Project 1 Pembelajaran Mesin Statistika
Pada kali ini, kita akan mensimulasikan bagaimana cara membangun model dengan metode regresi diantaranya best-subset, ridge, lasso, dan elastic-net.
Data akan digenerate dengan beberapa ketentuan tertentu untuk kemudian selanjutnya akan dilakukan ke tahap pembuatan model.
Untuk membangun model tersebut, berikut ini adalah metodologi atau algoritma yang digunakan.
Import Data
Pre Processing Data
Generate Model
Tuning Hyperparameter
Prediction
Import Data
Pada case ini kita akan menggunakan data simulasi yang dibangkitkan dengan beberapa ketentuan tertentu diantaranya sbb:
Bangkitkan data sebanyak n = 10000, dengan ketentuan sebagai berikut:
Bangkitkan X1, X2, …, X50 dari sebaran Normal(10, 2.k), yang mana
X1 dan X2berkorelasi sebesar0.95,X4 dan X5berkorelasi sebesar−0.85.Berdasarkan 10000 data yang dibangkitkan tersebut hitung korelasi X1 dan X2 serta korelasi X4 dan X5. Ini untuk mengecek bahwa simulasinya sudah benar.
X51 = 3.5(X1) + μ dan X52 = −0.65(X2) + μ, sedangkan μ menyebar Normal(2, 1.k).
β0 = 2.5; β1 = β2 = … = β20 = 3.5; β21 = β22 = … = β50 = 0; β51 = β52 = −4.5 .
Y = β0 + β1X1 + β2X2 + … + β52X52 + ε, sedangkan ε menyebar Normal(0, 1.2k).
Data Y, X1, X2, …, X52 hasil bangkitan tersebut disimpan dengan nama “DAT.SIM.01”.
library(rpart)
library(pROC)## Type 'citation("pROC")' for a citation.##
## Attaching package: 'pROC'## The following objects are masked from 'package:stats':
##
## cov, smooth, varlibrary(tidyverse)## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --## v ggplot2 3.3.5 v purrr 0.3.4
## v tibble 3.1.3 v dplyr 1.0.7
## v tidyr 1.1.3 v stringr 1.4.0
## v readr 2.0.1 v forcats 0.5.1## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag() masks stats::lag()library(mlr3verse)## Loading required package: mlr3library(mlr3extralearners)##
## Attaching package: 'mlr3extralearners'## The following objects are masked from 'package:mlr3':
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## lrn, lrnslibrary(precrec)##
## Attaching package: 'precrec'## The following object is masked from 'package:pROC':
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## auclibrary(adabag)## Loading required package: caret## Loading required package: lattice##
## Attaching package: 'caret'## The following object is masked from 'package:purrr':
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## lift## Loading required package: foreach##
## Attaching package: 'foreach'## The following objects are masked from 'package:purrr':
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## accumulate, when## Loading required package: doParallel## Loading required package: iterators## Loading required package: parallellibrary(ROCR)
library(ROCit)
library(magrittr)##
