sem..approved."
## [32] "Curricular.units.2nd.sem..grade."
## [33] "Curricular.units.2nd.sem..without.evaluations."
## [34] "Unemployment.rate"
## [35] "Inflation.rate"
## [36] "GDP"
## [37] "Target"summary(data)## Marital.status Application.mode Application.order Course
## Min. :1.000 Min. : 1.00 Min. :0.000 Min. : 33
## 1st Qu.:1.000 1st Qu.: 1.00 1st Qu.:1.000 1st Qu.:9085
## Median :1.000 Median :17.00 Median :1.000 Median :9238
## Mean :1.179 Mean :18.67 Mean :1.728 Mean :8857
## 3rd Qu.:1.000 3rd Qu.:39.00 3rd Qu.:2.000 3rd Qu.:9556
## Max. :6.000 Max. :57.00 Max. :9.000 Max. :9991
## Daytime.evening.attendance. Previous.qualification
## Min. :0.0000 Min. : 1.000
## 1st Qu.:1.0000 1st Qu.: 1.000
## Median :1.0000 Median : 1.000
## Mean :0.8908 Mean : 4.578
## 3rd Qu.:1.0000 3rd Qu.: 1.000
## Max. :1.0000 Max. :43.000
## Previous.qualification..grade. Nacionality Mother.s.qualification
## Min. : 95.0 Min. : 1.000 Min. : 1.00
## 1st Qu.:125.0 1st Qu.: 1.000 1st Qu.: 2.00
## Median :133.1 Median : 1.000 Median :19.00
## Mean :132.6 Mean : 1.873 Mean :19.56
## 3rd Qu.:140.0 3rd Qu.: 1.000 3rd Qu.:37.00
## Max. :190.0 Max. :109.000 Max. :44.00
## Father.s.qualification Mother.s.occupation Father.s.occupation Admission.grade
## Min. : 1.00 Min. : 0.00 Min. : 0.00 Min. : 95.0
## 1st Qu.: 3.00 1st Qu.: 4.00 1st Qu.: 4.00 1st Qu.:117.9
## Median :19.00 Median : 5.00 Median : 7.00 Median :126.1
## Mean :22.28 Mean : 10.96 Mean : 11.03 Mean :127.0
## 3rd Qu.:37.00 3rd Qu.: 9.00 3rd Qu.: 9.00 3rd Qu.:134.8
## Max. :44.00 Max. :194.00 Max. :195.00 Max. :190.0
## Displaced Educational.special.needs Debtor
## Min. :0.0000 Min. :0.00000 Min. :0.0000
## 1st Qu.:0.0000 1st Qu.:0.00000 1st Qu.:0.0000
## Median :1.0000 Median :0.00000 Median :0.0000
## Mean :0.5484 Mean :0.01153 Mean :0.1137
## 3rd Qu.:1.0000 3rd Qu.:0.00000 3rd Qu.:0.0000
## Max. :1.0000 Max. :1.00000 Max. :1.0000
## Tuition.fees.up.to.date Gender Scholarship.holder Age.at.enrollment
## Min. :0.0000 Min. :0.0000 Min. :0.0000 Min. :17.00
## 1st Qu.:1.0000 1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:19.00
## Median :1.0000 Median :0.0000 Median :0.0000 Median :20.00
## Mean :0.8807 Mean :0.3517 Mean :0.2484 Mean :23.27
## 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.0000 3rd Qu.:25.00
## Max. :1.0000 Max. :1.0000 Max. :1.0000 Max. :70.00
## International Curricular.units.1st.sem..credited.
## Min. :0.00000 Min. : 0.00
## 1st Qu.:0.00000 1st Qu.: 0.00
## Median :0.00000 Median : 0.00
## Mean :0.02486 Mean : 0.71
## 3rd Qu.:0.00000 3rd Qu.: 0.00
## Max. :1.00000 Max. :20.00
## Curricular.units.1st.sem..enrolled. Curricular.units.1st.sem..evaluations.
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 5.000 1st Qu.: 6.000
## Median : 6.000 Median : 8.000
## Mean : 6.271 Mean : 8.299
## 3rd Qu.: 7.000 3rd Qu.:10.000
## Max. :26.000 Max. :45.000
## Curricular.units.1st.sem..approved. Curricular.units.1st.sem..grade.
## Min. : 0.000 Min. : 0.00
## 1st Qu.: 3.000 1st Qu.:11.00
## Median : 5.000 Median :12.29
## Mean : 4.707 Mean :10.64
## 3rd Qu.: 6.000 3rd Qu.:13.40
## Max. :26.000 Max. :18.88
## Curricular.units.1st.sem..without.evaluations.
## Min. : 0.0000
## 1st Qu.: 0.0000
## Median : 0.0000
## Mean : 0.1377
## 3rd Qu.: 0.0000
## Max. :12.0000
## Curricular.units.2nd.sem..credited. Curricular.units.2nd.sem..enrolled.
## Min. : 0.0000 Min. : 0.000
## 1st Qu.: 0.0000 1st Qu.: 5.000
## Median : 0.0000 Median : 6.000
## Mean : 0.5418 Mean : 6.232
## 3rd Qu.: 0.0000 3rd Qu.: 7.000
## Max. :19.0000 Max. :23.000
## Curricular.units.2nd.sem..evaluations. Curricular.units.2nd.sem..approved.
## Min. : 0.000 Min. : 0.000
## 1st Qu.: 6.000 1st Qu.: 2.000
## Median : 8.000 Median : 5.000
## Mean : 8.063 Mean : 4.436
## 3rd Qu.:10.000 3rd Qu.: 6.000
## Max. :33.000 Max. :20.000
## Curricular.units.2nd.sem..grade.
## Min. : 0.00
## 1st Qu.:10.75
## Median :12.20
## Mean :10.23
## 3rd Qu.:13.33
## Max. :18.57
## Curricular.units.2nd.sem..without.evaluations. Unemployment.rate
## Min. : 0.0000 Min. : 7.60
## 1st Qu.: 0.0000 1st Qu.: 9.40
## Median : 0.0000 Median :11.10
## Mean : 0.1503 Mean :11.57
## 3rd Qu.: 0.0000 3rd Qu.:13.90
## Max. :12.0000 Max. :16.20
## Inflation.rate GDP Target
## Min. :-0.800 Min. :-4.060000 Length:4424
## 1st Qu.: 0.300 1st Qu.:-1.700000 Class :character
## Median : 1.400 Median : 0.320000 Mode :character
## Mean : 1.228 Mean : 0.001969
## 3rd Qu.: 2.600 3rd Qu.: 1.790000
## Max. : 3.700 Max. : 3.510000dim(data)## [1] 4424 37FEATURE SELECTION
df <- data[,c(
"Target",
"Age.at.enrollment",
"Admission.grade",
"Previous.qualification..grade.",
"Curricular.units.1st.sem..approved.",
"Curricular.units.2nd.sem..approved."
