Tugas Individu PSD
G1401211043_Yogi Nur Hamid
2023-09-28
packages:
lapply(c("car","lmtest"),library,character.only=T)[[1]]## Loading required package: carData## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric## [1] "car" "carData" "stats" "graphics" "grDevices" "utils"
## [7] "datasets" "methods" "base"INPUT DATA
data <- read.csv("C:/Users/ASUS/OneDrive/Documents/sem 5/Pengantar Sains Data/heart.csv")
head(data)## age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca thal
## 1 52 1 0 125 212 0 1 168 0 1.0 2 2 3
## 2 53 1 0 140 203 1 0 155 1 3.1 0 0 3
## 3 70 1 0 145 174 0 1 125 1 2.6 0 0 3
## 4 61 1 0 148 203 0 1 161 0 0.0 2 1 3
## 5 62 0 0 138 294 1 1 106 0 1.9 1 3 2
## 6 58 0 0 100 248 0 0 122 0 1.0 1 0 2
## target
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 1str(data)## 'data.frame': 1025 obs. of 14 variables:
## $ age : int 52 53 70 61 62 58 58 55 46 54 ...
## $ sex : int 1 1 1 1 0 0 1 1 1 1 ...
## $ cp : int 0 0 0 0 0 0 0 0 0 0 ...
## $ trestbps: int 125 140 145 148 138 100 114 160 120 122 ...
## $ chol : int 212 203 174 203 294 248 318 289 249 286 ...
## $ fbs : int 0 1 0 0 1 0 0 0 0 0 ...
## $ restecg : int 1 0 1 1 1 0 2 0 0 0 ...
## $ thalach : int 168 155 125 161 106 122 140 145 144 116 ...
## $ exang : int 0 1 1 0 0 0 0 1 0 1 ...
## $ oldpeak : num 1 3.1 2.6 0 1.9 1 4.4 0.8 0.8 3.2 ...
## $ slope : int 2 0 0 2 1 1 0 1 2 1 ...
## $ ca : int 2 0 0 1 3 0 3 1 0 2 ...
## $ thal : int 3 3 3 3 2 2 1 3 3 2 ...
## $ target : int 0 0 0 0 0 1 0 0 0 0 ...Tipe Data Berdasarkan hasil running kode di atas, kita bisa melihat bahwa seluruh dataset merupakan variabel numerik sehingga dapat diolah. Beberapa variabel merupakan variabel kategorik yang sudah dikuantitatifkan menjadi angka. Karena itu, dilihat dari tipe datanya, dataset ini sudah siap diolah.
Memeriksa missing data
sum(is.na(data)) # total keseluruhan NA bila ada## [1] 0colSums(is.na(data)) # total NA per kolo## age sex cp trestbps chol fbs restecg thalach
## 0 0 0 0 0 0 0 0
## exang oldpeak slope ca thal target
## 0 0 0 0 0 0Tidak terdapat missing data
Identifikasi Peubah
y <- data$target
x1 <- data$age
x2 <- data$sex
x3 <- data$cp
x4 <- data$trestbps
x5 <- data$chol
x6 <- data$fbs
x7 <- data$restecg
x8 <- data$thalach
x9 <- data$exang
x10 <- data$oldpeak
x11 <- data$slope
x12 <- data$ca
x13 <- data$thalVariables Definition
Age : It defines the age of pasien yang bersangkutan
Sex : It tells us the gender of pasien pada data set
0 = female
1 = male
CP : It defines whether ada nyeri pada dada dan jenis nyerinya
0 = Tipe angina
1 = Tipe angina anomali
2 = Bukan tipe angine
3 = Tidak ada nyeri
Trestbps : It shows us the bear per second (Detak jantung) saat kondisi beristirahat.
Chol : Kandungan kolesterol dalam darah
fbs : Fasting blood sugar (Gula darah ketika berpuasa jika di atas 120 = 1, maka ada indikasi gula darah tidak normal, vice versa)
restecg: resting electrocardiographic results
Value 0: normal
Value 1: having ST-T wave abnormality (T wave inversions and/or ST elevation or depression of > 0.05 mV)
Value 2: showing probable or definite left ventricular hypertrophy by Estes’ criteria
thalach: maximum heart rate achieved
exang: exercise induced angina atau ada sakit gak setelah exercise (1 = yes; 0 = no)
oldpeak: ST depression induced by exercise relative to rest (Kemiringan garis pada hasil tes elektrokardiogram atau EGK saat istirahat setelah melakukan exercise)
slope: the slope of the peak exercise ST segment (Jenis kemiringan pada oldpeak, dilihat dari gradiennya)
Value 1: upsloping
Value 2: flat
Value 3: Downsloping
ca: number of major vessels (0–3) colored by fluoroscopy (Major vessel yang diberi warna oleh fluoroscopy memiliki masalah atau tidak normal)
thal:
0 = normal
1 = fixed defect
2 = reversable defect
ANALISIS REGRESI KLASIK
Model awal
model.awal <- lm(y~x1+x2+x3+x4+x5+x6+x7+x8+x9+x10+x11+x12+x13)
model.awal##
## Call:
## lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 +
## x10 + x11 + x12 + x13)
##
## Coefficients:
## (Intercept) x1 x2 x3 x4 x5
## 0.879266 -0.001430 -0.210721 0.111820 -0.001818 -0.000458
## x6 x7 x8 x9 x10 x11
## 0.004225 0.044308 0.002878 -0.144644 -0.061020 0.076220
## x12 x13
## -0.095612 -0.115237Diperoleh model awal:
\[y = 0.879266 - 0.001430x_1 - 0.210721x_2 + 0.111820x_3 - 0.001818x_4 - 0.000458x_5 + 0.004225x_6 + 0.044308x_7 + 0.002878x_8 - 0.144644x_9 - 0.061020x_{10} + 0.076220x_{11} - 0.095612x_{12} - 0.115237x_{13} \]
summary(model.awal)##
## Call:
## lm(formula = y ~ x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 + x9 +
## x10 + x11 + x12 + x13)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.92108 -0.21388 0.04493 0.26507 0.95158
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8792656 0.1578856 5.569 3.28e-08 ***
## x1 -0.0014296 0.0014432 -0.991 0.322151
## x2 -0.2107215 0.0255809 -8.237 5.40e-16 ***
## x3 0.1118197 0.0120981 9.243 < 2e-16 ***
## x4 -0.0018183 0.0006758 -2.691 0.007247 **
## x5 -0.0004580 0.0002273 -2.015 0.044173 *
## x6 0.0042250 0.0320768 0.132 0.895237
## x7 0.0443080 0.0214084 2.070 0.038739 *
## x8 0.0028781 0.0006051 4.756 2.26e-06 ***
## x9 -0.1446437 0.0275997 -5.241 1.95e-07 ***
## x10 -0.0610202 0.0121847 -5.008 6.49e-07 ***
## x11 0.0762203 0.0227286 3.354 0.000828 ***
## x12 -0.0956120 0.0116263 -8.224 6.02e-16 ***
## x13 -0.1152366 0.0188241 -6.122 1.32e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3505 on 1011 degrees of freedom
## Multiple R-squared: 0.5149, Adjusted R-squared: 0.5087
## F-statistic: 82.56 on 13 and 1011 DF, p-value: < 2.2e-16Diperoleh nilai p-value < 2.2e-16 < 0.05 dengan nilai R-squared 50.87%.. Diketahui peubah x1 dan x6 tidak berpengaruh signifikan terhadap perubah y.