## Attaching package: 'magrittr'## The following object is masked from 'package:purrr':
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## set_names## The following object is masked from 'package:tidyr':
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## extractlibrary(visdat)
library(naniar)
library(UpSetR)##
## Attaching package: 'UpSetR'## The following object is masked from 'package:lattice':
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## histogramlibrary(laeken)
library(vcd)## Loading required package: gridlibrary(VIM)## Loading required package: colorspace##
## Attaching package: 'colorspace'## The following object is masked from 'package:pROC':
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## coords## VIM is ready to use.## Suggestions and bug-reports can be submitted at: https://github.com/statistikat/VIM/issues##
## Attaching package: 'VIM'## The following object is masked from 'package:datasets':
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## sleeplibrary(sm)## Package 'sm', version 2.2-5.7: type help(sm) for summary informationlibrary(ggplot2)
library(dplyr)
library(mlbench)
library(caret)
library(mlr3verse)
library(mlr3fselect)
library(DataExplorer)
library(skimr)##
## Attaching package: 'skimr'## The following object is masked from 'package:naniar':
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## n_complete## The following object is masked from 'package:mlr3':
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## partitionlibrary(corrplot)## corrplot 0.92 loadedlibrary(leaps)
library(olsrr)##
## Attaching package: 'olsrr'## The following object is masked from 'package:datasets':
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## riverslibrary(kableExtra) #Tampilan Tabel##
## Attaching package: 'kableExtra'## The following object is masked from 'package:dplyr':
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## group_rowslibrary(agricolae) #Pemeriksaan Asumsi
library(lmtest) #Untuk pengecekan asumsi## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
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## as.Date, as.Date.numericlibrary(car) #Untuk pengecekan asumsi## Loading required package: carData##
## Attaching package: 'car'## The following object is masked from 'package:ROCit':
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## logit## The following object is masked from 'package:dplyr':
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## recode## The following object is masked from 'package:purrr':
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## somelibrary(tseries) #Untuk pengecekan asumsi## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(glmnet)## Loading required package: Matrix##