)]
df$Target <- as.factor(df$Target)
str(df)## 'data.frame': 4424 obs. of 6 variables:
## $ Target : Factor w/ 3 levels "Dropout","Enrolled",..: 1 3 1 3 3 3 3 1 3 1 ...
## $ Age.at.enrollment : int 20 19 19 20 45 50 18 22 21 18 ...
## $ Admission.grade : num 127 142 125 120 142 ...
## $ Previous.qualification..grade. : num 122 160 122 122 100 ...
## $ Curricular.units.1st.sem..approved.: int 0 6 0 6 5 5 7 0 6 5 ...
## $ Curricular.units.2nd.sem..approved.: int 0 6 0 5 6 5 8 0 6 2 ...STANDARDISASI
X <- scale(
df[,-1]
)
df_scaled <- data.frame(
Target=df$Target,
X
)VISUALISASI AWAL
# Distribusi kelas Target
ggplot(
df_scaled,
aes(Target, fill=Target)
)+
geom_bar()+
ggtitle(
"Distribusi Status Akademik"
)
# Boxplot per Kelas
ggplot(
df_scaled,
aes(
Target,
Admission.grade,
fill=Target
)
)+
geom_boxplot()+
ggtitle(
"Admission Grade per Status"
)
# Pairplot
ggpairs(
df_scaled,
aes(color=Target)
)## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
## `stat_bin()` using `bins = 30`. Pick better value `binwidth`.
# Heatmap Korelasi
cor_matrix <- cor(
df_scaled[,-1]
)
corrplot(
cor_matrix,
method="color",
addCoef.col="black"
)
## ANALISIS DISKRIMINAN
# Uji Normalitas
MVN::mvn(
df_scaled[,-1],
mvn_test = "hz"
)## $multivariate_normality
## Test Statistic p.value Method MVN
## 1 Henze-Zirkler 62.305 <0.001 asymptotic ✗ Not normal
##
## $univariate_normality
## Test Variable Statistic p.value
## 1 Anderson-Darling Age.at.enrollment 470.094 <0.001
## 2 Anderson-Darling Admission.grade 20.391 <0.001
## 3 Anderson-Darling Previous.qualification..grade. 29.303 <0.001
## 4 Anderson-Darling Curricular.units.1st.sem..approved. 142.968 <0.001
## 5 Anderson-Darling Curricular.units.2nd.sem..approved. 113.301 <0.001
## Normality
## 1 ✗ Not normal
## 2 ✗ Not normal
## 3 ✗ Not normal
## 4 ✗ Not normal
## 5 ✗ Not normal
##
## $descriptives
## Variable n Mean Std.Dev Median Min Max
## 1 Age.at.enrollment 4424 0 1 -0.430 -0.826 6.159
## 2 Admission.grade 4424 0 1 -0.061 -2.208 4.352
## 3 Previous.qualification..grade. 4424 0 1 0.037 -2.852 4.351
## 4 Curricular.units.1st.sem..approved. 4424 0 1 0.095 -1.521 6.882
## 5 Curricular.units.2nd.sem..approved. 4424 0 1 0.187 -1.471 5.163
## 25th 75th Skew Kurtosis
## 1 -0.562 0.229 2.054 7.121
## 2 -0.627 0.540 0.530 3.661
## 3 -0.577 0.560 0.313 3.966
## 4 -0.552 0.418 0.766 6.092
## 5 -0.808 0.519 0.306 3.843
##
## $data
## Age.at.enrollment Admission.grade Previous.qualification..grade.
## 1 -0.43031418 0.022226256 -0.80475029
## 2 -0.56210442 1.071804984 2.07658458
## 3 -0.56210442 -0.150401825 -0.80475029
## 4 -0.43031418 -0.509468232 -0.80475029
## 5 2.86444168 1.002753752 -2.47289153
## 6 3.52339286 -0.840914146 0.03690279
## 7 -0.69389465 0.098182611 0.71174175
## 8 -0.16673371 -0.958301240 -1.03222410
## 9 -0.29852395 0.160328720 0.33261874
## 10 -0.69389465 -0.274694043 0.40844334
## 11 -0.69389465 0.250095322 0.48426794
## 12 -0.69389465 -0.530183601 0.25679414
## 13 -0.56210442 0.222474829 0.02932033
## 14 -0.29852395 -1.048067842 -1.71464551
## 15 -0.69389465 0.698928330 1.24251396
## 16 -0.43031418 -0.433511876 -0.42562728
## 17 -0.69389465 0.719643700 0.33261874
## 18 -0.69389465 0.022226256 0.18096954
## 19 -0.43031418 0.643687345 0.33261874
## 20 -0.69389465 -0.164212071 0.56009254
## 21 -0.29852395 -0.461132369 -0.80475029
## 22 -0.43031418 -0.357555521 -0.42562728
## 23 -0.69389465 -0.102065962 0.71174175
## 24 -0.56210442 -0.834009023 -0.57727648
## 25 -0.56210442 -0.212547934 -0.50145188
## 26 -0.69389465 2.073047849 1.39416317
## 27 -0.29852395 -0.730432174 -1.33552250
## 28 -0.69389465 0.277715814 0.40844334
## 29 -0.43031418 -0.336840151 0.18096954
## 30 -0.56210442 -0.564709217 -0.42562728
## 31 -0.29852395 1.589689225 1.31833856
## 32 -0.43031418 0.208664582 -0.57727648
## 33 -0.69389465 0.816315425 0.78756635
## 34 -0.56210442 0.519395127 0.40844334
## 35 1.41474910 0.305336307 -0.19815347
## 36 1.81011981 -1.690244301 -0.19815347
## 37 2.60086121 0.125803104 0.03690279
## 38 4.18234403 -0.281599166 0.56009254
## 39 2.07370028 -0.903060255 -0.95639949
## 40 -0.43031418 -0.481847739 -0.95639949
## 41 -0.69389465 -0.405891384 -0.50145188
## 42 -0.16673371 -0.454227246 0.02932033
## 43 -0.16673371 -1.821441642 -2.24541773
## 44 -0.43031418 -0.385176014 -0.95639949
## 45 0.75579793 -1.193075430 0.03690279
## 46 0.09684676 0.491774634 1.62163697
## 47 -0.69389465 0.042941625 -0.19815347
## 48 -0.16673371 0.374387539 -0.04650427
## 49 -0.29852395 0.443438771 -0.19815347
## 50 -0.56210442 -0.060635223 0.48426794
## 51 0.09684676 -0.930680748 -0.19815347
## 52 -0.56210442 -0.392081137 0.48426794
## 53 -0.43031418 -0.357555521 -0.42562728
## 54 -0.56210442 2.231865683 2.60735680
## 55 0.49221746 -0.481847739 -0.19815347
## 56 -0.69389465 0.146518473 -0.19815347
## 57 2.07370028 0.208664582 -0.19815347
## 58 0.49221746 1.955660755 -0.27397808
## 59 -0.69389465 0.885366657 0.63591715
## 60 -0.69389465 -0.813293653 -0.57727648
## 61 -0.69389465 -0.834009023 -0.57727648
## 62 -0.29852395 0.339861923 -0.19815347
## 63 -0.56210442 -0.067540346 0.02932033
## 64 -0.56210442 0.222474829 -0.42562728
## 65 0.09684676 -0.419701630 -1.25969790
## 66 0.75579793 -0.067540346 0.03690279
## 67 -0.56210442 0.084372364 0.48426794
## 