Pencilan, Leverage, Amatan Berpengaruh
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
##
## riversols_plot_resid_lev(model.awal)
s <- sqrt(anova(model.awal)["Residuals", "Mean Sq"])
n = dim(data)[1]
p = length(model.awal$coefficients)
hii=hatvalues(model.awal)
Obs = c(1:n)
ei = model.awal$residuals
ri = ei/(s*sqrt(1-hii))
Di = (ri^2/p)*(hii/(1-hii))
summ <- cbind.data.frame(Obs, data, hii, ri, Di)Pendeteksian Pencilan
for (i in 1:dim(summ)[1]){
absri <- abs(summ$ri)
pencilan <- which(absri > 2)
}
pencilan <- as.vector(pencilan)
pencilan## [1] 23 39 43 112 221 266 359 362 365 392 430 457 505 522 529
## [16] 544 625 630 631 639 643 647 657 671 710 720 721 744 747 750
## [31] 760 779 806 832 844 855 862 865 875 897 914 919 925 938 939
## [46] 956 963 984 986 1004 1017Pendeteksian Titik Leverage
for (i in 1:dim(summ)[1]){
cutoff <- 2*p/n
titik_leverage <- which(hii > cutoff)
}
titik_leverage<-as.vector(titik_leverage)
titik_leverage## [1] 7 15 30 70 151 159 176 193 211 295 357 394 465 509 510
## [16] 527 570 588 610 662 683 687 689 709 735 794 894 928 968 987
## [31] 1014gabungan<-as.vector(sort(rbind(c(titik_leverage,pencilan))))
gabungan<-unique(gabungan)
gabungan## [1] 7 15 23 30 39 43 70 112 151 159 176 193 211 221 266
## [16] 295 357 359 362 365 392 394 430 457 465 505 509 510 522 527
## [31] 529 544 570 588 610 625 630 631 639 643 647 657 662 671 683
## [46] 687 689 709 710 720 721 735 744 747 750 760 779 794 806 832
## [61] 844 855 862 865 875 894 897 914 919 925 928 938 939 956 963
## [76] 968 984 986 987 1004 1014 1017Amatan Berpengaruh
DFFITS
u<-2/sqrt(p/n)
dfft<-dffits(model.awal)
dfftabs<-abs(dfft)
dffit<-which(dfftabs>u)
dffit<-as.vector(dffit)DFBETAS
s<-2/sqrt(n)
dfbt<-dfbetas(model.awal)
dfbtabs<-abs(dfbt)
dbts<-NULL
for(i in 1:ncol(dfbtabs)){
dfbts<-as.vector(which(dfbtabs[,1]>s))
dbts<-rbind(c(dbts,dfbts))
}
dbts<-as.vector(dbts)Jarak COOK
for (i in 1:dim(summ)[1]){
fcrit <- qf(0.95, p, n-p)
jarakcook <- which(Di > fcrit)
}
jarakcook <- as.vector(jarakcook)Diperoleh amatan berpengaruh:
gabungan_ab<-as.vector(rbind(c(dffit,jarakcook,dbts)))
gabungan_ab<-unique(gabungan_ab)
gabungan_ab## [1] 6 23 66 82 138 148 152 225 227 237 247 258 266 277 327
## [16] 350 392 415 422 430 457 460 487 505 529 601 625 630 631 639
## [31] 647 664 710 721 747 799 836 840 855 862 863 881 892 896 897
## [46] 899 902 914 938 950 952 962 1017 1019Pencilan/Leverage yang bukan Amatan Berpengaruh
dibuang<-NULL
k<-1
for(i in 1:length(gabungan)){
skor<-0
cek<-gabungan[i]
for(j in 1:length(gabungan_ab)){
if(cek != gabungan_ab[j]){
skor<- skor+1
if(skor==length(gabungan_ab)){
dibuang[k]<-cek
k<-k+1
}
}
}
}
dibuang<-unique(dibuang)
dibuang## [1] 7 15 30 39 43 70 112 151 159 176 193 211 221 295 357
## [16] 359 362 365 394 465 509 510 522 527 544 570 588 610 643 657
## [31] 662 671 683 687 689 709 720 735 744 750 760 779 794 806 832
## [46] 844 865 875 894 919 925 928 939 956 963 968 984 986 987 1004
## [61] 1014Data Baru
data.baru <- data[-c(7, 15, 30, 39, 43, 70, 112, 151, 159, 176, 193, 211, 221, 295, 357, 359, 362, 365, 394, 465, 509, 510, 522, 527, 544, 570, 588, 610, 643, 657, 662, 671, 683, 687, 689, 709, 720, 735, 744, 750, 760, 779, 794, 806, 832, 844, 865, 875, 894, 919, 925, 928, 939, 956, 963, 968, 984, 986, 987, 1004, 1014),]
head(data.baru)## age sex cp trestbps chol fbs restecg thalach exang oldpeak slope ca thal
## 1 52 1 0 125 212 0 1 168 0 1.0 2 2 3
## 2 53 1 0 140 203 1 0 155 1 3.1 0 0 3
## 3 70 1 0 145 174 0 1 125 1 2.6 0 0 3
## 4 61 1 0 148 203 0 1 161 0 0.0 2 1 3
## 5 62 0 0 138 294 1 1 106 0 1.9 1 3 2
## 6 58 0 0 100 248 0 0 122 0 1.0 1 0 2
## target
## 1 0
## 2 0
## 3 0
## 4 0
## 5 0
## 6 1y.baru <- data.baru$target
x1.baru <- data.baru$age
x2.baru <- data.baru$sex
x3.baru <- data.baru$cp
x4.baru <- data.baru$trestbps
x5.baru <- data.baru$chol
x6.baru <- data.baru$fbs
x7.baru <- data.baru$restecg
x8.baru <- data.baru$thalach
x9.baru <- data.baru$exang
x10.baru <- data.baru$oldpeak
x11.baru <- data.baru$slope
x12.baru <- data.baru$ca
x13.baru <- data.baru$thalModel Baru
Model setelah dilakukan penanganan pencilan, leverage, dan amatan berpengaruh
model.baru <- lm(y.baru ~ x1.baru+x2.baru+x3.baru+x4.baru+x5.baru+x6.baru+x7.baru+x8.baru+x9.baru+x10.baru+x11.baru+x12.baru+x13.baru)
model.baru##
## Call:
## lm(formula = y.baru ~ x1.baru + x2.baru + x3.baru + x4.baru +
## x5.baru + x6.baru + x7.baru + x8.baru + x9.baru + x10.baru +
## x11.baru + x12.baru + x13.baru)
##
## Coefficients:
## (Intercept) x1.baru x2.baru x3.baru x4.baru x5.baru
## 0.8196897 -0.0006504 -0.2105847 0.1094563 -0.0012237 -0.0004599
## x6.baru x7.baru x8.baru x9.baru x10.baru x11.baru
## -0.0048811 0.0305692 0.0032659 -0.1282687 -0.0472500 0.1036999
## x12.baru x13.baru
## -0.1186849 -0.1799735Diperoleh model baru:
\[y = 0.8196897 - 0.0006504x_1 - 0.2105847x_2 + 0.1094563x_3 - 0.0012237x_4 - 0.0004599x_5 - 0.0048811x_6 + 0.0305692x_7 + 0.0032659x_8 - 0.1282687x_9 - 0.0472500x_{10} + 0.1036999x_{11} - 0.1186849x_{12} - 0.1799735x_{13} \]
summary(model.baru)##
## Call:
## lm(formula = y.baru ~ x1.baru + x2.baru + x3.baru + x4.baru +
## x5.baru + x6.baru + x7.baru + x8.baru + x9.baru + x10.baru +
## x11.baru + x12.baru + x13.baru)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.92797 -0.20641 0.04604 0.23749 0.70771
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8196897 0.1507743 5.437 6.91e-08 ***
## x1.baru -0.0006504 0.0013598 -0.478 0.6325
## x2.baru -0.2105847 0.0246468 -8.544 < 2e-16 ***
## x3.baru 0.1094563 0.0116323 9.410 < 2e-16 ***
## x4.baru -0.0012237 0.0006721 -1.821 0.0689 .
## x5.baru -0.0004599 0.0002311 -1.990 0.0469 *
## x6.baru -0.0048811 0.0317004 -0.154 0.8777
## x7.baru 0.0305692 0.0212509 1.438 0.1506
## x8.baru 0.0032659 0.0006029 5.417 7.69e-08 ***
## x9.baru -0.1282687 0.0263021 -4.877 1.26e-06 ***
## x10.baru -0.0472500 0.0119915 -3.940 8.73e-05 ***
## x11.baru 0.1036999 0.0221807 4.675 3.36e-06 ***
## x12.baru -0.1186849 0.0115532 -10.273 < 2e-16 ***
## x13.baru -0.1799735 0.0189454 -9.500 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3237 on 950 degrees of freedom
## Multiple R-squared: 0.5864, Adjusted R-squared: 0.5807
## F-statistic: 103.6 on 13 and 950 DF, p-value: < 2.2e-16Diperoleh nilai p-value < 2.2e-16 < 0.05 dengan nilai R-squared 58.07%. Diketahui peubah x1, x4, x6 dan x7 tidak berpengaruh signifikan terhadap perubah y.
Multikolinearitas
vif(model.baru)## x1.baru x2.baru x3.baru x4.baru x5.baru x6.baru x7.baru x8.baru