## Attaching package: 'Matrix'## The following objects are masked from 'package:tidyr':
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## expand, pack, unpack## Loaded glmnet 4.1-2library(glmnetUtils)##
## Attaching package: 'glmnetUtils'## The following objects are masked from 'package:glmnet':
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## cv.glmnet, glmnetlibrary(broom)
library(ggpubr)
library(modelr)##
## Attaching package: 'modelr'## The following object is masked from 'package:broom':
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## bootstrap## The following object is masked from 'package:mlr3':
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## resamplelibrary(precrec)
library(adabag)
library(rpart.plot)
k <- 7
sigmaX<- 2.7
meanX <- 10
jumlah<-10000
set.seed(10)
dataX <- replicate(50,rnorm(jumlah,mean=meanX,sd= sigmaX))
dataX<-as.data.frame(dataX)
correlatedValue = function(x, r){
r2 = r**2
ve = 1-r2
SD = sqrt(ve)
e = rnorm(length(x), mean=0, sd=SD)
y = r*x + e
return(y)
}
set.seed(043)
X1 = rnorm(10000, 10, 2.7)
X2 = correlatedValue(x=X1, r=.7480)
cor(X1,X2)## [1] 0.9500737set.seed(0431)
X4 = rnorm(10000, 10, 2.7)
X5 = correlatedValue(x=X4, r=-(0.519))
cor(X4,X5)## [1] -0.8575801#soal nomor 3
set.seed(0432)
miu<- rnorm(jumlah,2,1.7)
V51<-X1*3.5 + miu
V52<-X2*(-0.65)+miu
#soal nomor 4
dataX$V1<- X1
dataX$V2<-X2
dataX<- cbind(dataX,V51,V52)
dim(dataX)## [1] 10000 52head(dataX)class(dataX)## [1] "data.frame"dataX$V1<- as.integer(dataX$V1)
dataX$V2<- as.integer(dataX$V2)
dataX$V3<- as.integer(dataX$V3)
dataX$V4<- as.integer(dataX$V4)
dataX$V5<- as.integer(dataX$V5)
dataX$V6<- as.integer(dataX$V6)
dataX$V7<- as.integer(dataX$V7)
dataX$V8<- as.integer(dataX$V8)
dataX$V9<- as.integer(dataX$V9)
dataX$V10<- as.integer(dataX$V10)
dataX$V11<- as.integer(dataX$V11)
dataX$V12<- as.integer(dataX$V12)
dataX$V13<- as.integer(dataX$V13)
dataX$V14<- as.integer(dataX$V14)
dataX$V15<- as.integer(dataX$V15)
dataX$V16<- as.integer(dataX$V16)
dataX$V17<- as.integer(dataX$V17)
dataX$V18<- as.integer(dataX$V18)
dataX$V19<- as.integer(dataX$V19)
dataX$V20<- as.integer(dataX$V20)
dataX$V21<- as.integer(dataX$V21)
dataX$V22<- as.integer(dataX$V22)
dataX$V23<- as.integer(dataX$V23)
dataX$V24<- as.integer(dataX$V24)
dataX$V25<- as.integer(dataX$V25)
dataX$V26<- as.integer(dataX$V26)
dataX$V27<- as.integer(dataX$V27)
dataX$V28<- as.integer(dataX$V28)
dataX$V29<- as.integer(dataX$V29)
dataX$V30<- as.integer(dataX$V30)
dataX$V31<- as.integer(dataX$V31)
dataX$V32<- as.integer(dataX$V32)
dataX$V33<- as.integer(dataX$V33)
dataX$V34<- as.integer(dataX$V34)
dataX$V35<- as.integer(dataX$V35)
dataX$V36<- as.integer(dataX$V36)
dataX$V37<- as.integer(dataX$V37)
dataX$V38<- as.integer(dataX$V38)
dataX$V39<- as.integer(dataX$V39)
dataX$V40<- as.integer(dataX$V40)
dataX$V41<- as.integer(dataX$V41)
dataX$V42<- as.integer(dataX$V42)