68 -0.03494348 0.208664582 -0.19815347
## 69 -0.56210442 -0.474942616 -0.57727648
## 70 0.36042723 -1.862872381 2.07658458
## 71 -0.69389465 0.484869511 1.16668936
## 72 0.09684676 0.263905568 1.31833856
## 73 -0.56210442 0.609161729 0.63591715
## 74 -0.69389465 -1.054972965 -1.10804870
## 75 -0.69389465 0.408913155 0.71174175
## 76 -0.69389465 -0.792578283 -0.95639949
## 77 -0.29852395 -1.448564988 -2.01794392
## 78 -0.56210442 -0.461132369 -0.88057489
## 79 -0.16673371 0.263905568 1.31833856
## 80 1.28295887 -0.689001435 -0.95639949
## 81 -0.43031418 -1.158549814 -1.41134710
## 82 1.54653934 1.983281248 0.56009254
## 83 0.09684676 3.688846681 2.07658458
## 84 -0.69389465 -0.102065962 -0.95639949
## 85 1.28295887 -1.172360060 -0.19815347
## 86 -0.16673371 2.349252778 2.07658458
## 87 0.22863699 -1.862872381 -0.95639949
## 88 -0.43031418 -0.647570696 -0.65310109
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## 1844 -0.43031418 -0.412796507 -0.34980268
## 1845 -0.56210442 -0.502563109 0.02932033
## 1846 -0.56210442 0.277715814 0.40844334
## 1847 -0.56210442 -0.695906558 -0.50145188
## 1848 2.33728075 0.208664582 0.56009254
## 1849 -0.56210442 0.747264193 0.78756635
## 1850 -0.56210442 -0.336840151 0.18096954
## 1851 -0.03494348 -0.481847739 -0.95639949
## 1852 -0.69389465 0.415818279 1.16668936
## 1853 -0.56210442 -0.813293653 -0.50145188
## 1854 -0.43031418 2.280201546 2.07658458
## 1855 1.54653934 -1.427849619 0.56009254
## 1856 1.41474910 -1.655718685 0.03690279
## 1857 -0.56210442 0.622971975 0.25679414
## 1858 -0.16673371 1.348009912 1.31833856
## 1859 -0.43031418 0.305336307 -0.19815347
## 1860 0.49221746 0.208664582 -0.19815347
## 1861 0.88758816 0.692023207 -1.71464551
## 1862 1.41474910 -0.074445469 -1.71464551
## 1863 -0.43031418 -1.041162719 -0.88057489
## 1864 -0.69389465 0.291526061 -0.42562728
## 1865 0.36042723 0.291526061 0.56009254
## 1866 0.36042723 0.899176903 -0.19815347
## 1867 0.36042723 -0.378270891 -0.19815347
## 1868 1.01937840 1.831368537 -2.47289153
## 1869 -0.43031418 1.051089614 0.48426794
## 1870 -0.56210442 0.284620938 1.31833856
## 1871 -0.03494348 0.250095322 0.03690279
## 1872 -0.43031418 -0.827103899 -1.03222410
## 1873 -0.43031418 -0.136591578 2.83483060
## 1874 0.75579793 -2.035500461 0.03690279
## 1875 -0.43031418 0.512490004 0.02932033
## 1876 0.09684676 -0.564709217 -0.57727648
## 1877 1.81011981 -1.137834444 0.03690279
## 1878 -0.69389465 -0.253978673 0.78756635
## 1879 -0.69389465 0.871556411 -0.42562728
## 1880 -0.69389465 0.816315425 1.84911078
## 1881 2.33728075 2.280201546 2.07658458
## 1882 1.54653934 0.899176903 0.56009254
## 1883 -0.56210442 -0.606139957 -0.34980268
## 1884 -0.69389465 1.631119964 0.93921555
## 1885 3.25981239 -0.813293653 0.03690279
## 1886 -0.56210442 -0.067540346 -0.04650427
## 1887 0.88758816 2.280201546 2.07658458
## 1888 3.65518309 2.280201546 2.07658458
## 1889 -0.69389465 3.965051609 3.92670487
## 1890 -0.69389465 2.003996617 1.24251396
## 1891 -0.69389465 1.603499471 1.01504016
## 1892 -0.69389465 -0.046824977 0.48426794
## 1893 -0.69389465 1.320389419 1.46998777
## 1894 -0.69389465 1.265148434 1.09086476
## 1895 -0.03494348 -0.702811682 -0.88057489
## 1896 -0.56210442 0.353672170 -0.65310109
## 1897 -0.29852395 -1.683339178 -2.09376852
## 1898 -0.69389465 -1.013542226 -0.88057489
## 1899 -0.69389465 1.955660755 0.78756635
## 1900 -0.29852395 1.852083907 1.31833856
## 1901 -0.43031418 -1.172360060 -0.50145188
## 1902 0.09684676 0.084372364 0.03690279
## 1903 -0.69389465 -0.454227246 -0.42562728
## 1904 -0.69389465 1.796842921 2.07658458
## 1905 -0.56210442 -0.626855326 -0.88057489
## 1906 -0.43031418 1.285863803 1.31833856
## 1907 -0.69389465 -0.495657985 -1.18387330
## 1908 -0.69389465 -0.012299361 0.63591715
## 1909 -0.56210442 -1.441659865 -1.56299631
## 1910 -0.56210442 0.712738577 1.16668936
## 1911 -0.69389465 -0.792578283 -0.95639949
## 1912 -0.43031418 0.036036502 -0.04650427
## 1913 -0.69389465 -0.737337298 -0.57727648
## 1914 -0.69389465 -0.951396117 -0.72892569
## 1915 -0.69389465 0.388197786 0.71174175
## 1916 -0.69389465 0.346767046 1.16668936
## 1917 -0.69389465 0.229379952 0.25679414
## 1918 -0.43031418 -0.709716805 -0.72892569
## 1919 -0.16673371 0.484869511 0.18096954
## 1920 -0.43031418 -1.862872381 1.39416317
## 1921 -0.43031418 0.899176903 0.56009254
## 1922 -0.69389465 0.843935918 0.25679414
## 1923 -0.69389465 0.388197786 0.71174175
## 1924 -0.69389465 0.167233843 0.71174175
## 1925 -0.69389465 -0.095160839 -0.42562728
## 1926 -0.56210442 0.160328720 -0.12232887
## 1927 -0.56210442 0.098182611 0.10514493
## 1928 -0.69389465 0.892271780 0.71174175
## 1929 -0.69389465 -0.150401825 -0.72892569
## 1930 -0.69389465 0.105087734 0.02932033
## 1931 -0.69389465 -0.633760450 -0.57727648
## 1932 -0.56210442 -0.820198776 -0.95639949
## 1933 -0.69389465 -0.619950203 -0.57727648
## 1934 0.22863699 -0.481847739 0.03690279
## 1935 -0.56210442 -0.509468232 0.03690279
## 1936 -0.69389465 0.429628525 0.78756635
## 1937 -0.56210442 1.023469121 1.09086476
## 1938 -0.69389465 0.229379952 0.71174175
## 1939 0.09684676 -1.862872381 1.31833856
## 1940 -0.29852395 -0.854724392 -0.65310109
## 1941 -0.69389465 -0.247073550 0.25679414
## 1942 -0.69389465 -0.730432174 -1.25969790
## 