## 1.447900 1.171099 1.306364 1.175918 1.156434 1.099799 1.097817 1.715542
## x9.baru x10.baru x11.baru x12.baru x13.baru
## 1.426921 1.655015 1.653244 1.205480 1.182393Tidak terddapat multikolinearitas (VIF < 10).
Pemilihan Peubah
ols_step_both_p(model.baru, details =TRUE)## Stepwise Selection Method
## ---------------------------
##
## Candidate Terms:
##
## 1. x1.baru
## 2. x2.baru
## 3. x3.baru
## 4. x4.baru
## 5. x5.baru
## 6. x6.baru
## 7. x7.baru
## 8. x8.baru
## 9. x9.baru
## 10. x10.baru
## 11. x11.baru
## 12. x12.baru
## 13. x13.baru
##
## We are selecting variables based on p value...
##
##
## Stepwise Selection: Step 1
##
## - x9.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.460 RMSE 0.444
## R-Squared 0.212 Coef. Var 85.435
## Adj. R-Squared 0.211 MSE 0.197
## Pred R-Squared 0.209 MAE 0.393
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 50.970 1 50.970 258.537 0.0000
## Residual 189.656 962 0.197
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.684 0.018 38.906 0.000 0.650 0.719
## x9.baru -0.486 0.030 -0.460 -16.079 0.000 -0.545 -0.426
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 2
##
## - x12.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.581 RMSE 0.407
## R-Squared 0.337 Coef. Var 78.374
## Adj. R-Squared 0.336 MSE 0.166
## Pred R-Squared 0.333 MAE 0.341
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 81.190 2 40.595 244.688 0.0000
## Residual 159.435 961 0.166
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.794 0.018 43.946 0.000 0.759 0.830
## x9.baru -0.428 0.028 -0.406 -15.265 0.000 -0.483 -0.373
## x12.baru -0.181 0.013 -0.359 -13.496 0.000 -0.207 -0.155
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.581 RMSE 0.407
## R-Squared 0.337 Coef. Var 78.374
## Adj. R-Squared 0.336 MSE 0.166
## Pred R-Squared 0.333 MAE 0.341
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 81.190 2 40.595 244.688 0.0000
## Residual 159.435 961 0.166
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.794 0.018 43.946 0.000 0.759 0.830
## x9.baru -0.428 0.028 -0.406 -15.265 0.000 -0.483 -0.373
## x12.baru -0.181 0.013 -0.359 -13.496 0.000 -0.207 -0.155
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 3
##
## - x13.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.652 RMSE 0.379
## R-Squared 0.426 Coef. Var 73.007
## Adj. R-Squared 0.424 MSE 0.144
## Pred R-Squared 0.420 MAE 0.312
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 102.422 3 34.141 237.152 0.0000
## Residual 138.203 960 0.144
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 1.356 0.049 27.552 0.000 1.259 1.452
## x9.baru -0.361 0.027 -0.342 -13.534 0.000 -0.414 -0.309
## x12.baru -0.163 0.013 -0.323 -12.956 0.000 -0.188 -0.138
## x13.baru -0.256 0.021 -0.307 -12.144 0.000 -0.298 -0.215
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.652 RMSE 0.379
## R-Squared 0.426 Coef. Var 73.007
## Adj. R-Squared 0.424 MSE 0.144
## Pred R-Squared 0.420 MAE 0.312
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 102.422 3 34.141 237.152 0.0000
## Residual 138.203 960 0.144
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 1.356 0.049 27.552 0.000 1.259 1.452
## x9.baru -0.361 0.027 -0.342 -13.534 0.000 -0.414 -0.309
## x12.baru -0.163 0.013 -0.323 -12.956 0.000 -0.188 -0.138
## x13.baru -0.256 0.021 -0.307 -12.144 0.000 -0.298 -0.215
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 4
##
## - x8.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.695 RMSE 0.360
## R-Squared 0.483 Coef. Var 69.332
## Adj. R-Squared 0.480 MSE 0.130
## Pred R-Squared 0.477 MAE 0.286
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 116.115 4 29.029 223.585 0.0000
## Residual 124.510 959 0.130
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.431 0.102 4.242 0.000 0.231 0.630
## x9.baru -0.262 0.027 -0.248 -9.639 0.000 -0.315 -0.208
## x12.baru -0.142 0.012 -0.281 -11.681 0.000 -0.165 -0.118
## x13.baru -0.253 0.020 -0.303 -12.605 0.000 -0.292 -0.213
## x8.baru 0.006 0.001 0.263 10.270 0.000 0.005 0.007
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.695 RMSE 0.360
## R-Squared 0.483 Coef. Var 69.332
## Adj. R-Squared 0.480 MSE 0.130
## Pred R-Squared 0.477 MAE 0.286
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 116.115 4 29.029 223.585 0.0000
## Residual 124.510 959 0.130
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.431 0.102 4.242 0.000 0.231 0.630
## x9.baru -0.262 0.027 -0.248 -9.639 0.000 -0.315 -0.208
## x12.baru -0.142 0.012 -0.281 -11.681 0.000 -0.165 -0.118
## x13.baru -0.253 0.020 -0.303 -12.605 0.000 -0.292 -0.213
## x8.baru 0.006 0.001 0.263 10.270 0.000 0.005 0.007
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 5
##
## - x3.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.717 RMSE 0.349
## R-Squared 0.514 Coef. Var 67.208
## Adj. R-Squared 0.512 MSE 0.122
## Pred R-Squared 0.508 MAE 0.275
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 123.748 5 24.750 202.863 0.0000
## Residual 116.878 958 0.122
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.381 0.099 3.863 0.000 0.187 0.574
## x9.baru -0.199 0.027 -0.189 -7.251 0.000 -0.253 -0.145
## x12.baru -0.133 0.012 -0.263 -11.262 0.000 -0.156 -0.110
## x13.baru -0.236 0.020 -0.283 -12.076 0.000 -0.274 -0.198
## x8.baru 0.005 0.001 0.230 9.138 0.000 0.004 0.006
## x3.baru 0.097 0.012 0.200 7.910 0.000 0.073 0.122
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.717 RMSE 0.349
## R-Squared 0.514 Coef. Var 67.208
## Adj. R-Squared 0.512 MSE 0.122
## Pred R-Squared 0.508 MAE 0.275
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 123.748 5 24.750 202.863 0.0000
## Residual 116.878 958 0.122
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.381 0.099 3.863 0.000 0.187 0.574
## x9.baru -0.199 0.027 -0.189 -7.251 0.000 -0.253 -0.145
## x12.baru -0.133 0.012 -0.263 -11.262 0.000 -0.156 -0.110
## x13.baru -0.236 0.020 -0.283 -12.076 0.000 -0.274 -0.198
## x8.baru 0.005 0.001 0.230 9.138 0.000 0.004 0.006
## x3.baru 0.097 0.012 0.200 7.910 0.000 0.073 0.122
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 6
##
## - x2.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.739 RMSE 0.338
## R-Squared 0.546 Coef. Var 64.988
## Adj. R-Squared 0.543 MSE 0.114
## Pred R-Squared 0.539 MAE 0.268
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 131.457 6 21.910 192.066 0.0000
## Residual 109.168 957 0.114
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.422 0.095 4.416 0.000 0.234 0.609
## x9.baru -0.176 0.027 -0.167 -6.604 0.000 -0.229 -0.124
## x12.baru -0.127 0.011 -0.251 -11.088 0.000 -0.149 -0.104
## x13.baru -0.204 0.019 -0.244 -10.552 0.000 -0.242 -0.166
## x8.baru 0.005 0.001 0.233 9.584 0.000 0.004 0.006
## x3.baru 0.101 0.012 0.206 8.453 0.000 0.077 0.124
## x2.baru -0.203 0.025 -0.186 -8.221 0.000 -0.251 -0.154
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.739 RMSE 0.338
## R-Squared 0.546 Coef. Var 64.988
## Adj. R-Squared 0.543 MSE 0.114
## Pred R-Squared 0.539 MAE 0.268
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 131.457 6 21.910 192.066 0.0000
## Residual 109.168 957 0.114
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.422 0.095 4.416 0.000 0.234 0.609
## x9.baru -0.176 0.027 -0.167 -6.604 0.000 -0.229 -0.124
## x12.baru -0.127 0.011 -0.251 -11.088 0.000 -0.149 -0.104
## x13.baru -0.204 0.019 -0.244 -10.552 0.000 -0.242 -0.166
## x8.baru 0.005 0.001 0.233 9.584 0.000 0.004 0.006
## x3.baru 0.101 0.012 0.206 8.453 0.000 0.077 0.124
## x2.baru -0.203 0.025 -0.186 -8.221 0.000 -0.251 -0.154
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 7
##
## - x11.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.756 RMSE 0.328
## R-Squared 0.572 Coef. Var 63.138
## Adj. R-Squared 0.569 MSE 0.108
## Pred R-Squared 0.565 MAE 0.261
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 137.692 7 19.670 182.69 0.0000
## Residual 102.933 956 0.108
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.430 0.093 4.641 0.000 0.248 0.612
## x9.baru -0.147 0.026 -0.140 -5.615 0.000 -0.199 -0.096
## x12.baru -0.134 0.011 -0.266 -12.022 0.000 -0.156 -0.112
## x13.baru -0.196 0.019 -0.235 -10.448 0.000 -0.233 -0.159
## x8.baru 0.003 0.001 0.158 6.172 0.000 0.002 0.005
## x3.baru 0.107 0.012 0.219 9.209 0.000 0.084 0.130
## x2.baru -0.203 0.024 -0.186 -8.470 0.000 -0.250 -0.156
## x11.baru 0.151 0.020 0.182 7.610 0.000 0.112 0.189
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.756 RMSE 0.328
## R-Squared 0.572 Coef. Var 63.138
## Adj. R-Squared 0.569 MSE 0.108
## Pred R-Squared 0.565 MAE 0.261
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 137.692 7 19.670 182.69 0.0000
## Residual 102.933 956 0.108
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.430 0.093 4.641 0.000 0.248 0.612
## x9.baru -0.147 0.026 -0.140 -5.615 0.000 -0.199 -0.096
## x12.baru -0.134 0.011 -0.266 -12.022 0.000 -0.156 -0.112
## x13.baru -0.196 0.019 -0.235 -10.448 0.000 -0.233 -0.159
## x8.baru 0.003 0.001 0.158 6.172 0.000 0.002 0.005
## x3.baru 0.107 0.012 0.219 9.209 0.000 0.084 0.130
## x2.baru -0.203 0.024 -0.186 -8.470 0.000 -0.250 -0.156
## x11.baru 0.151 0.020 0.182 7.610 0.000 0.112 0.189
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 8
##
## - x10.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.762 RMSE 0.325
## R-Squared 0.580 Coef. Var 62.588
## Adj. R-Squared 0.577 MSE 0.106
## Pred R-Squared 0.572 MAE 0.261
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 139.584 8 17.448 164.91 0.0000
## Residual 101.042 955 0.106
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.536 0.095 5.628 0.000 0.349 0.723
## x9.baru -0.133 0.026 -0.126 -5.054 0.000 -0.184 -0.081
## x12.baru -0.127 0.011 -0.252 -11.384 0.000 -0.149 -0.105
## x13.baru -0.184 0.019 -0.221 -9.793 0.000 -0.221 -0.147
## x8.baru 0.003 0.001 0.147 5.769 0.000 0.002 0.004
## x3.baru 0.108 0.012 0.222 9.403 0.000 0.086 0.131
## x2.baru -0.197 0.024 -0.180 -8.269 0.000 -0.243 -0.150
## x11.baru 0.108 0.022 0.130 4.871 0.000 0.064 0.151
## x10.baru -0.051 0.012 -0.113 -4.228 0.000 -0.074 -0.027
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.762 RMSE 0.325