dataX$V43<- as.integer(dataX$V43)
dataX$V44<- as.integer(dataX$V44)
dataX$V45<- as.integer(dataX$V45)
dataX$V46<- as.integer(dataX$V46)
dataX$V47<- as.integer(dataX$V47)
dataX$V48<- as.integer(dataX$V48)
dataX$V49<- as.integer(dataX$V49)
dataX$V50<- as.integer(dataX$V50)
dataX$V51<- as.integer(dataX$V51)
dataX$V52<- as.integer(dataX$V52)
dim(dataX)## [1] 10000 52glimpse(dataX)## Rows: 10,000
## Columns: 52
## $ V1 <int> 9, 5, 8, 11, 7, 9, 11, 9, 8, 4, 14, 7, 9, 12, 11, 15, 13, 5, 10, 8~
## $ V2 <int> 6, 5, 6, 7, 5, 6, 7, 8, 5, 3, 11, 6, 7, 9, 7, 10, 8, 4, 7, 6, 6, 8~
## $ V3 <int> 12, 9, 14, 11, 7, 5, 17, 4, 5, 8, 16, 12, 16, 13, 13, 8, 12, 10, 9~
## $ V4 <int> 7, 9, 6, 14, 13, 14, 10, 6, 8, 9, 5, 4, 12, 6, 7, 14, 11, 13, 7, 1~
## $ V5 <int> 14, 7, 3, 8, 16, 9, 12, 7, 7, 13, 9, 4, 7, 7, 6, 11, 9, 9, 7, 6, 1~
## $ V6 <int> 14, 15, 11, 7, 11, 6, 6, 6, 8, 12, 10, 9, 11, 5, 9, 11, 15, 6, 10,~
## $ V7 <int> 11, 10, 13, 10, 8, 13, 7, 7, 7, 12, 13, 12, 10, 11, 3, 12, 14, 14,~
## $ V8 <int> 9, 10, 9, 6, 7, 11, 7, 3, 5, 5, 8, 10, 11, 8, 8, 9, 10, 11, 8, 10,~
## $ V9 <int> 12, 9, 8, 9, 8, 10, 12, 5, 7, 9, 8, 7, 11, 1, 10, 7, 5, 10, 9, 8, ~
## $ V10 <int> 14, 12, 17, 8, 13, 9, 14, 6, 11, 14, 4, 13, 7, 13, 12, 10, 7, 11, ~
## $ V11 <int> 10, 10, 12, 7, 10, 10, 7, 13, 7, 12, 9, 11, 8, 11, 8, 13, 0, 9, 10~
## $ V12 <int> 12, 12, 5, 15, 0, 10, 9, 7, 15, 11, 8, 9, 8, 9, 10, 9, 11, 12, 12,~
## $ V13 <int> 6, 14, 6, 8, 6, 10, 8, 10, 8, 8, 11, 7, 12, 14, 9, 6, 11, 9, 6, 9,~
## $ V14 <int> 10, 8, 8, 10, 14, 8, 5, 8, 9, 6, 12, 9, 11, 10, 13, 12, 12, 13, 12~
## $ V15 <int> 10, 12, 12, 11, 5, 4, 10, 13, 6, 10, 9, 4, 12, 15, 16, 10, 11, 11,~
## $ V16 <int> 9, 8, 8, 12, 12, 8, 11, 5, 10, 13, 13, 12, 7, 6, 14, 4, 13, 8, 14,~
## $ V17 <int> 12, 4, 10, 12, 7, 4, 9, 11, 13, 8, 10, 10, 9, 12, 13, 9, 8, 7, 7, ~
## $ V18 <int> 8, 10, 6, 9, 13, 9, 8, 8, 8, 9, 13, 8, 10, 11, 12, 8, 13, 11, 10, ~
## $ V19 <int> 14, 11, 8, 10, 12, 3, 9, 10, 16, 9, 9, 10, 11, 7, 9, 11, 11, 12, 9~
## $ V20 <int> 9, 9, 12, 7, 9, 9, 11, 12, 7, 9, 11, 3, 11, 6, 4, 10, 9, 9, 12, 6,~
## $ V21 <int> 10, 6, 7, 5, 13, 10, 7, 11, 7, 9, 10, 13, 12, 12, 7, 5, 7, 6, 9, 1~
## $ V22 <int> 13, 11, 6, 4, 13, 7, 10, 9, 12, 10, 6, 13, 7, 13, 10, 5, 11, 11, 1~
## $ V23 <int> 10, 9, 11, 8, 9, 4, 6, 12, 16, 6, 10, 11, 10, 4, 8, 8, 10, 9, 7, 6~
## $ V24 <int> 14, 11, 7, 11, 7, 12, 8, 8, 11, 6, 6, 7, 12, 11, 8, 10, 8, 7, 9, 8~
## $ V25 <int> 9, 11, 9, 9, 11, 11, 10, 15, 5, 9, 11, 9, 12, 8, 10, 9, 13, 13, 13~
## $ V26 <int> 7, 12, 7, 10, 9, 9, 5, 5, 11, 11, 11, 9, 15, 10, 5, 6, 10, 6, 10, ~
## $ V27 <int> 9, 9, 14, 9, 8, 6, 6, 13, 10, 12, 10, 9, 9, 9, 11, 10, 9, 12, 10, ~
## $ V28 <int> 13, 15, 10, 12, 11, 13, 10, 7, 8, 9, 8, 11, 11, 6, 7, 13, 13, 10, ~
## $ V29 <int> 13, 11, 11, 13, 13, 10, 11, 10, 11, 7, 12, 11, 10, 10, 8, 8, 8, 6,~