1943 -0.43031418 -0.260883796 -0.42562728
## 1944 -0.56210442 -0.226358180 -1.18387330
## 1945 -0.56210442 0.042941625 -1.25969790
## 1946 0.88758816 -0.682096312 -0.27397808
## 1947 -0.69389465 1.541353362 1.84911078
## 1948 -0.69389465 -0.095160839 0.18096954
## 1949 -0.69389465 1.244433064 0.48426794
## 1950 -0.43031418 -0.827103899 -1.33552250
## 1951 -0.56210442 -0.875439762 -0.72892569
## 1952 -0.56210442 -0.067540346 0.56009254
## 1953 -0.56210442 -0.205642810 0.40844334
## 1954 -0.69389465 -0.302314535 -0.04650427
## 1955 -0.82568489 0.471059264 0.56009254
## 1956 -0.56210442 -0.930680748 -1.18387330
## 1957 -0.69389465 -0.302314535 -0.57727648
## 1958 0.22863699 0.899176903 0.56009254
## 1959 -0.56210442 -1.379513756 0.03690279
## 1960 0.09684676 0.208664582 -0.19815347
## 1961 -0.56210442 -0.191832564 0.10514493
## 1962 -0.43031418 -0.081350593 -0.34980268
## 1963 -0.43031418 -1.310462524 -1.33552250
## 1964 -0.43031418 -0.813293653 -1.03222410
## 1965 -0.56210442 0.160328720 -0.12232887
## 1966 1.01937840 -0.481847739 -0.95639949
## 1967 -0.43031418 -0.709716805 -0.95639949
## 1968 -0.69389465 -0.412796507 0.18096954
## 1969 -0.69389465 0.084372364 1.01504016
## 1970 -0.69389465 -0.405891384 0.02932033
## 1971 -0.43031418 -0.992826857 -0.80475029
## 1972 -0.43031418 -0.253978673 -0.34980268
## 1973 -0.56210442 0.167233843 -0.27397808
## 1974 -0.29852395 -0.488752862 -0.80475029
## 1975 -0.69389465 0.319146554 0.56009254
## 1976 -0.29852395 -0.481847739 0.78756635
## 1977 -0.56210442 -1.172360060 -1.10804870
## 1978 -0.43031418 1.106330600 0.56009254
## 1979 -0.43031418 0.899176903 0.56009254
## 1980 -0.69389465 -0.537088725 -0.72892569
## 1981 -0.69389465 -0.184927441 0.56009254
## 1982 -0.69389465 -1.096403705 -1.25969790
## 1983 -0.29852395 1.589689225 1.31833856
## 1984 -0.69389465 1.403250898 1.09086476
## 1985 -0.69389465 1.417061144 2.22823379
## 1986 -0.43031418 -1.310462524 -1.86629472
## 1987 1.15116863 0.208664582 -0.19815347
## 1988 1.41474910 0.208664582 0.56009254
## 1989 -0.03494348 -1.241411292 -1.25969790
## 1990 -0.69389465 -1.034257596 -0.95639949
## 1991 -0.69389465 -0.398986260 -0.04650427
## 1992 1.41474910 0.899176903 0.56009254
## 1993 0.22863699 -0.516373355 -0.95639949
## 1994 -0.29852395 -0.074445469 0.25679414
## 1995 -0.43031418 -0.378270891 0.02932033
## 1996 -0.69389465 -0.378270891 -0.50145188
## 1997 -0.69389465 0.374387539 0.71174175
## 1998 -0.69389465 -0.316124782 -0.88057489
## 1999 0.09684676 -1.172360060 0.10514493
## 2000 1.15116863 -0.454227246 0.56009254
## 2001 0.09684676 -1.517616221 0.03690279
## 2002 -0.69389465 0.747264193 1.84911078
## 2003 0.62400770 -0.619950203 -0.95639949
## 2004 -0.69389465 -0.336840151 0.10514493
## 2005 0.09684676 0.899176903 0.56009254
## 2006 -0.56210442 1.120140846 0.02932033
## 2007 2.73265145 -0.447322123 1.01504016
## 2008 -0.69389465 -0.516373355 -0.19815347
## 2009 -0.69389465 1.417061144 1.39416317
## 2010 -0.16673371 0.181044089 0.03690279
## 2011 -0.69389465 -0.060635223 -0.04650427
## 2012 2.73265145 2.280201546 -1.71464551
## 2013 1.28295887 -1.483090605 0.03690279
## 2014 1.15116863 -2.173602926 -1.71464551
## 2015 1.54653934 -1.344988140 0.03690279
## 2016 -0.43031418 -1.441659865 -2.09376852
## 2017 0.09684676 -0.737337298 2.07658458
## 2018 -0.56210442 0.719643700 0.86339095
## 2019 -0.29852395 -1.738580163 -2.47289153
## 2020 -0.56210442 1.182286955 0.78756635
## 2021 0.49221746 -1.324272771 2.07658458
## 2022 0.88758816 0.084372364 0.56009254
## 2023 -0.29852395 -0.689001435 0.03690279
## 2024 -0.56210442 -1.144739567 -1.25969790
## 2025 1.41474910 2.970713867 -0.95639949
## 2026 -0.69389465 -1.862872381 0.63591715
## 2027 -0.29852395 -0.689001435 -1.71464551
## 2028 -0.82568489 0.450343895 -0.42562728
## 2029 -0.56210442 0.070562118 -0.04650427
## 2030 -0.69389465 -0.336840151 0.18096954
## 2031 -0.56210442 0.443438771 0.18096954
## 2032 2.86444168 -1.034257596 0.56009254
## 2033 0.36042723 0.208664582 0.03690279
## 2034 3.65518309 -1.862872381 -2.47289153
## 2035 3.39160262 2.418304010 0.03690279
## 2036 -0.16673371 1.796842921 -2.47289153
## 2037 -0.16673371 0.305336307 0.33261874
## 2038 1.28295887 0.084372364 -0.95639949
## 2039 -0.43031418 1.513732869 1.23493150
## 2040 -0.69389465 0.098182611 0.10514493
## 2041 -0.43031418 -0.461132369 -0.34980268
## 2042 1.81011981 -1.862872381 0.03690279
## 2043 -0.69389465 -0.060635223 -0.12232887
## 2044 -0.56210442 -1.054972965 -1.10804870
## 2045 -0.29852395 0.899176903 0.56009254
## 2046 -0.43031418 -0.329935028 0.02932033
## 2047 -0.56210442 -0.571614341 -0.50145188
## 2048 -0.43031418 -0.378270891 -0.57727648
## 2049 -0.69389465 0.519395127 0.40844334
## 2050 -0.56210442 0.001510886 0.56009254
## 2051 -0.69389465 -0.882344885 -0.65310109
## 2052 -0.69389465 -0.115876209 0.02932033
## 2053 -0.69389465 -0.454227246 -0.42562728
## 2054 -0.56210442 -0.274694043 0.40844334
## 2055 -0.69389465 0.243190198 0.71174175
## 2056 -0.56210442 -0.102065962 -0.19815347
## 2057 0.09684676 0.471059264 -0.19815347
## 2058 -0.43031418 1.589689225 1.31833856
## 2059 -0.29852395 0.243190198 -0.42562728
## 2060 -0.43031418 0.899176903 0.56009254
## 2061 -0.56210442 -0.523278478 -0.50145188
## 2062 -0.56210442 -0.392081137 