## R-Squared 0.580 Coef. Var 62.588
## Adj. R-Squared 0.577 MSE 0.106
## Pred R-Squared 0.572 MAE 0.261
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 139.584 8 17.448 164.91 0.0000
## Residual 101.042 955 0.106
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.536 0.095 5.628 0.000 0.349 0.723
## x9.baru -0.133 0.026 -0.126 -5.054 0.000 -0.184 -0.081
## x12.baru -0.127 0.011 -0.252 -11.384 0.000 -0.149 -0.105
## x13.baru -0.184 0.019 -0.221 -9.793 0.000 -0.221 -0.147
## x8.baru 0.003 0.001 0.147 5.769 0.000 0.002 0.004
## x3.baru 0.108 0.012 0.222 9.403 0.000 0.086 0.131
## x2.baru -0.197 0.024 -0.180 -8.269 0.000 -0.243 -0.150
## x11.baru 0.108 0.022 0.130 4.871 0.000 0.064 0.151
## x10.baru -0.051 0.012 -0.113 -4.228 0.000 -0.074 -0.027
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 9
##
## - x5.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.764 RMSE 0.324
## R-Squared 0.583 Coef. Var 62.385
## Adj. R-Squared 0.579 MSE 0.105
## Pred R-Squared 0.574 MAE 0.262
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 140.343 9 15.594 148.345 0.0000
## Residual 100.282 954 0.105
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.673 0.108 6.246 0.000 0.462 0.884
## x9.baru -0.129 0.026 -0.122 -4.933 0.000 -0.180 -0.078
## x12.baru -0.124 0.011 -0.246 -11.070 0.000 -0.146 -0.102
## x13.baru -0.179 0.019 -0.214 -9.492 0.000 -0.216 -0.142
## x8.baru 0.003 0.001 0.148 5.814 0.000 0.002 0.004
## x3.baru 0.107 0.011 0.219 9.305 0.000 0.084 0.129
## x2.baru -0.211 0.024 -0.193 -8.685 0.000 -0.259 -0.163
## x11.baru 0.110 0.022 0.133 4.985 0.000 0.067 0.153
## x10.baru -0.050 0.012 -0.111 -4.158 0.000 -0.073 -0.026
## x5.baru -0.001 0.000 -0.058 -2.688 0.007 -0.001 0.000
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.764 RMSE 0.324
## R-Squared 0.583 Coef. Var 62.385
## Adj. R-Squared 0.579 MSE 0.105
## Pred R-Squared 0.574 MAE 0.262
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 140.343 9 15.594 148.345 0.0000
## Residual 100.282 954 0.105
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.673 0.108 6.246 0.000 0.462 0.884
## x9.baru -0.129 0.026 -0.122 -4.933 0.000 -0.180 -0.078
## x12.baru -0.124 0.011 -0.246 -11.070 0.000 -0.146 -0.102
## x13.baru -0.179 0.019 -0.214 -9.492 0.000 -0.216 -0.142
## x8.baru 0.003 0.001 0.148 5.814 0.000 0.002 0.004
## x3.baru 0.107 0.011 0.219 9.305 0.000 0.084 0.129
## x2.baru -0.211 0.024 -0.193 -8.685 0.000 -0.259 -0.163
## x11.baru 0.110 0.022 0.133 4.985 0.000 0.067 0.153
## x10.baru -0.050 0.012 -0.111 -4.158 0.000 -0.073 -0.026
## x5.baru -0.001 0.000 -0.058 -2.688 0.007 -0.001 0.000
## -----------------------------------------------------------------------------------------
##
##
##
## Stepwise Selection: Step 10
##
## - x4.baru added
##
## Model Summary
## --------------------------------------------------------------
## R 0.765 RMSE 0.324
## R-Squared 0.585 Coef. Var 62.261
## Adj. R-Squared 0.581 MSE 0.105
## Pred R-Squared 0.575 MAE 0.262
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 140.844 10 14.084 134.518 0.0000
## Residual 99.782 953 0.105
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.823 0.127 6.454 0.000 0.573 1.073
## x9.baru -0.128 0.026 -0.122 -4.909 0.000 -0.180 -0.077
## x12.baru -0.121 0.011 -0.241 -10.803 0.000 -0.143 -0.099
## x13.baru -0.177 0.019 -0.213 -9.418 0.000 -0.214 -0.140
## x8.baru 0.003 0.001 0.152 5.970 0.000 0.002 0.004
## x3.baru 0.109 0.012 0.224 9.497 0.000 0.087 0.132
## x2.baru -0.214 0.024 -0.196 -8.800 0.000 -0.261 -0.166
## x11.baru 0.107 0.022 0.129 4.857 0.000 0.064 0.150
## x10.baru -0.047 0.012 -0.106 -3.953 0.000 -0.071 -0.024
## x5.baru -0.001 0.000 -0.052 -2.379 0.018 -0.001 0.000
## x4.baru -0.001 0.001 -0.047 -2.186 0.029 -0.003 0.000
## -----------------------------------------------------------------------------------------
##
##
##
## Model Summary
## --------------------------------------------------------------
## R 0.765 RMSE 0.324
## R-Squared 0.585 Coef. Var 62.261
## Adj. R-Squared 0.581 MSE 0.105
## Pred R-Squared 0.575 MAE 0.262
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 140.844 10 14.084 134.518 0.0000
## Residual 99.782 953 0.105
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.823 0.127 6.454 0.000 0.573 1.073
## x9.baru -0.128 0.026 -0.122 -4.909 0.000 -0.180 -0.077
## x12.baru -0.121 0.011 -0.241 -10.803 0.000 -0.143 -0.099
## x13.baru -0.177 0.019 -0.213 -9.418 0.000 -0.214 -0.140
## x8.baru 0.003 0.001 0.152 5.970 0.000 0.002 0.004
## x3.baru 0.109 0.012 0.224 9.497 0.000 0.087 0.132
## x2.baru -0.214 0.024 -0.196 -8.800 0.000 -0.261 -0.166
## x11.baru 0.107 0.022 0.129 4.857 0.000 0.064 0.150
## x10.baru -0.047 0.012 -0.106 -3.953 0.000 -0.071 -0.024
## x5.baru -0.001 0.000 -0.052 -2.379 0.018 -0.001 0.000
## x4.baru -0.001 0.001 -0.047 -2.186 0.029 -0.003 0.000
## -----------------------------------------------------------------------------------------
##
##
##
## No more variables to be added/removed.
##
##
## Final Model Output
## ------------------
##
## Model Summary
## --------------------------------------------------------------
## R 0.765 RMSE 0.324
## R-Squared 0.585 Coef. Var 62.261
## Adj. R-Squared 0.581 MSE 0.105
## Pred R-Squared 0.575 MAE 0.262
## --------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ---------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ---------------------------------------------------------------------
## Regression 140.844 10 14.084 134.518 0.0000
## Residual 99.782 953 0.105
## Total 240.626 963
## ---------------------------------------------------------------------
##
## Parameter Estimates
## -----------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## -----------------------------------------------------------------------------------------
## (Intercept) 0.823 0.127 6.454 0.000 0.573 1.073
## x9.baru -0.128 0.026 -0.122 -4.909 0.000 -0.180 -0.077
## x12.baru -0.121 0.011 -0.241 -10.803 0.000 -0.143 -0.099
## x13.baru -0.177 0.019 -0.213 -9.418 0.000 -0.214 -0.140
## x8.baru 0.003 0.001 0.152 5.970 0.000 0.002 0.004
## x3.baru 0.109 0.012 0.224 9.497 0.000 0.087 0.132
## x2.baru -0.214 0.024 -0.196 -8.800 0.000 -0.261 -0.166
## x11.baru 0.107 0.022 0.129 4.857 0.000 0.064 0.150
## x10.baru -0.047 0.012 -0.106 -3.953 0.000 -0.071 -0.024
## x5.baru -0.001 0.000 -0.052 -2.379 0.018 -0.001 0.000
## x4.baru -0.001 0.001 -0.047 -2.186 0.029 -0.003 0.000
## -----------------------------------------------------------------------------------------##
## Stepwise Selection Summary
## ---------------------------------------------------------------------------------------
## Added/ Adj.
## Step Variable Removed R-Square R-Square C(p) AIC RMSE
## ---------------------------------------------------------------------------------------
## 1 x9.baru addition 0.212 0.211 850.4020 1174.3640 0.4440
## 2 x12.baru addition 0.337 0.336 563.9270 1009.0404 0.4073
## 3 x13.baru addition 0.426 0.424 363.2510 873.2726 0.3794
## 4 x8.baru addition 0.483 0.480 234.5410 774.6911 0.3603
## 5 x3.baru addition 0.514 0.512 163.6830 715.7084 0.3493
## 6 x2.baru addition 0.546 0.543 92.0890 651.9257 0.3377
## 7 x11.baru addition 0.572 0.569 34.5730 597.2344 0.3281
## 8 x10.baru addition 0.580 0.577 18.5170 581.3557 0.3253
## 9 x5.baru addition 0.583 0.579 13.2670 576.0818 0.3242
## 10 x4.baru addition 0.585 0.581 10.4890 573.2579 0.3236
## ---------------------------------------------------------------------------------------Hasil penyeleksian peubah pada model digambarkan oleh best subset dan stepwise bahwa mengeluarkan 3 peubah yaitu x1, x2, dan x7. Selanjutnya akan dibuat model tanpa peubah yang dikeluarkan tersebut.
Model Stepwise
model.stepwise <- lm(y.baru ~ x2.baru+x3.baru+x4.baru+x5.baru+x8.baru+x9.baru+x10.baru+x11.baru+x12.baru+x13.baru)
model.stepwise##
## Call:
## lm(formula = y.baru ~ x2.baru + x3.baru + x4.baru + x5.baru +
## x8.baru + x9.baru + x10.baru + x11.baru + x12.baru + x13.baru)
##
## Coefficients:
## (Intercept) x2.baru x3.baru x4.baru x5.baru x8.baru
## 0.822657 -0.213773 0.109360 -0.001403 -0.000536 0.003353
## x9.baru x10.baru x11.baru x12.baru x13.baru
## -0.128254 -0.047259 0.106986 -0.121362 -0.177478Diperoleh model hasil seleksi stepwise:
\[y = 0.822657 - 0.213773x_2 + 0.109360x_3 - 0.001403x_4 - 0.000536x_5 + 0.003353x_8 - 0.128254x_9 - 0.047259x_{10} + 0.106986x_{11} - 0.121362x_{12} - 0.177478x_{13} \]
summary(model.stepwise)##
## Call:
## lm(formula = y.baru ~ x2.baru + x3.baru + x4.baru + x5.baru +
## x8.baru + x9.baru + x10.baru + x11.baru + x12.baru + x13.baru)
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.91440 -0.20136 0.05301 0.24880 0.70236
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.8226570 0.1274632 6.454 1.73e-10 ***
## x2.baru -0.2137729 0.0242928 -8.800 < 2e-16 ***
## x3.baru 0.1093604 0.0115147 9.497 < 2e-16 ***
## x4.baru -0.0014034 0.0006419 -2.186 0.0290 *
## x5.baru -0.0005360 0.0002253 -2.379 0.0176 *
## x8.baru 0.0033526 0.0005616 5.970 3.35e-09 ***
## x9.baru -0.1282544 0.0261242 -4.909 1.07e-06 ***
## x10.baru -0.0472593 0.0119561 -3.953 8.30e-05 ***
## x11.baru 0.1069860 0.0220273 4.857 1.39e-06 ***
## x12.baru -0.1213620 0.0112337 -10.803 < 2e-16 ***
## x13.baru -0.1774780 0.0188442 -9.418 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.3236 on 953 degrees of freedom
## Multiple R-squared: 0.5853, Adjusted R-squared: 0.581
## F-statistic: 134.5 on 10 and 953 DF, p-value: < 2.2e-16Diperoleh nilai p-value < 2.2e-16 < 0.05 dengan nilai R-squared 58.1%. Semua peubah penjelas pada model ini berpengaruh signifikan terhadap peubah respon.