## $ V30 <int> 12, 9, 5, 7, 9, 12, 6, 8, 8, 9, 6, 10, 13, 8, 9, 4, 8, 9, 11, 11, ~
## $ V31 <int> 8, 7, 10, 9, 9, 11, 9, 12, 10, 7, 13, 11, 10, 9, 8, 14, 9, 13, 16,~
## $ V32 <int> 10, 10, 8, 8, 4, 8, 11, 10, 11, 10, 8, 10, 6, 7, 6, 7, 11, 9, 2, 5~
## $ V33 <int> 8, 6, 9, 8, 8, 9, 11, 11, 6, 9, 9, 13, 5, 10, 10, 11, 9, 13, 9, 11~
## $ V34 <int> 9, 12, 11, 13, 11, 10, 6, 9, 10, 9, 15, 7, 10, 10, 10, 8, 4, 12, 1~
## $ V35 <int> 7, 11, 14, 6, 13, 6, 7, 10, 9, 6, 11, 7, 10, 8, 6, 9, 7, 10, 10, 8~
## $ V36 <int> 13, 9, 8, 11, 9, 11, 8, 9, 10, 13, 12, 15, 17, 10, 9, 10, 9, 13, 1~
## $ V37 <int> 11, 3, 8, 11, 10, 10, 11, 13, 13, 7, 13, 4, 11, 8, 11, 6, 16, 6, 9~
## $ V38 <int> 5, 8, 9, 14, 14, 10, 7, 11, 11, 12, 8, 14, 11, 10, 12, 10, 10, 12,~
## $ V39 <int> 9, 5, 8, 12, 13, 9, 10, 8, 10, 10, 11, 13, 14, 10, 11, 8, 5, 5, 5,~
## $ V40 <int> 12, 11, 6, 7, 9, 11, 8, 7, 8, 12, 11, 10, 3, 8, 9, 9, 9, 11, 7, 12~
## $ V41 <int> 11, 11, 7, 13, 14, 7, 9, 6, 10, 10, 12, 11, 7, 7, 6, 9, 9, 6, 10, ~
## $ V42 <int> 7, 9, 11, 12, 6, 15, 8, 9, 9, 7, 14, 8, 7, 11, 8, 8, 7, 16, 6, 10,~
## $ V43 <int> 7, 12, 11, 11, 8, 10, 10, 7, 11, 10, 13, 8, 5, 10, 9, 10, 8, 11, 1~
## $ V44 <int> 11, 11, 12, 10, 8, 10, 11, 9, 8, 15, 9, 13, 10, 10, 11, 11, 11, 10~
## $ V45 <int> 10, 10, 13, 8, 7, 6, 12, 10, 11, 10, 7, 14, 8, 7, 9, 7, 11, 8, 8, ~
## $ V46 <int> 10, 9, 7, 8, 8, 14, 9, 11, 10, 7, 7, 13, 8, 9, 4, 10, 8, 12, 11, 1~
## $ V47 <int> 9, 9, 11, 12, 9, 7, 7, 13, 12, 9, 10, 7, 8, 15, 6, 10, 7, 8, 6, 8,~
## $ V48 <int> 9, 8, 9, 12, 9, 11, 11, 11, 11, 8, 6, 9, 9, 8, 6, 6, 12, 7, 14, 10~
## $ V49 <int> 7, 5, 12, 8, 13, 9, 13, 9, 10, 14, 3, 5, 5, 7, 8, 8, 10, 10, 11, 1~
## $ V50 <int> 12, 5, 7, 8, 7, 13, 12, 10, 7, 7, 12, 5, 8, 8, 7, 13, 9, 13, 10, 9~
## $ V51 <int> 35, 24, 33, 42, 29, 35, 39, 35, 30, 18, 53, 28, 32, 45, 44, 53, 51~
## $ V52 <int> -3, 0, -1, -1, 0, -1, -3, -4, -1, 0, -5, -1, -3, -5, -1, -7, -2, -~#Soal nomor 4
set.seed(0435)
epsilon<- rnorm(jumlah, 0, 1.27)
epsilon<-as.integer(epsilon)
Y<- 2.5 + 3.5*dataX$V1+ 3.5*dataX$V2 + 3.5*dataX$V3 + 3.5*dataX$V4 + 3.5*dataX$V5 + 3.5*dataX$V6 + 3.5*dataX$V7 + 3.5*dataX$V8 + 3.5*dataX$V9 + 3.5*dataX$V10 + 3.5*dataX$V11 + 3.5*dataX$V12 + 3.5*dataX$V13 + 3.5*dataX$V14 + 3.5*dataX$V15 + 3.5*dataX$V16 + 3.5*dataX$V17 + 3.5*dataX$V18 + 3.5*dataX$V19 + 3.5*dataX$V20 - 4.5*dataX$V51 - 4.5*dataX$V52 + epsilon
Y<-as.integer(Y)
dataX<- cbind(Y, dataX)
DAT.SIM.01<- dataX
dim(DAT.SIM.01)## [1] 10000 53head(DAT.SIM.01)glimpse(DAT.SIM.01)## Rows: 10,000