0.48426794
## 2063 -0.69389465 -0.046824977 0.63591715
## 2064 -0.56210442 -1.061878089 -0.95639949
## 2065 -0.29852395 -1.082593458 -0.95639949
## 2066 -0.56210442 -0.309219659 0.10514493
## 2067 -0.69389465 -0.723527051 -0.34980268
## 2068 -0.82568489 0.346767046 0.02932033
## 2069 -0.56210442 -0.226358180 -0.72892569
## 2070 -0.03494348 -0.689001435 -1.10804870
## 2071 -0.56210442 -0.723527051 -1.48717171
## 2072 -0.69389465 -0.378270891 0.18096954
## 2073 -0.43031418 -1.517616221 0.03690279
## 2074 -0.56210442 -0.392081137 -0.19815347
## 2075 -0.69389465 0.629877098 0.18096954
## 2076 -0.56210442 -0.233263303 0.02932033
## 2077 -0.56210442 0.139613350 -0.72892569
## 2078 -0.69389465 0.678212961 0.93921555
## 2079 -0.69389465 0.443438771 1.01504016
## 2080 -0.56210442 0.622971975 0.86339095
## 2081 -0.56210442 -0.081350593 0.86339095
## 2082 -0.56210442 -0.447322123 -0.12232887
## 2083 -0.29852395 0.222474829 0.63591715
## 2084 -0.69389465 0.616066852 0.40844334
## 2085 -0.56210442 -0.723527051 -0.42562728
## 2086 -0.69389465 -0.205642810 -0.65310109
## 2087 0.88758816 0.899176903 0.56009254
## 2088 -0.69389465 1.651835333 1.84911078
## 2089 -0.43031418 0.022226256 -0.27397808
## 2090 0.22863699 -1.862872381 0.03690279
## 2091 -0.69389465 0.125803104 0.71174175
## 2092 -0.29852395 -0.502563109 0.02932033
## 2093 -0.69389465 0.954417889 1.77328618
## 2094 -0.69389465 0.761074439 1.39416317
## 2095 0.75579793 0.408913155 0.18096954
## 2096 -0.43031418 0.899176903 0.56009254
## 2097 0.36042723 0.899176903 0.56009254
## 2098 -0.29852395 -1.911208244 -2.47289153
## 2099 -0.56210442 -0.530183601 -0.50145188
## 2100 -0.56210442 -0.951396117 -0.72892569
## 2101 -0.29852395 -0.689001435 0.03690279
## 2102 -0.43031418 -0.274694043 0.33261874
## 2103 -0.69389465 0.015321132 0.40844334
## 2104 -0.43031418 0.968228135 -0.34980268
## 2105 -0.43031418 -0.364460644 0.25679414
## 2106 -0.69389465 -0.405891384 -0.42562728
## 2107 -0.69389465 1.320389419 0.93921555
## 2108 -0.69389465 1.071804984 0.56009254
## 2109 -0.69389465 -0.012299361 0.40844334
## 2110 -0.16673371 1.589689225 1.31833856
## 2111 -0.56210442 1.589689225 1.31833856
## 2112 -0.56210442 0.519395127 -0.12232887
## 2113 -0.69389465 0.174138966 0.25679414
## 2114 -0.43031418 -0.951396117 -1.18387330
## 2115 -0.69389465 0.912987150 1.92493538
## 2116 -0.29852395 -0.537088725 -0.27397808
## 2117 -0.56210442 0.947512766 0.56009254
## 2118 -0.69389465 1.057994737 0.63591715
## 2119 -0.69389465 0.201759459 -0.04650427
## 2120 -0.69389465 0.540110496 0.02932033
## 2121 -0.29852395 -1.579762329 -1.79047011
## 2122 -0.56210442 -0.316124782 0.18096954
## 2123 -0.56210442 -0.440417000 -0.80475029
## 2124 -0.56210442 -1.006637103 -1.10804870
## 2125 -0.69389465 2.135193958 3.13812901
## 2126 -0.56210442 -0.074445469 0.71174175
## 2127 -0.43031418 -0.592329710 -0.12232887
## 2128 -0.69389465 0.263905568 0.48426794
## 2129 -0.56210442 3.433357122 2.83483060
## 2130 -0.69389465 2.059237603 3.74472583
## 2131 -0.69389465 -0.012299361 -0.57727648
## 2132 -0.56210442 0.070562118 0.71174175
## 2133 -0.43031418 -0.909965378 -1.03222410
## 2134 -0.56210442 -0.426606753 -0.34980268
## 2135 -0.69389465 0.263905568 1.31833856
## 2136 0.22863699 -1.793821149 0.03690279
## 2137 -0.69389465 -0.060635223 -0.12232887
## 2138 -0.56210442 -0.909965378 -1.10804870
## 2139 -0.56210442 -0.599234833 -0.80475029
## 2140 -0.43031418 0.063656995 -1.25969790
## 2141 -0.69389465 0.284620938 0.33261874
## 2142 -0.43031418 -0.626855326 -0.34980268
## 2143 -0.29852395 -0.778768037 -0.72892569
## 2144 -0.56210442 0.968228135 0.03690279
## 2145 2.46907098 -0.481847739 -1.71464551
## 2146 -0.69389465 0.332956800 0.78756635
## 2147 -0.56210442 0.284620938 1.31833856
## 2148 -0.69389465 -0.633760450 -0.27397808
## 2149 -0.29852395 0.899176903 0.56009254
## 2150 -0.43031418 -1.310462524 0.03690279
## 2151 -0.43031418 -0.281599166 -0.04650427
## 2152 -0.29852395 0.208664582 -0.19815347
## 2153 -0.56210442 -0.067540346 0.33261874
## 2154 -0.29852395 0.484869511 0.03690279
## 2155 -0.56210442 0.505584880 0.78756635
## 2156 -0.56210442 0.809410302 1.16668936
## 2157 -0.69389465 1.127045969 0.33261874
## 2158 -0.16673371 2.280201546 2.07658458
## 2159 -0.29852395 -1.103308828 -1.56299631
## 2160 -0.69389465 0.105087734 0.02932033
## 2161 -0.43031418 0.415818279 0.71174175
## 2162 -0.69389465 -0.854724392 -0.72892569
## 2163 -0.43031418 -1.579762329 -2.24541773
## 2164 -0.03494348 0.042941625 0.56009254
## 2165 -0.69389465 1.658740457 2.00075998
## 2166 -0.43031418 0.602256605 0.56009254
## 2167 -0.69389465 0.747264193 1.16668936
## 2168 -0.43031418 -0.668286066 -1.56299631
## 2169 -0.69389465 -0.398986260 -0.12232887
## 2170 -0.43031418 0.160328720 0.93921555
## 2171 -0.56210442 -0.274694043 0.03690279
## 2172 -0.29852395 0.899176903 0.56009254
## 2173 1.28295887 0.899176903 0.56009254
## 2174 0.09684676 1.216812571 1.31833856
## 2175 -0.43031418 -0.599234833 -0.95639949
## 2176 -0.69389465 1.838273660 1.77328618
## 2177 -0.69389465 2.162814451 2.60735680
## 2178 0.75579793 -1.862872381 0.03690279
## 2179 -0.69389465 0.547015620 1.09086476
## 2180 -0.56210442 1.037279368 -0.27397808
## 2181 -0.56210442 0.022226256 0.25679414
## 2182 -0.69389465 -0.723527051 -0.34980268
## 2183 -0.56210442 0.802505178 0.56009254
## 2184 -0.43031418 0.415818279 0.63591715
## 2185 -0.56210442 0.636782221 0.02932033
## 2186 -0.56210442 -0.619950203 -0.57727648
## 2187 -0.69389465 -0.012299361 -0.65310109
## 2188 -0.69389465 0.105087734 0.56009254
## 2189 -0.56210442 0.201759459 0.56009254
## 2190 -0.43031418 -0.081350593 0.33261874
## 2191 -0.69389465 0.160328720 0.86339095
## 2192 -0.69389465 -0.157306948 0.40844334
## 2193 1.54653934 1.928040262 -0.19815347
## 2194 -0.69389465 0.022226256 0.71174175
## 2195 -0.56210442 0.139613350 0.25679414
## 2196 -0.56210442 -2.000974845 0.03690279
## 2197 -0.43031418 -0.343745275 -0.19815347
## 2198 -0.56210442 -0.999731980 -1.18387330
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## 1868 -1.52108545 -1.4713606
## 1869 2.35709072 2.1773497
## 1870 0.41800264 -0.4762578
## 1871 -1.52108545 -1.4713606
## 1872 -1.19790410 -1.4713606
## 1873 0.74118399 1.5139478
## 1874 -1.52108545 -1.4713606
## 1875 0.41800264 -0.1445568
## 1876 0.41800264 0.5188450
## 1877 -1.52108545 -1.4713606
## 1878 -1.52108545 -1.4713606
## 1879 -1.52108545 -1.4713606
## 1880 0.74118399 0.8505460
## 1881 0.09482129 0.5188450
## 1882 -0.22836006 -0.4762578
## 1883 -1.52108545 -1.4713606
## 1884 -1.52108545 -1.4713606
## 1885 -0.22836006 -0.4762578
## 1886 0.41800264 0.5188450
## 1887 0.41800264 -0.1445568
## 1888 -1.52108545 -1.4713606
## 1889 0.41800264 0.1871441
## 1890 -1.52108545 -1.4713606
## 1891 -1.52108545 -1.4713606
## 1892 1.06436533 1.1822469
## 1893 -0.22836006 -1.4713606
## 1894 -1.52108545 -1.4713606
## 1895 3.97299746 4.1675553
## 1896 -0.87472275 -0.4762578
## 1897 -0.22836006 -0.8079587
## 1898 0.09482129 -0.1445568
## 1899 -1.52108545 -1.4713606
## 1900 1.71072803 1.1822469
## 1901 0.41800264 0.5188450
## 1902 1.38754668 1.5139478
## 1903 0.41800264 0.5188450
## 1904 0.41800264 0.5188450
## 1905 0.41800264 0.5188450
## 1906 0.41800264 0.5188450
## 1907 0.74118399 1.1822469
## 1908 0.74118399 0.8505460
## 1909 0.09482129 0.1871441
## 1910 0.41800264 0.5188450
## 1911 0.09482129 0.1871441
## 1912 1.06436533 1.1822469
## 1913 0.74118399 1.1822469
## 1914 -0.55154140 -1.4713606
## 1915 0.09482129 0.1871441
## 1916 0.41800264 0.5188450
## 1917 0.41800264 0.5188450
## 1918 0.74118399 1.1822469
## 1919 0.09482129 0.1871441
## 1920 0.09482129 0.1871441
## 1921 0.09482129 -0.8079587
## 1922 0.41800264 0.5188450
## 1923 0.09482129 -0.4762578
## 1924 0.09482129 -0.1445568
## 1925 -1.19790410 -1.4713606
## 1926 1.06436533 0.1871441
## 1927 0.09482129 0.1871441
## 1928 0.41800264 0.5188450
## 1929 0.09482129 0.1871441
## 1930 0.74118399 1.1822469
## 1931 0.74118399 1.1822469
## 1932 0.41800264 0.5188450
## 1933 0.09482129 -0.1445568
## 1934 1.06436533 1.1822469
## 1935 0.41800264 0.8505460
## 1936 0.74118399 1.1822469
## 1937 0.41800264 -0.1445568
## 1938 0.41800264 0.5188450
## 1939 0.09482129 -1.1396596
## 1940 0.09482129 0.1871441
## 1941 0.41800264 0.5188450
## 1942 0.41800264 0.5188450
## 1943 0.41800264 0.5188450
## 1944 0.41800264 0.1871441
## 1945 0.41800264 0.5188450
## 1946 0.74118399 1.1822469
## 1947 1.06436533 1.1822469
## 1948 -0.22836006 -0.4762578
## 1949 0.41800264 0.5188450
## 1950 0.41800264 0.8505460
## 1951 -1.52108545 -1.4713606
## 1952 -1.52108545 -1.4713606
## 1953 -1.52108545 -1.4713606
## 1954 0.41800264 0.5188450
## 1955 0.09482129 0.1871441
## 1956 0.41800264 0.5188450
## 1957 0.09482129 -0.8079587
## 1958 0.74118399 0.8505460
## 1959 0.09482129 0.5188450
## 1960 1.06436533 0.5188450
## 1961 0.41800264 0.5188450
## 1962 -1.52108545 -1.4713606
## 1963 0.09482129 0.1871441
## 1964 0.74118399 1.1822469
## 1965 -0.22836006 -0.4762578
## 1966 2.03390938 2.5090506
## 1967 -0.55154140 -0.4762578
## 1968 -0.55154140 0.1871441
## 1969 -0.22836006 -0.4762578
## 1970 0.41800264 0.1871441
## 1971 1.06436533 -0.4762578
## 1972 0.41800264 0.5188450
## 1973 0.09482129 0.1871441
## 1974 0.09482129 0.1871441
## 1975 0.74118399 1.1822469
## 1976 1.71072803 1.8456488
## 1977 -0.22836006 0.8505460
## 1978 0.41800264 0.1871441
## 1979 0.41800264 -0.4762578
## 1980 0.09482129 0.5188450
## 1981 -0.22836006 0.1871441
## 1982 0.41800264 0.5188450
## 1983 -0.55154140 0.1871441
## 1984 0.41800264 0.5188450
## 1985 1.06436533 1.1822469
## 1986 -0.22836006 -0.1445568
## 1987 1.06436533 1.1822469
## 1988 -1.52108545 -1.4713606
## 1989 0.41800264 1.1822469
## 1990 -0.22836006 0.1871441
## 1991 0.09482129 0.1871441
## 1992 -1.52108545 -1.4713606
## 1993 0.41800264 -0.1445568
## 1994 0.09482129 0.1871441
## 1995 -1.52108545 -1.4713606
## 1996 0.41800264 0.5188450
## 1997 0.41800264 0.5188450
## 1998 0.41800264 0.5188450
## 1999 -1.19790410 -1.4713606
## 2000 3.00345342 2.8407516
## 2001 0.41800264 -0.4762578
## 2002 0.41800264 -1.4713606
## 2003 0.41800264 0.1871441
## 2004 0.41800264 -0.1445568
## 2005 -1.52108545 -1.4713606
## 2006 0.09482129 0.1871441
## 2007 0.41800264 0.5188450
## 2008 0.41800264 0.5188450
## 2009 -1.52108545 -1.4713606
## 2010 -1.52108545 -1.4713606
## 2011 0.41800264 0.5188450
## 2012 0.09482129 0.1871441
## 2013 0.09482129 0.1871441
## 2014 -1.52108545 -1.4713606
## 2015 -1.52108545 -1.4713606
## 2016 0.41800264 0.5188450
## 2017 0.09482129 0.1871441
## 2018 0.74118399 1.1822469
## 2019 0.09482129 0.1871441
## 2020 0.41800264 0.5188450
## 2021 -1.52108545 -1.4713606
## 2022 -1.52108545 -1.4713606
## 2023 -1.52108545 -1.4713606
## 2024 0.41800264 0.5188450
## 2025 -0.87472275 -0.1445568
## 2026 0.74118399 0.8505460
## 2027 -1.52108545 -1.4713606
## 2028 -1.52108545 -1.4713606
## 2029 0.41800264 0.5188450
## 2030 0.41800264 0.5188450
## 2031 0.74118399 1.1822469
## 2032 0.09482129 -1.4713606
## 2033 0.41800264 -0.1445568
## 2034 -1.52108545 -1.4713606
## 2035 0.41800264 0.5188450
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## 2037 -0.87472275 -1.1396596