Uji Asumsi
Normalitas
H0 : Sisaan menyebar normal
H1 : Sisaan tidak menyebar normal
uji.normal<-function(x, object.name="x", graph=TRUE, graph.transformed=TRUE){
lapply(c("fitdistrplus", "kSamples", "rcompanion"), library, character.only=T)
if(any(x<0))x<-x-min(x)+1
mean <- fitdist(x, "norm")$estimate[1]; sd <- fitdist(x, "norm")$estimate[2]
uji<-ks.test(x, "pnorm", mean=mean, sd=sd)
uji1<- ad.test(x, rnorm(length(x), mean=mean, sd=sd))
pvalue<-uji$p.value
PVALUE1<-uji1$ad[1,3]
PVALUE2<-uji1$ad[2,3]
t<-transformTukey(x,quiet = TRUE,plotit = FALSE)
pt<-ks.test(t, "pnorm", mean=fitdist(t,"norm")$estimate[1],
sd=fitdist(t,"norm")$estimate[2])$p.value
lambda<-transformTukey(x,returnLambda =TRUE,quiet=TRUE,plotit = FALSE)
if(graph==TRUE){
if(graph.transformed==FALSE){
par(mfrow=c(1,2))
hist(x, freq=F, col="steelblue", border="white",
main=paste("Histogram of ",object.name),xlab=object.name)
lines(density(x),lwd=2, col="coral")
qqnorm(x,col="coral");qqline(x,col="steelblue",lwd=2)
}
else{
par(mfrow=c(2,2))
hist(x, freq=F, col="steelblue", border="white",
main=paste("Histogram of ",object.name),xlab=object.name)
lines(density(x),lwd=2, col="coral")
hist(t, main=paste("Histogram of ",object.name,"transformed"),
xlab=paste(object.name,"transformed"), freq=F,
col="steelblue",border = "white")
lines(density(t),lwd=2, col="coral")
qqnorm(x,col="coral");qqline(x,col="steelblue",lwd=2)
qqnorm(t, col="coral");qqline(t,col="steelblue", lwd=2)
}
}
z<-ifelse((PVALUE1>=0.05 & PVALUE2<0.05 ||PVALUE1<0.05 & PVALUE2>=0.05),
ifelse(pvalue>=0.05,
return(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Terima H0, data menyebar normal")),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Tolak H0, data tidak menyebar normal"),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal"))))),
ifelse(((pvalue >= 0.05)&(PVALUE1 >= 0.05||PVALUE2>= 0.05)),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Terima H0, data menyebar normal"),
`Hasil Uji Anderson`=
data.frame(`P-Value`=
rbind(`Versi 1`=PVALUE1, `Versi 2`=PVALUE2),
Keputusan=rep("Terima H0, data menyebar normal", 2)))),
ifelse((pvalue >= 0.05&(PVALUE1 < 0.05||PVALUE2 < 0.05)),
return(list(`Hasil Uji Kolmogorov Smirnov`= data.frame(`P-Value`=pvalue,
Keputusan="Terima H0, data menyebar normal"),
`Hasil Uji Anderson`=data.frame(`P-Value`=
rbind(`Versi 1`=PVALUE1,`Versi 2`=PVALUE2),
Keputusan= rep("Tolak H0, data tidak menyebar normal",2)),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=
data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal")))),
ifelse(pvalue < 0.05&(PVALUE1 >= 0.05||PVALUE2 >= 0.05),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Tolak H0, data tidak menyebar normal"),
`Hasil Uji Anderson`=data.frame(`P-Value`= rbind(`Versi 1`=PVALUE1,`Versi 2`=PVALUE2),
Keputusan=rep("Terima H0, data menyebar normal",2)),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal")))),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Tolak H0, data tidak menyebar normal"),
`Hasil Uji Anderson`=data.frame(`P-Value`=rbind(`Versi 1`=PVALUE1,
`Versi 2`=PVALUE2),
Keputusan=rep("Tolak H0, data tidak menyebar normal",2)),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal"))))))))
return(z)
}
uji.normal1<-function(x, object.name="x", graph=TRUE, graph.transformed=TRUE){
lapply(c("fitdistrplus", "kSamples", "rcompanion"), library, character.only=T)
if(any(x<0))x<-x-min(x)+1
mean <- mean(x); sd <- sd(x)
uji<-ks.test(x, "pnorm", mean=mean, sd=sd)
uji1<- ad.test(x, rnorm(length(x), mean=mean, sd=sd))
pvalue<-uji$p.value
PVALUE1<-uji1$ad[1,3]
PVALUE2<-uji1$ad[2,3]
t<-transformTukey(x,quiet = TRUE,plotit = FALSE)
pt<-ks.test(t, "pnorm", mean=mean(t),
sd=sd(t))$p.value
lambda<-transformTukey(x,returnLambda =TRUE,quiet=TRUE,plotit = FALSE)
if(graph==TRUE){
if(graph.transformed==FALSE){
par(mfrow=c(1,2))
hist(x, freq=F, col="steelblue", border="white",
main=paste("Histogram of ",object.name),xlab=object.name)
lines(density(x),lwd=2, col="coral")
qqnorm(x,col="coral");qqline(x,col="steelblue",lwd=2)
}
else{
par(mfrow=c(2,2))
hist(x, freq=F, col="steelblue", border="white",
main=paste("Histogram of ",object.name),xlab=object.name)
lines(density(x),lwd=2, col="coral")
hist(t, main=paste("Histogram of ",object.name,"transformed"),
xlab=paste(object.name,"transformed"), freq=F,
col="steelblue",border = "white")
lines(density(t),lwd=2, col="coral")
qqnorm(x,col="coral");qqline(x,col="steelblue",lwd=2)
qqnorm(t, col="coral");qqline(t,col="steelblue", lwd=2)
}
}
z<-ifelse((PVALUE1>=0.05 & PVALUE2<0.05 ||PVALUE1<0.05 & PVALUE2>=0.05),
ifelse(pvalue>=0.05,
return(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Terima H0, data menyebar normal")),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Tolak H0, data tidak menyebar normal"),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal"))))),
ifelse(((pvalue >= 0.05)&(PVALUE1 >= 0.05||PVALUE2>= 0.05)),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Terima H0, data menyebar normal"),
`Hasil Uji Anderson`=
data.frame(`P-Value`=
rbind(`Versi 1`=PVALUE1, `Versi 2`=PVALUE2),
Keputusan=rep("Terima H0, data menyebar normal", 2)))),
ifelse((pvalue >= 0.05&(PVALUE1 < 0.05||PVALUE2 < 0.05)),
return(list(`Hasil Uji Kolmogorov Smirnov`= data.frame(`P-Value`=pvalue,
Keputusan="Terima H0, data menyebar normal"),
`Hasil Uji Anderson`=data.frame(`P-Value`=
rbind(`Versi 1`=PVALUE1,`Versi 2`=PVALUE2),
Keputusan= rep("Tolak H0, data tidak menyebar normal",2)),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=
data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal")))),
ifelse(pvalue < 0.05&(PVALUE1 >= 0.05||PVALUE2 >= 0.05),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Tolak H0, data tidak menyebar normal"),
`Hasil Uji Anderson`=data.frame(`P-Value`= rbind(`Versi 1`=PVALUE1,`Versi 2`=PVALUE2),
Keputusan=rep("Terima H0, data menyebar normal",2)),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal")))),
return(list(`Hasil Uji Kolmogorov Smirnov`=data.frame(`P-Value`=pvalue,
Keputusan="Tolak H0, data tidak menyebar normal"),
`Hasil Uji Anderson`=data.frame(`P-Value`=rbind(`Versi 1`=PVALUE1,
`Versi 2`=PVALUE2),
Keputusan=rep("Tolak H0, data tidak menyebar normal",2)),
`lambda transformasi`=lambda,
`Data Hasil Transformasi Tukey`= t,
`Setelah transformasi~Uji Kolmogorov-Smirnov`=data.frame(`P-Value`=pt,
`Keputusan`=ifelse(pt>=0.05,
"Terima H0, data menyebar normal",
"Tolak H0, data tidak menyebar normal"))))))))
return(z)
}
uji.normal(model.stepwise$residuals,"residuals",graph.transformed = F)## Loading required package: MASS##