## Columns: 53
## $ Y <int> 587, 556, 495, 491, 512, 434, 505, 416, 467, 565, 497, 466, 572, 4~
## $ V1 <int> 9, 5, 8, 11, 7, 9, 11, 9, 8, 4, 14, 7, 9, 12, 11, 15, 13, 5, 10, 8~
## $ V2 <int> 6, 5, 6, 7, 5, 6, 7, 8, 5, 3, 11, 6, 7, 9, 7, 10, 8, 4, 7, 6, 6, 8~
## $ V3 <int> 12, 9, 14, 11, 7, 5, 17, 4, 5, 8, 16, 12, 16, 13, 13, 8, 12, 10, 9~
## $ V4 <int> 7, 9, 6, 14, 13, 14, 10, 6, 8, 9, 5, 4, 12, 6, 7, 14, 11, 13, 7, 1~
## $ V5 <int> 14, 7, 3, 8, 16, 9, 12, 7, 7, 13, 9, 4, 7, 7, 6, 11, 9, 9, 7, 6, 1~
## $ V6 <int> 14, 15, 11, 7, 11, 6, 6, 6, 8, 12, 10, 9, 11, 5, 9, 11, 15, 6, 10,~
## $ V7 <int> 11, 10, 13, 10, 8, 13, 7, 7, 7, 12, 13, 12, 10, 11, 3, 12, 14, 14,~
## $ V8 <int> 9, 10, 9, 6, 7, 11, 7, 3, 5, 5, 8, 10, 11, 8, 8, 9, 10, 11, 8, 10,~
## $ V9 <int> 12, 9, 8, 9, 8, 10, 12, 5, 7, 9, 8, 7, 11, 1, 10, 7, 5, 10, 9, 8, ~
## $ V10 <int> 14, 12, 17, 8, 13, 9, 14, 6, 11, 14, 4, 13, 7, 13, 12, 10, 7, 11, ~
## $ V11 <int> 10, 10, 12, 7, 10, 10, 7, 13, 7, 12, 9, 11, 8, 11, 8, 13, 0, 9, 10~
## $ V12 <int> 12, 12, 5, 15, 0, 10, 9, 7, 15, 11, 8, 9, 8, 9, 10, 9, 11, 12, 12,~
## $ V13 <int> 6, 14, 6, 8, 6, 10, 8, 10, 8, 8, 11, 7, 12, 14, 9, 6, 11, 9, 6, 9,~
## $ V14 <int> 10, 8, 8, 10, 14, 8, 5, 8, 9, 6, 12, 9, 11, 10, 13, 12, 12, 13, 12~
## $ V15 <int> 10, 12, 12, 11, 5, 4, 10, 13, 6, 10, 9, 4, 12, 15, 16, 10, 11, 11,~
## $ V16 <int> 9, 8, 8, 12, 12, 8, 11, 5, 10, 13, 13, 12, 7, 6, 14, 4, 13, 8, 14,~
## $ V17 <int> 12, 4, 10, 12, 7, 4, 9, 11, 13, 8, 10, 10, 9, 12, 13, 9, 8, 7, 7, ~
## $ V18 <int> 8, 10, 6, 9, 13, 9, 8, 8, 8, 9, 13, 8, 10, 11, 12, 8, 13, 11, 10, ~
## $ V19 <int> 14, 11, 8, 10, 12, 3, 9, 10, 16, 9, 9, 10, 11, 7, 9, 11, 11, 12, 9~
## $ V20 <int> 9, 9, 12, 7, 9, 9, 11, 12, 7, 9, 11, 3, 11, 6, 4, 10, 9, 9, 12, 6,~
## $ V21 <int> 10, 6, 7, 5, 13, 10, 7, 11, 7, 9, 10, 13, 12, 12, 7, 5, 7, 6, 9, 1~
## $ V22 <int> 13, 11, 6, 4, 13, 7, 10, 9, 12, 10, 6, 13, 7, 13, 10, 5, 11, 11, 1~
## $ V23 <int> 10, 9, 11, 8, 9, 4, 6, 12, 16, 6, 10, 11, 10, 4, 8, 8, 10, 9, 7, 6~
## $ V24 <int> 14, 11, 7, 11, 7, 12, 8, 8, 11, 6, 6, 7, 12, 11, 8, 10, 8, 7, 9, 8~
## $ V25 <int> 9, 11, 9, 9, 11, 11, 10, 15, 5, 9, 11, 9, 12, 8, 10, 9, 13, 13, 13~
## $ V26 <int> 7, 12, 7, 10, 9, 9, 5, 5, 11, 11, 11, 9, 15, 10, 5, 6, 10, 6, 10, ~
## $ V27 <int> 9, 9, 14, 9, 8, 6, 6, 13, 10, 12, 10, 9, 9, 9, 11, 10, 9, 12, 10, ~
## $ V28 <int> 13, 15, 10, 12, 11, 13, 10, 7, 8, 9, 8, 11, 11, 6, 7, 13, 13, 10, ~
## $ V29 <int> 13, 11, 11, 13, 13, 10, 11, 10, 11, 7, 12, 11, 10, 10, 8, 8, 8, 6,~
## $ V30 <int> 12, 9, 5, 7, 9, 12, 6, 8, 8, 9, 6, 10, 13, 8, 9, 4, 8, 9, 11, 11, ~
## $ V31 <int> 8, 7, 10, 9, 9, 11, 9, 12, 10, 7, 13, 11, 10, 9, 8, 14, 9, 13, 16,~
## $ V32 <int> 10, 10, 8, 8, 4, 8, 11, 10, 11, 10, 8, 10, 6, 7, 6, 7, 11, 9, 2, 5~
## $ V33 <int> 8, 6, 9, 8, 8, 9, 11, 11, 6, 9, 9, 13, 5, 10, 10, 11, 9, 13, 9, 11~
## $ V34 <int> 9, 12, 11, 13, 11, 10, 6, 9, 10, 9, 15, 7, 10, 10, 10, 8, 4, 12, 1~
## $ V35 <int> 7, 11, 14, 6, 13, 6, 7, 10, 9, 6, 11, 7, 10, 8, 6, 9, 7, 10, 10, 8~
## $ V36 <int> 13, 9, 8, 11, 9, 11, 8, 9, 10, 13, 12, 15, 17, 10, 9, 10, 9, 13, 1~
## $ V37 <int> 