## 2038 -0.87472275 -0.8079587
## 2039 0.09482129 -0.1445568
## 2040 0.41800264 0.5188450
## 2041 -0.55154140 -0.8079587
## 2042 0.74118399 1.8456488
## 2043 0.41800264 0.5188450
## 2044 0.41800264 0.5188450
## 2045 0.41800264 -0.1445568
## 2046 0.41800264 0.8505460
## 2047 -1.52108545 -1.4713606
## 2048 -0.22836006 -0.1445568
## 2049 0.74118399 1.1822469
## 2050 0.74118399 0.8505460
## 2051 -0.22836006 0.1871441
## 2052 0.41800264 0.5188450
## 2053 -0.87472275 -1.4713606
## 2054 0.09482129 0.5188450
## 2055 0.74118399 1.1822469
## 2056 0.41800264 0.5188450
## 2057 2.35709072 2.1773497
## 2058 0.41800264 -0.8079587
## 2059 0.09482129 -0.1445568
## 2060 -0.22836006 0.1871441
## 2061 0.74118399 1.1822469
## 2062 0.74118399 1.1822469
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## 2065 0.09482129 0.1871441
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## 2068 0.41800264 0.5188450
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## 2074 0.09482129 0.1871441
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## 2076 0.41800264 0.5188450
## 2077 0.41800264 0.5188450
## 2078 1.06436533 1.1822469
## 2079 0.74118399 0.8505460
## 2080 0.41800264 0.5188450
## 2081 0.74118399 0.8505460
## 2082 0.41800264 0.5188450
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## 2085 0.41800264 0.5188450
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## 2087 -1.52108545 -1.4713606
## 2088 0.41800264 0.1871441
## 2089 0.41800264 0.5188450
## 2090 0.09482129 0.1871441
## 2091 0.41800264 0.5188450
## 2092 0.09482129 -0.4762578
## 2093 0.74118399 0.8505460
## 2094 0.41800264 0.5188450
## 2095 0.41800264 0.1871441
## 2096 3.00345342 2.5090506
## 2097 -1.52108545 -1.4713606
## 2098 0.09482129 0.5188450
## 2099 1.06436533 1.1822469
## 2100 0.41800264 0.1871441
## 2101 0.09482129 0.1871441
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## 2103 0.74118399 1.1822469
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## 2105 0.41800264 0.5188450
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## 2117 0.41800264 0.5188450
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## 2122 0.09482129 -0.1445568
## 2123 0.09482129 0.1871441
## 2124 0.09482129 -1.4713606
## 2125 -1.52108545 -1.4713606
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## 2127 0.41800264 1.1822469
## 2128 0.41800264 0.5188450
## 2129 -1.52108545 -1.4713606
## 2130 0.41800264 0.5188450
## 2131 0.41800264 -0.1445568
## 2132 0.41800264 0.5188450
## 2133 -0.55154140 0.1871441
## 2134 0.74118399 1.1822469
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## 2138 0.41800264 0.5188450
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## 2140 -0.87472275 -0.8079587
## 2141 0.74118399 0.8505460
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## 2143 0.41800264 0.5188450
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## 2145 0.41800264 0.5188450
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## 2179 0.74118399 1.1822469
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## 2187 0.41800264 0.1871441
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## 2214 0.09482129 -0.4762578
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## 2249 -1.52108545 -1.4713606
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## 4394 -0.55154140 -0.4762578
## 4395 1.06436533 1.1822469
## 4396 0.41800264 0.1871441
## 4397 0.41800264 0.5188450
## 4398 0.09482129 -0.4762578
## 4399 -0.22836006 -0.1445568
## 4400 0.41800264 0.5188450
## 4401 -0.22836006 -0.4762578
## 4402 -0.55154140 -1.4713606
## 4403 0.09482129 0.5188450
## 4404 0.41800264 0.8505460
## 4405 -1.19790410 -0.8079587
## 4406 0.74118399 0.8505460
## 4407 -0.22836006 -0.8079587
## 4408 0.41800264 0.5188450
## 4409 0.09482129 0.5188450
## 4410 0.09482129 0.1871441
## 4411 0.41800264 0.1871441
## 4412 0.41800264 -0.4762578
## 4413 -0.22836006 0.1871441
## 4414 0.09482129 -0.8079587
## 4415 0.09482129 0.1871441
## 4416 -0.55154140 -0.4762578
## 4417 2.35709072 2.5090506
## 4418 0.41800264 0.5188450
## 4419 0.41800264 0.8505460
## 4420 0.09482129 0.1871441
## 4421 0.41800264 -0.8079587
## 4422 0.74118399 -1.1396596
## 4423 0.09482129 0.1871441
## 4424 0.41800264 0.5188450
##
## $subset
## NULL
##
## $outlierMethod
## [1] "none"
##
## attr(,"class")
## [1] "mvn"# Box's M
boxM(
df_scaled[,-1],
df_scaled$Target
)##
## Box's M-test for Homogeneity of Covariance Matrices
##
## data: df_scaled[, -1]
## Chi-Sq (approx.) = 650.15, df = 30, p-value < 2.2e-16# Split Data
set.seed(123)
index <- sample(
1:nrow(df_scaled),
0.7*nrow(df_scaled)
)
train <- df_scaled[index,]
test <- df_scaled[-index,]# LDA
fit_lda <- lda(
Target~.,
data=train
)
fit_lda## Call:
## lda(Target ~ ., data = train)
##
## Prior probabilities of groups:
## Dropout Enrolled Graduate
## 0.3191214 0.1828165 0.4980620
##
## Group means:
## Age.at.enrollment Admission.grade Previous.qualification..grade.
## Dropout 0.36829729 -0.1368222 -0.1084456
## Enrolled -0.07964971 -0.1302598 -0.1196630
## Graduate -0.18767315 0.1344950 0.1179102
## Curricular.units.1st.sem..approved.
## Dropout -0.6784588
## Enrolled -0.1175877
## Graduate 0.4968069
## Curricular.units.2nd.sem..approved.
## Dropout -0.81265891
## Enrolled -0.09943143
## Graduate 0.57929119
##
## Coefficients of linear discriminants:
## LD1 LD2
## Age.at.enrollment -0.3362552 0.6494575
## Admission.grade 0.1344681 0.3591485
## Previous.qualification..grade. 0.0376309 0.4193250
## Curricular.units.1st.sem..approved. -0.3416258 0.7457136
## Curricular.units.2nd.sem..approved. 1.5234119 -0.5179817
##
## Proportion of trace:
## LD1 LD2
## 0.9889 0.0111fit_lda$scaling## LD1 LD2
## Age.at.enrollment -0.3362552 0.6494575
## Admission.grade 0.1344681 0.3591485
## Previous.qualification..grade. 0.0376309 0.4193250
## Curricular.units.1st.sem..approved. -0.3416258 0.7457136
## Curricular.units.2nd.sem..approved. 1.5234119 -0.5179817# Prediksi
pred_lda <- predict(
fit_lda,
test
)# Confussion Matrix
cm <- table(
Prediksi=pred_lda$class,
Aktual=test$Target
)
cm## Aktual
## Prediksi Dropout Enrolled Graduate
## Dropout 334 93 54
## Enrolled 0 0 0
## Graduate 99 135 613mean(
pred_lda$class==test$Target
)## [1] 0.7131024#Visualisasi
cm_df <- as.data.frame(cm)
ggplot(
cm_df,
aes(
Aktual,
Prediksi,
fill=Freq
)
)+
geom_tile()+
geom_text(
aes(label=Freq)
)+
ggtitle(
"Confusion Matrix LDA"
)
# Plot Canonical Discriminant
lda_values <- predict(
fit_lda
)$x
plot(
lda_values,
col=as.numeric(train$Target),
pch=19,
main="Discriminant Function Plot"
)
## MULTINOMIAL LOGISTIC
# Multinomial Berganda
fit_full <- multinom(
Target~
Age.at.enrollment+
Admission.grade+
Previous.qualification..grade.+
Curricular.units.1st.sem..approved.+
Curricular.units.2nd.sem..approved.,
data=df_scaled
)## # weights: 21 (12 variable)
## initial value 4860.260765
## iter 10 value 3951.020229
## iter 20 value 3301.190658
## final value 3301.165041
## convergedsummary(
fit_full
)## Call:
## multinom(formula = Target ~ Age.at.enrollment + Admission.grade +
## Previous.qualification..grade. + Curricular.units.1st.sem..approved. +
## Curricular.units.2nd.sem..approved., data = df_scaled)
##
## Coefficients:
## (Intercept) Age.at.enrollment Admission.grade
## Enrolled -0.01950758 -0.4150483 0.05984933
## Graduate 0.69274506 -0.5498639 0.24479767
## Previous.qualification..grade. Curricular.units.1st.sem..approved.
## Enrolled -0.01426110 -0.2260134
## Graduate 0.08255453 -0.2668455
## Curricular.units.2nd.sem..approved.
## Enrolled 1.255554
## Graduate 2.516379
##
## Std. Errors:
## (Intercept) Age.at.enrollment Admission.grade
## Enrolled 0.05587048 0.05022936 0.05870802
## Graduate 0.05064882 0.04786196 0.05730785
## Previous.qualification..grade. Curricular.units.1st.sem..approved.
## Enrolled 0.05915241 0.1150957
## Graduate 0.05672743 0.1139353
## Curricular.units.2nd.sem..approved.
## Enrolled 0.1172860
## Graduate 0.1192341
##
## Residual Deviance: 6602.33
## AIC: 6626.33# Rasio Risiko Relatif
exp(
coef(fit_full)
)## (Intercept) Age.at.enrollment Admission.grade
## Enrolled 0.9806815 0.6603084 1.061677
## Graduate 1.9991959 0.5770283 1.277363
## Previous.qualification..grade. Curricular.units.1st.sem..approved.
## Enrolled 0.9858401 0.7977074
## Graduate 1.0860579 0.7657914
## Curricular.units.2nd.sem..approved.
## Enrolled 3.509781
## Graduate 12.383679# Marginal Effects
avg_comparisons(
fit_full,
variables=
"Admission.grade",
type="probs"
)##
## Group Estimate Std. Error z Pr(>|z|) S 2.5 % 97.5 %
## Dropout -0.0206 0.00617 -3.34 <0.001 10.2 -0.0327 -0.00854
## Enrolled -0.0119 0.00702 -1.69 0.0909 3.5 -0.0256 0.00189
## Graduate 0.0325 0.00760 4.28 <0.001 15.7 0.0176 0.04739
##
## Term: Admission.grade
## Type: probs
## Comparison: +1# Pseudo R2
pR2(
fit_full
)## fitting null model for pseudo-r2
## # weights: 6 (2 variable)
## initial value 4860.260765
## final value 4511.832789
## converged## llh llhNull G2 McFadden r2ML
## -3301.1650412 -4511.8327885 2421.3354947 0.2683317 0.4215008
## r2CU
## 0.4845209# Prediksi
pred_multi <- predict(
fit_full
)
table(
Prediksi=pred_multi,
Aktual=df_scaled$Target
)## Aktual
## Prediksi Dropout Enrolled Graduate
## Dropout 1093 310 163
## Enrolled 0 0 0
## Graduate 328 484 2046mean(
pred_multi==
df_scaled$Target
)## [1] 0.7095389# Visual Probabilitas Prediksi
prob <- predict(
fit_full,
type="probs"
)
prob_df <- as.data.frame(
prob
)
head(prob_df)## Dropout Enrolled Graduate
## 1 0.73952273 0.1952575 0.06521978
## 2 0.05845569 0.1307854 0.81075890
## 3 0.73157897 0.2019231 0.06649792
## 4 0.18794077 0.2488128 0.56324639
## 5 0.31560433 0.1946858 0.48970982
## 6 0.61178656 0.1635603 0.22465313ggplot(
prob_df,
aes(Graduate)
)+
geom_histogram(
bins=30
)+
ggtitle(
"Probabilitas Prediksi Graduate"
)