## Attaching package: 'MASS'## The following object is masked from 'package:olsrr':
##
## cement## Loading required package: survival## Loading required package: SuppDists## Warning in ks.test.default(x, "pnorm", mean = mean, sd = sd): ties should not
## be present for the Kolmogorov-Smirnov test## Warning in ks.test.default(t, "pnorm", mean = fitdist(t, "norm")$estimate[1], :
## ties should not be present for the Kolmogorov-Smirnov test
## $`Hasil Uji Kolmogorov Smirnov`
## P.Value Keputusan
## 1 7.003125e-05 Tolak H0, data tidak menyebar normal
##
## $`Hasil Uji Anderson`
## P.Value Keputusan
## Versi 1 0.011966 Tolak H0, data tidak menyebar normal
## Versi 2 0.012389 Tolak H0, data tidak menyebar normal
##
## $`lambda transformasi`
## lambda
## 2.1
##
## $`Data Hasil Transformasi Tukey`
## 1 2 3 4 5 6 7 8
## 2.825218 3.842257 4.138848 2.416141 3.394072 5.496406 3.899300 2.280837
## 9 10 11 12 13 14 15 16
## 4.338133 5.404912 3.044838 3.399823 6.117575 3.399823 4.710552 4.449444
## 17 18 19 20 21 22 23 24
## 3.984218 4.216169 1.604555 5.654608 7.346630 3.285161 3.522610 2.583019
## 25 26 27 28 29 30 31 32
## 4.665274 1.513965 1.676180 2.408508 3.984218 3.868065 3.815985 4.141673
## 33 34 35 36 37 38 39 40
## 1.867507 5.774271 5.114122 2.188416 4.122570 5.988313 2.280837 4.251644
## 41 42 43 44 45 46 47 48
## 5.075186 4.856527 3.255376 4.686524 3.485172 3.320862 2.572362 6.401417
## 49 50 51 52 53 54 55 56
## 3.332805 5.095641 5.095641 5.344676 5.058096 1.949157 1.595488 4.072576
## 57 58 59 60 61 62 63 64
## 4.686524 3.633571 4.755249 4.072576 1.657985 5.628903 2.442453 3.152761
## 65 66 67 68 69 70 71 72
## 4.612186 3.468940 2.994765 2.760630 3.483327 4.451654 5.209612 4.277782
## 73 74 75 76 77 78 79 80
## 5.553832 5.553832 2.140751 2.190671 1.867507 6.401417 3.152761 4.531596
## 81 82 83 84 85 86 87 88
## 4.216169 1.925675 2.910850 4.140749 3.234114 4.163358 4.277782 2.408508
## 89 90 91 92 93 94 95 96
## 5.033715 5.686621 5.054150 5.245732 1.728469 4.684075 3.692119 5.409094
## 97 98 99 100 101 102 103 104
## 5.795788 4.451654 2.958708 3.264194 2.699381 3.367698 1.878040 3.069414
## 105 106 107 108 109 110 111 112
## 1.556224 3.483327 4.183637 1.536774 2.583019 3.216439 3.591637 4.072576
## 113 114 115 116 117 118 119 120
## 4.847755 5.795788 2.408508 4.810856 4.593344 4.238259 3.096781 6.267365
## 121 122 123 124 125 126 127 128
## 5.628903 6.620695 5.227656 3.096781 3.671784 4.856527 4.141673 5.795788
## 129 130 131 132 133 134 135 136
## 2.460203 4.251644 5.600864 4.451654 4.771164 4.761255 1.711550 2.083291
## 137 138 139 140 141 142 143 144
## 3.429028 5.430512 3.498291 3.608874 1.851350 5.418027 4.224940 2.037325
## 145 146 147 148 149 150 151 152
## 2.788617 5.988313 4.836321 5.795788 5.220552 5.988313 4.195467 3.177239
## 153 154 155 156 157 158 159 160
## 5.747597 3.177239 2.405696 2.994765 4.612186 2.886844 5.242137 5.475266
## 161 162 163 164 165 166 167 168
## 4.335114 5.681443 4.426142 5.653166 2.871335 4.166267 4.426142 4.253283
## 169 170 171 172 173 174 175 176
## 1.556224 3.774603 4.277782 5.354837 3.492446 4.304280 4.806439 4.811851
## 177 178 179 180 181 182 183 184
## 3.498291 2.994765 3.216439 2.780679 3.929925 5.588177 5.553214 4.905199
## 185 186 187 188 189 190 191 192
## 4.755249 2.319630 4.878890 3.902881 3.390674 4.163358 3.429028 5.418027
## 193 194 195 196 197 198 199 200
## 5.602642 4.686524 4.944902 1.536774 3.929925 6.401417 3.367698 3.633571
## 201 202 203 204 205 206 207 208
## 3.299167 5.475266 4.806439 4.831798 3.783557 4.195467 4.979854 4.338133
## 209 210 211 212 213 214 215 216
## 3.216439 5.354837 2.871335 5.684293 5.554685 2.190671 4.525950 4.331234
## 217 218 219 220 221 222 223 224
## 3.255376 2.788617 4.622727 4.082223 3.925161 4.345282 5.602642 2.190671
## 225 226 227 228 229 230 231 232
## 1.936919 3.485172 1.904785 5.135293 1.949157 6.401417 1.604555 5.229079
## 233 234 235 236 237 238 239 240
## 4.317218 2.037325 4.979854 3.947763 4.304280 3.264194 4.335114 4.149644
## 241 242 243 244 245 246 247 248
## 4.811851 3.330906 5.633173 4.199687 5.600864 2.005166 6.267365 4.068335
## 249 250 251 252 253 254 255 256
## 5.554685 4.812195 4.251644 2.460203 7.346630 5.245732 2.892079 2.424284
## 257 258 259 260 261 262 263 264
## 4.268858 6.024135 5.459415 3.947763 3.069414 5.550852 4.426142 6.764856
## 265 266 267 268 269 270 271 272
## 4.317218 3.899300 3.999631 4.196988 4.413725 3.869208 5.354837 2.424284
## 273 274 275 276 277 278 279 280
## 4.268858 4.841697 5.379491 3.388250 1.878040 6.620695 4.875619 6.241610
## 281 282 283 284 285 286 287 288
## 4.755249 3.633571 2.892079 3.329327 4.413725 4.809455 3.449885 6.243980
## 289 290 291 292 293 294 295 296
## 4.251644 4.810856 3.660555 5.071593 4.525950 4.531596 1.536774 4.907264
## 297 298 299 300 301 302 303 304
## 4.238259 3.483327 3.815985 5.693779 5.220552 4.944902 4.841697 3.285161
## 305 306 307 308 309 310 311 312
## 2.760630 2.574886 5.252781 3.795430 4.727722 3.096935 5.058096 4.907264
## 313 314 315 316 317 318 319 320
## 2.037325 2.814923 4.380324 2.574886 3.152761 2.425601 5.731995 4.003961
## 321 322 323 324 325 326 327 328
## 4.588102 3.329327 5.409094 6.280962 1.676180 3.336831 6.401417 4.068335
## 329 330 331 332 333 334 335 336
## 3.923460 5.407552 4.195467 3.096935 3.299167 3.234114 5.175330 2.261046
## 337 338 339 340 341 342 343 344
## 6.267365 3.390674 4.183637 6.368887 1.936919 5.656911 4.905199 2.574886
## 345 346 347 348 349 350 351 352
## 4.812195 3.692119 5.887695 5.887695 2.274866 2.309547 6.445090 4.711438
## 353 354 355 356 357 358 359 360
## 3.044838 4.149644 4.003961 1.772720 5.138263 5.550852 5.390706 7.514827
## 361 362 363 364 365 366 367 368
## 2.892079 2.958708 3.920133 2.424284 3.613683 3.329327 2.534709 4.711438
## 369 370 371 372 373 374 375 376
## 3.522610 3.177239 4.253283 4.698027 1.513965 1.771359 4.711438 4.836321
## 377 378 379 380 381 382 383 384
## 4.686524 2.728120 3.498291 5.550852 4.698027 3.332805 5.404912 5.276986
## 385 386 387 388 389 390 391 392
## 3.449885 3.468940 1.676180 4.216169 2.319630 5.656911 1.867507 3.999631
## 393 394 395 396 397 398 399 400
## 2.994765 2.814923 4.380324 1.657985 3.869208 6.280962 6.620695 4.163358
## 401 402 403 404 405 406 407 408
## 4.122570 5.054150 5.460654 5.242137 1.513965 4.727722 2.585569 3.939963
## 409 410 411 412 413 414 415 416
## 4.380367 5.175330 1.000000 1.949157 3.754003 3.902881 5.731995 3.707926
## 417 418 419 420 421 422 423 424
## 5.242137 1.925675 4.671534 4.046382 1.772720 1.904785 3.492446 4.761255
## 425 426 427 428 429 430 431 432
## 4.380367 4.046382 4.331234 5.887695 3.899300 3.608874 1.768468 4.209482
## 433 434 435 436 437 438 439 440
## 4.380097 3.255376 4.380097 3.754003 5.553214 1.000000 3.947763 5.681443
## 441 442 443 444 445 446 447 448
## 5.684293 3.492475 5.209612 2.958708 6.024135 6.401417 4.317218 3.264194
## 449 450 451 452 453 454 455 456
## 6.241610 4.905199 3.096781 4.841697 5.321972 5.054767 2.309547 5.409094
## 457 458 459 460 461 462 463 464
## 4.811851 2.188416 4.224940 5.154903 2.585569 4.209482 6.117575 4.413725
## 465 466 467 468 469 470 471 472
## 1.728469 3.367698 1.851350 3.783557 5.135293 6.241610 5.054150 4.380367
## 473 474 475 476 477 478 479 480
## 2.780679 4.149644 5.229079 7.021804 2.728120 1.595488 5.704308 5.138263
## 481 482 483 484 485 486 487 488