11, 3, 8, 11, 10, 10, 11, 13, 13, 7, 13, 4, 11, 8, 11, 6, 16, 6, 9~
## $ V38 <int> 5, 8, 9, 14, 14, 10, 7, 11, 11, 12, 8, 14, 11, 10, 12, 10, 10, 12,~
## $ V39 <int> 9, 5, 8, 12, 13, 9, 10, 8, 10, 10, 11, 13, 14, 10, 11, 8, 5, 5, 5,~
## $ V40 <int> 12, 11, 6, 7, 9, 11, 8, 7, 8, 12, 11, 10, 3, 8, 9, 9, 9, 11, 7, 12~
## $ V41 <int> 11, 11, 7, 13, 14, 7, 9, 6, 10, 10, 12, 11, 7, 7, 6, 9, 9, 6, 10, ~
## $ V42 <int> 7, 9, 11, 12, 6, 15, 8, 9, 9, 7, 14, 8, 7, 11, 8, 8, 7, 16, 6, 10,~
## $ V43 <int> 7, 12, 11, 11, 8, 10, 10, 7, 11, 10, 13, 8, 5, 10, 9, 10, 8, 11, 1~
## $ V44 <int> 11, 11, 12, 10, 8, 10, 11, 9, 8, 15, 9, 13, 10, 10, 11, 11, 11, 10~
## $ V45 <int> 10, 10, 13, 8, 7, 6, 12, 10, 11, 10, 7, 14, 8, 7, 9, 7, 11, 8, 8, ~
## $ V46 <int> 10, 9, 7, 8, 8, 14, 9, 11, 10, 7, 7, 13, 8, 9, 4, 10, 8, 12, 11, 1~
## $ V47 <int> 9, 9, 11, 12, 9, 7, 7, 13, 12, 9, 10, 7, 8, 15, 6, 10, 7, 8, 6, 8,~
## $ V48 <int> 9, 8, 9, 12, 9, 11, 11, 11, 11, 8, 6, 9, 9, 8, 6, 6, 12, 7, 14, 10~
## $ V49 <int> 7, 5, 12, 8, 13, 9, 13, 9, 10, 14, 3, 5, 5, 7, 8, 8, 10, 10, 11, 1~
## $ V50 <int> 12, 5, 7, 8, 7, 13, 12, 10, 7, 7, 12, 5, 8, 8, 7, 13, 9, 13, 10, 9~
## $ V51 <int> 35, 24, 33, 42, 29, 35, 39, 35, 30, 18, 53, 28, 32, 45, 44, 53, 51~
## $ V52 <int> -3, 0, -1, -1, 0, -1, -3, -4, -1, 0, -5, -1, -3, -5, -1, -7, -2, -~Pre-Processing Data
Sebelum dilakukan pembuatan model, terlebih dahulu dilakukan splitting data dan pengecekan data sebagai berikut.
Split Data
Data tersebut akan kita bagi dua yaitu data training dan data test, data training adalah data yang nantinya akan digunakan untuk membangun model, sedangkan data test akan digunakan utuk mengukur akurasi model yang sudah dibuat. Data test dan data training akan dibagi dengan proporsi 20%:80%.
set.seed(1238)
index <- createDataPartition(DAT.SIM.01$Y , p = 0.8,list = FALSE)
#membagi data menjadi data train dan data test
train.dataindex <- DAT.SIM.01[index,]
dim(train.dataindex)## [1] 8002 53test.dataindex <- DAT.SIM.01[-index,]
dim(test.dataindex)## [1] 1998 53Variabel respon
Melihat sebaran variabel respon apakah sudah berdistribusi normal.
#Cek Normalitas variabel respon
ggpubr::gghistogram(data = train.dataindex, x = "Y",fill = "darkgreen")+scale_y_continuous(expand = c(0,0))## Warning: Using `bins = 30` by default. Pick better value with the argument
## `bins`.
variabel respon berdistribusi normal
Missing Values
Memeriksa apakah ada missing values pada data yang akan kita gunakan.
#Cek data hilang
anyNA(train.dataindex)## [1] FALSEsum(anyNA(train.dataindex))## [1] 0tidak ada data hilang
Generate Model
Pada tahap ini, kita akan membangun model dengan beberapa metode diantaranya best-subset, ridge, lasso, dan elastic-net.
Best-Subset Model
Pertama kita akan mencoba membangun model regresi dengan metode best-subset.