## 5.404912 4.199687 5.138263 4.196988 1.000000 4.525950 4.238259 3.869208
## 489 490 491 492 493 494 495 496
## 5.135293 3.591637 1.929616 3.069414 4.531596 3.332805 4.588102 3.999631
## 497 498 499 500 501 502 503 504
## 3.332805 2.416141 2.760630 3.937095 2.416141 2.274866 3.671784 4.163358
## 505 506 507 508 509 510 511 512
## 7.538828 5.553214 3.067221 3.923460 1.711550 4.356740 3.234114 4.684075
## 513 514 515 516 517 518 519 520
## 4.076899 4.809455 2.280837 5.602642 4.875619 4.050899 5.633173 6.280962
## 521 522 523 524 525 526 527 528
## 2.309547 4.380324 5.654608 3.608874 6.186807 3.492475 4.338133 3.044838
## 529 530 531 532 533 534 535 536
## 5.628903 2.319630 3.231919 2.760630 4.812195 2.871335 2.892079 5.321972
## 537 538 539 540 541 542 543 544
## 3.923460 3.522610 1.929616 2.886844 4.356740 4.243020 5.054767 3.939963
## 545 546 547 548 549 550 551 552
## 3.422010 4.810856 3.429028 1.929616 4.082223 5.681443 5.418027 4.380324
## 553 554 555 556 557 558 559 560
## 5.633173 3.920133 5.433663 4.050899 4.943371 3.591637 4.149644 5.220552
## 561 562 563 564 565 566 567 568
## 2.780679 2.583019 4.338133 5.693779 2.425601 3.815985 2.425601 2.640530
## 569 570 571 572 573 574 575 576
## 2.416141 5.390706 6.401417 1.772720 4.594136 2.261046 4.979854 3.388250
## 577 578 579 580 581 582 583 584
## 4.594136 4.046382 4.268858 2.439625 2.442453 2.640530 3.044838 3.104255
## 585 586 587 588 589 590 591 592
## 2.460203 5.095641 2.585569 4.076899 5.893069 3.925161 4.831798 1.728469
## 593 594 595 596 597 598 599 600
## 4.761255 3.483327 3.394072 2.083291 7.538828 3.492475 2.424284 2.005166
## 601 602 603 604 605 606 607 608
## 4.518854 1.401568 1.771359 4.831798 4.196988 3.585372 2.825218 5.252781
## 609 610 611 612 613 614 615 616
## 1.925675 3.388250 1.401568 5.321972 5.656911 3.774603 6.491151 4.068335
## 617 618 619 620 621 622 623 624
## 3.299167 1.000000 7.514827 5.404912 4.196988 5.071593 4.195467 5.191890
## 625 626 627 628 629 630 631 632
## 4.426142 3.925161 4.771164 3.947763 2.780679 5.114122 3.585372 5.430512
## 633 634 635 636 637 638 639 640
## 5.496406 5.191890 4.593344 4.413725 1.936919 4.072576 3.096935 2.825218
## 641 642 643 644 645 646 647 648
## 6.186807 5.988313 4.836321 2.319630 3.336831 3.216439 3.707926 2.728120
## 649 650 651 652 653 654 655 656
## 4.847755 4.612186 3.591637 1.604555 4.209482 2.788617 3.422010 6.445090
## 657 658 659 660 661 662 663 664
## 4.656121 3.842257 4.594136 2.687766 2.534709 4.076899 1.949157 2.439625
## 665 666 667 668 669 670 671 672
## 2.534709 5.054767 3.330906 5.379491 6.368887 6.243980 5.154903 2.188416
## 673 674 675 676 677 678 679 680
## 4.907264 1.771359 5.588177 3.330906 4.335114 5.191890 5.774271 5.276986
## 681 682 683 684 685 686 687 688
## 3.104255 1.676180 4.656121 1.161979 4.878890 3.937095 4.692053 5.693779
## 689 690 691 692 693 694 695 696
## 3.067221 2.405696 5.588177 4.979854 4.656121 4.531596 1.768468 6.243980
## 697 698 699 700 701 702 703 704
## 3.395344 4.141673 3.613683 4.671534 2.788617 2.862827 4.050899 3.707926
## 705 706 707 708 709 710 711 712
## 4.836321 3.902881 5.747597 1.161979 3.485172 4.068335 4.943371 4.122570
## 713 714 715 716 717 718 719 720
## 5.058096 6.491151 3.671784 5.209612 4.253283 5.550852 3.449885 2.814923
## 721 722 723 724 725 726 727 728
## 4.345282 5.588177 3.320862 4.277782 4.183637 4.183637 4.140749 5.433663
## 729 730 731 732 733 734 735 736
## 4.268858 4.856527 5.686621 1.904785 3.754003 3.795430 5.747597 2.583019
## 737 738 739 740 741 742 743 744
## 5.245732 3.399823 2.408508 3.920133 7.514827 5.653166 5.554685 3.899300
## 745 746 747 748 749 750 751 752
## 3.231919 6.117575 3.394072 3.367698 4.166267 4.166267 4.140749 2.083291
## 753 754 755 756 757 758 759 760
## 5.033715 4.856527 3.754003 1.657985 5.893069 4.671534 4.698027 1.711550
## 761 762 763 764 765 766 767 768
## 1.768468 5.321972 2.814923 4.665274 6.243980 4.003961 3.498291 1.936919
## 769 770 771 772 773 774 775 776
## 2.910850 3.842257 5.033715 6.445090 5.276986 4.878890 4.944902 2.460203
## 777 778 779 780 781 782 783 784
## 3.468940 2.910850 3.336831 5.704308 3.585372 3.285161 4.304280 2.188416
## 785 786 787 788 789 790 791 792
## 4.665274 4.449444 5.747597 6.186807 5.095641 2.442453 2.190671 4.356740
## 793 794 795 796 797 798 799 800
## 5.407552 5.774271 5.684293 4.138848 4.199687 2.274866 3.492446 2.886844
## 801 802 803 804 805 806 807 808
## 4.199687 3.585372 3.320862 2.862827 1.772720 5.731995 2.862827 4.671534
## 809 810 811 812 813 814 815 816
## 1.401568 5.433663 4.692053 5.893069 4.692053 2.699381 1.768468 1.161979
## 817 818 819 820 821 822 823 824
## 1.657985 2.825218 3.096781 3.929925 4.771164 5.653166 4.622727 3.795430
## 825 826 827 828 829 830 831 832
## 4.224940 5.602642 5.227656 4.588102 3.468940 3.692119 3.471615 5.114122
## 833 834 835 836 837 838 839 840
## 6.764856 1.595488 3.868065 2.405696 4.138848 4.811851 4.238259 6.368887
## 841 842 843 844 845 846 847 848
## 3.067221 4.209482 3.104255 5.600864 4.166267 2.699381 2.261046 7.538828
## 849 850 851 852 853 854 855 856
## 5.553832 5.460654 7.021804 2.083291 5.460654 2.910850 1.536774 4.943371
## 857 858 859 860 861 862 863 864
## 4.253283 5.075186 3.984218 5.071593 3.390674 2.140751 1.513965 3.330906
## 865 866 867 868 869 870 871 872
## 7.346630 2.439625 2.280837 3.783557 4.046382 2.005166 2.687766 3.920133
## 873 874 875 876 877 878 879 880
## 5.459415 5.704308 3.868065 3.069414 4.449444 4.588102 3.783557 1.878040
## 881 882 883 884 885 886 887 888
## 4.710552 2.005166 4.304280 5.653166 5.475266 1.161979 4.380097 2.572362
## 889 890 891 892 893 894 895 896
## 3.660555 4.518854 6.491151 3.255376 5.344676 3.937095 3.939963 4.138848
## 897 898 899 900 901 902 903 904
## 6.764856 4.905199 2.261046 3.422010 5.686621 5.252781 4.345282 2.140751
## 905 906 907 908 909 910 911 912
## 4.593344 4.518854 3.660555 5.496406 2.572362 3.395344 4.684075 4.875619
## 913 914 915 916 917 918 919 920
## 3.842257 4.809455 6.401417 5.407552 2.958708 5.229079 6.024135 2.687766
## 921 922 923 924 925 926 927 928
## 2.425601 4.331234 1.556224 4.727722 5.227656 2.687766 5.654608 7.021804
## 929 930 931 932 933 934 935 936
## 1.595488 3.492446 5.379491 4.622727 3.485172 4.243020 5.175330 3.613683
## 937 938 939 940 941 942 943 944
## 5.459415 3.774603 3.471615 2.442453 3.231919 2.640530 5.075186 2.439625
## 945 946 947 948 949 950 951 952
## 4.710552 3.104255 4.216169 5.344676 4.847755 1.878040 2.699381 4.806439
## 953 954 955 956 957 958 959 960
## 2.309547 3.395344 5.154903 1.401568 5.245732 1.851350 5.430512 5.390706
## 961 962 963 964
## 4.082223 3.264194 4.243020 3.471615
##
## $`Setelah transformasi~Uji Kolmogorov-Smirnov`
## P.Value Keputusan
## 1 0.0740086 Terima H0, data menyebar normalHasil menunjukkan bahwa p-value > α=5% sehingga tak tolak H0 atau tidak cukup bukti untuk menyatakan bahwa sisaan tidak menyebar normal. Dengan kata lain, asumsi normalitas sisaan terpenuhi.
Homoskedastisitas dan Non-Autokorelasi
par(mfrow=c(1,2))
plot(model.stepwise,c(1,3))
gqtest(model.stepwise)##
## Goldfeld-Quandt test
##
## data: model.stepwise
## GQ = 1.0619, df1 = 471, df2 = 471, p-value = 0.2573
## alternative hypothesis: variance increases from segment 1 to 2bgtest(model.stepwise)##
## Breusch-Godfrey test for serial correlation of order up to 1
##
## data: model.stepwise
## LM test = 0.029058, df = 1, p-value = 0.8646Homoskedastisitas dan non-autokorelasi pada sisaan terpenuhi (p-value > 0,05)
REGRESI RIDGE
lapply(c("glmnet","lmridge"),library,character.only=T)[[1]]## Loading required package: Matrix## Loaded glmnet 4.1-8##
## Attaching package: 'lmridge'## The following object is masked from 'package:car':
##
## vif## [1] "glmnet" "Matrix" "rcompanion" "kSamples" "SuppDists"
## [6] "fitdistrplus" "survival" "MASS" "olsrr" "lmtest"
## [11] "zoo" "car" "carData" "stats" "graphics"
## [16] "grDevices" "utils" "datasets" "methods" "base"Pakai glmnet
x <- cbind(x1.baru,x2.baru,x3.baru,x4.baru,x5.baru,x6.baru,x7.baru,x8.baru,x9.baru,x10.baru,x11.baru,x12.baru,x13.baru)
head(x)## x1.baru x2.baru x3.baru x4.baru x5.baru x6.baru x7.baru x8.baru x9.baru
## [1,] 52 1 0 125 212 0 1 168 0
## [2,] 53 1 0 140 203 1 0 155 1
## [3,] 70 1 0 145 174 0 1 125 1
## [4,] 61 1 0 148 203 0 1 161 0
## [5,] 62 0 0 138 294 1 1 106 0
## [6,] 58 0 0 100 248 0 0 122 0
## x10.baru x11.baru x12.baru x13.baru
## [1,] 1.0 2 2 3
## [2,] 3.1 0 0 3
## [3,] 2.6 0 0 3
## [4,] 0.0 2 1 3
## [5,] 1.9 1 3 2
## [6,] 1.0 1 0 2y <- y.baru
head(y)## [1] 0 0 0 0 0 1library(glmnet)
cv.r<-cv.glmnet(x,y,alpha=0);plot(cv.r)
best.lr <- cv.r$lambda.min
ridge1 <- glmnet(x,y,alpha=0,lambda=best.lr)
coef(ridge1)## 14 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 0.8185968424
## x1.baru -0.0009311693
## x2.baru -0.2015610981
## x3.baru 0.1049972989
## x4.baru -0.0011383153
## x5.baru -0.0004369786
## x6.baru -0.0055399043
## x7.baru 0.0315308584
## x8.baru 0.0031880599
## x9.baru -0.1308416008
## x10.baru -0.0486776293
## x11.baru 0.0983858906
## x12.baru -0.1131000466
## x13.baru -0.1737622899Diperoleh model:
\[y = 0.8185968424 - 0.0009311693x_1 - 0.2015610981x_2 + 0.1049972989x_3 - 0.0011383153x_4 - 0.0004369786x_5 - 0.0055399043x_6 + 0.0315308584x_7 + 0.0031880599x_8 - 0.1308416008x_9 - 0.0486776293x_{10} + 0.0983858906x_{11} - 0.1131000466x_{12} - 0.1737622899x_{13} \]
#Fungsi R-squared
rsq<-function(bestmodel,bestlambda,x,y){
#y duga
y.duga <- predict(bestmodel, s = bestlambda, newx = x)
#JKG dan JKT
jkt <- sum((y - mean(y))^2)
jkg <- sum((y.duga- y)^2)
#find R-Squared
rsq <- 1 - jkg/jkt
return(rsq)
}
rsq(ridge1,best.lr,x,y)## [1] 0.585907Diperoleh nilai R-squared 58,59%.
Pakai lmridge
dataridge <- cbind.data.frame(y.baru,x1.baru,x2.baru,x3.baru,x4.baru,x5.baru,x6.baru,x7.baru,x8.baru,x9.baru,x10.baru,x11.baru,x12.baru,x13.baru)
head(dataridge)## y.baru x1.baru x2.baru x3.baru x4.baru x5.baru x6.baru x7.baru x8.baru
## 1 0 52 1 0 125 212 0 1 168
## 2 0 53 1 0 140 203 1 0 155
## 3 0 70 1 0 145 174 0 1 125
## 4 0 61 1 0 148 203 0 1 161
## 5 0 62 0 0 138 294 1 1 106
## 6 1 58 0 0 100 248 0 0 122
## x9.baru x10.baru x11.baru x12.baru x13.baru
## 1 0 1.0 2 2 3
## 2 1 3.1 0 0 3
## 3 1 2.6 0 0 3
## 4 0 0.0 2 1 3
## 5 0 1.9 1 3 2
## 6 0 1.0 1 0 2library(lmridge)
ridge2 <- lmridge(y.baru ~ x1.baru+x2.baru+x3.baru+x4.baru+x5.baru+x6.baru+x7.baru+x8.baru+x9.baru+x10.baru+x11.baru+x12.baru+x13.baru,dataridge,scaling="centered")
plot(ridge2)
vif(ridge2)## x1.baru x2.baru x3.baru x4.baru x5.baru x6.baru x7.baru x8.baru x9.baru
## k=0 2e-05 0.0058 0.00129 0 0 0.00959 0.00431 0 0.0066
## x10.baru x11.baru x12.baru x13.baru
## k=0 0.00137 0.0047 0.00127 0.00343summary(ridge2)##
## Call:
## lmridge.default(formula = y.baru ~ x1.baru + x2.baru + x3.baru +
## x4.baru + x5.baru + x6.baru + x7.baru + x8.baru + x9.baru +
## x10.baru + x11.baru + x12.baru + x13.baru, data = dataridge,
## scaling = "centered")
##
##
## Coefficients: for Ridge parameter K= 0
## Estimate Estimate (Sc) StdErr (Sc) t-value (Sc) Pr(>|t|)
## Intercept 0.8197 0.8197 0.1690 4.8493 <2e-16 ***
## x1.baru -0.0006 -0.0007 0.0014 -0.4786 0.6323
## x2.baru -0.2106 -0.2106 0.0246 -8.5486 <2e-16 ***
## x3.baru 0.1095 0.1095 0.0116 9.4147 <2e-16 ***
## x4.baru -0.0012 -0.0012 0.0007 -1.8218 0.0688 .
## x5.baru -0.0005 -0.0005 0.0002 -1.9908 0.0468 *
## x6.baru -0.0049 -0.0049 0.0317 -0.1541 0.8776
## x7.baru 0.0306 0.0306 0.0212 1.4392 0.1504
## x8.baru 0.0033 0.0033 0.0006 5.4196 <2e-16 ***
## x9.baru -0.1283 -0.1283 0.0263 -4.8793 <2e-16 ***
## x10.baru -0.0472 -0.0472 0.0120 -3.9424 0.0001 ***
## x11.baru 0.1037 0.1037 0.0222 4.6777 <2e-16 ***
## x12.baru -0.1187 -0.1187 0.0115 -10.2783 <2e-16 ***
## x13.baru -0.1800 -0.1800 0.0189 -9.5046 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Ridge Summary
## R2 adj-R2 DF ridge F AIC BIC
## 0.58640 0.58120 13.00051 103.72028 -2162.97662 4524.08206
## Ridge minimum MSE= 0.004017763 at K= 0
## P-value for F-test ( 13.00051 , 950.9989 ) = 4.854977e-172
## -------------------------------------------------------------------Diperoleh model:
\[y = 0.8197 - 0.0006x_1 - 0.2106x_2 + 0.1095x_3 - 0.0012x_4 - 0.0005x_5 - 0.0049x_6 + 0.0306x_7 + 0.0033x_8 - 0.1283x_9 - 0.0472x_{10} + 0.1037x_{11} - 0.1187x_{12} - vx_{13} \]
Diketahui peubah x1, x4, x6, dan x7 tidak berpengaruh signifikan terhadap peubah y pada model ini.
REGRESI LASSO
cv.l <- cv.glmnet(x,y,alpha=1);plot(cv.l)
best.ll<-cv.l$lambda.min
lasso<-glmnet(x,y,alpha=1,lambda=best.ll)
coef(lasso)## 14 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 0.8022736903
## x1.baru -0.0006054159
## x2.baru -0.2069681478
## x3.baru 0.1082865603
## x4.baru -0.0011575125
## x5.baru -0.0004320266
## x6.baru -0.0009880365
## x7.baru 0.0289848139
## x8.baru 0.0032475834
## x9.baru -0.1280434311
## x10.baru -0.0472376826
## x11.baru 0.1020847376
## x12.baru -0.1181967076
## x13.baru -0.1787333453Diperoleh model:
\[y = 0.7811930062 - 0.0005428009x_1 - 0.2028381565x_2 + 0.1071349655x_3 - 0.0010756846x_4 - 0.0004005884x_5 + 0.0270610189x_7 + 0.0032299498x_8 - 0.1275548574x_9 - 0.0473143997x_{10} + 0.1001968298x_{11} - 0.1175102931x_{12} - 0.1774380229x_{13} \]
rsq(lasso,best.ll,x,y)## [1] 0.5863303Diketahui adanya seleksi pada model yaitu tereliminasinya peubah x6 dengan nilai R-squared 58,61%.
RSE (Residual Standard Error) Model Regresi Ridge dan Model Regresi LASSO
Model Regresi Ridge
# Prediksi model ridge pada data pelatihan
train_predictionsridge <- predict(ridge2,newx = x)
# Hitung residu (selisih antara prediksi dan nilai sebenarnya)
residualsridge <- y - train_predictionsridge
# Hitung varian residu
dfridge <- length(y) - length(ridge2$beta)
residual_varianceridge <- sum(residualsridge^2) / dfridge
# Hitung RSE
rseridge <- sqrt(residual_varianceridge)
# Tampilkan hasil RSE
print(paste("Residual Standard Error (RSE):",rseridge))## [1] "Residual Standard Error (RSE): 0.321307802742746"Model Regresi LASSO
# Prediksi model Lasso pada data pelatihan
train_predictionsLasso <- predict(lasso,newx = x)
# Hitung residu (selisih antara prediksi dan nilai sebenarnya)
residualsLasso <- y - train_predictionsLasso
# Hitung varian residu
dfLasso <- length(y) - length(lasso$beta)
residual_varianceLasso <- sum(residualsLasso^2) / dfLasso
# Hitung RSE
rseLasso <- sqrt(residual_varianceLasso)
# Tampilkan hasil RSE
print(paste("Residual Standard Error (RSE):",rseLasso))## [1] "Residual Standard Error (RSE): 0.323524690910896"PERBANDINGAN MODEL
RSE Model Awal (setelah penagnganan pencilan) : 0.3237
RSE Model Stepwise : 0.3236
RSE Model Ridge : 0.3213
RSE Model LASSO : 0.3236
INTERPRETASI
Penentuan model terbaik akan dipilih berdasarkan nilai RSE (residual standard error) terkecil. Pada kasus ini, model yang paling optimal adalah Model Regresi Ridge. Diketahui juga data tidak mengandung multikolinearitas sehingga tidak diperlukan adanya seleksi peubah. Hal ini terbukti dalam regresi ridge yang mempertahankan semua peubah penjelasnya, sehingga peubah-peubah tersebut tetap digunakan dalam model regresi.