#Model regresi
Mod_best<- lm(formula = Y~., data = train.dataindex)
#Summary model
summary(Mod_best)##
## Call:
## lm(formula = Y ~ ., data = train.dataindex)
##
## Residuals:
## Min 1Q Median 3Q Max
## -4.2256 -0.3381 0.0963 0.3282 4.2846
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.542e+00 2.659e-01 9.558 <2e-16 ***
## V1 3.450e+00 3.354e-02 102.855 <2e-16 ***
## V2 3.496e+00 1.716e-02 203.755 <2e-16 ***
## V3 3.493e+00 3.947e-03 885.054 <2e-16 ***
## V4 3.494e+00 4.014e-03 870.545 <2e-16 ***
## V5 3.502e+00 3.928e-03 891.742 <2e-16 ***
## V6 3.500e+00 3.974e-03 880.779 <2e-16 ***
## V7 3.506e+00 3.960e-03 885.242 <2e-16 ***
## V8 3.498e+00 3.950e-03 885.575 <2e-16 ***
## V9 3.500e+00 3.942e-03 887.920 <2e-16 ***
## V10 3.496e+00 3.978e-03 878.734 <2e-16 ***
## V11 3.501e+00 4.039e-03 866.873 <2e-16 ***
## V12 3.509e+00 4.011e-03 874.663 <2e-16 ***
## V13 3.499e+00 3.943e-03 887.552 <2e-16 ***
## V14 3.501e+00 3.945e-03 887.411 <2e-16 ***
## V15 3.502e+00 3.942e-03 888.392 <2e-16 ***
## V16 3.501e+00 3.936e-03 889.564 <2e-16 ***
## V17 3.491e+00 4.048e-03 862.423 <2e-16 ***
## V18 3.505e+00 4.023e-03 871.229 <2e-16 ***
## V19 3.503e+00 3.975e-03 881.251 <2e-16 ***
## V20 3.495e+00 3.952e-03 884.398 <2e-16 ***
## V21 -2.670e-03 3.908e-03 -0.683 0.4945
## V22 -2.924e-03 3.892e-03 -0.751 0.4525
## V23 -1.509e-03 3.991e-03 -0.378 0.7054
## V24 -5.948e-03 4.036e-03 -1.474 0.1405
## V25 -1.902e-03 3.962e-03 -0.480 0.6312
## V26 -2.184e-04 3.989e-03 -0.055 0.9563
## V27 -9.050e-03 3.957e-03 -2.287 0.0222 *
## V28 9.333e-04 3.968e-03 0.235 0.8141
## V29 2.579e-03 3.954e-03 0.652 0.5143
## V30 -1.937e-03 3.995e-03 -0.485 0.6277
## V31 -9.729e-04 3.965e-03 -0.245 0.8062
## V32 9.689e-05 3.959e-03 0.024 0.9805
## V33 5.102e-03 3.982e-03 1.281 0.2002
## V34 9.922e-04 3.981e-03 0.249 0.8032
## V35 -2.666e-03 3.937e-03 -0.677 0.4983
## V36 4.275e-03 3.946e-03 1.083 0.2787
## V37 -9.511e-03 3.904e-03 -2.437 0.0148 *
## V38 1.471e-03 3.978e-03 0.370 0.7116
## V39 1.474e-03 4.002e-03 0.368 0.7127
## V40 5.177e-04 4.011e-03 0.129 0.8973
## V41 8.871e-04 3.919e-03 0.226 0.8209
## V42 -5.734e-03 3.970e-03 -1.444 0.1487
## V43 -2.044e-03 3.933e-03 -0.520 0.6032
## V44 -3.273e-03 3.976e-03 -0.823 0.4105
## V45 -2.258e-03 3.989e-03 -0.566 0.5714
## V46 6.746e-04 4.000e-03 0.169 0.8661
## V47 3.829e-03 3.926e-03 0.975 0.3295
## V48 -1.578e-03 3.985e-03 -0.396 0.6921
## V49 2.964e-03 4.001e-03 0.741 0.4589
## V50 3.860e-03 3.929e-03 0.982 0.3260
## V51 -4.488e+00 9.713e-03 -462.023 <2e-16 ***
## V52 -4.517e+00 1.189e-02 -379.898 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9608 on 7949 degrees of freedom
## Multiple R-squared: 0.9996, Adjusted R-squared: 0.9996
## F-statistic: 3.756e+05 on 52 and 7949 DF, p-value: < 2.2e-16Seleksi variabel dengan metode forward dan backward
#forward Selection
mod_forwd<-ols_step_forward_aic(Mod_best, details = T )## Forward Selection Method
## ------------------------
##
## Candidate Terms:
##
## 1 . V1
## 2 . V2
## 3 . V3
## 4 . V4
## 5 . V5
## 6 . V6
## 7 . V7
## 8 . V8
## 9 . V9
## 10 . V10
## 11 . V11
## 12 . V12
## 13 . V13
## 14 . V14
## 15 . V15
## 16 . V16
## 17 . V17
## 18 . V18
## 19 . V19
## 20 . V20
## 21 . V21
## 22 . V22
## 23 . V23
## 24 . V24
## 25 . V25
## 26 . V26
## 27 . V27
## 28 . V28
## 29 . V29
## 30 . V30
## 31 . V31
## 32 . V32
## 33 . V33
## 34 . V34
## 35 . V35
## 36 . V36
## 37 . V37
## 38 . V38
## 39 . V39
## 40 . V40
## 41 . V41
## 42 . V42
## 43 . V43
## 44 . V44
## 45 . V45
## 46 . V46
## 47 . V47
## 48 . V48
## 49 . V49
## 50 . V50
## 51 . V51
## 52 . V52
##
## Step 0: AIC = 84491.59
## Y ~ 1
##
## ---------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------------
## V51 1 82368.667 4206265.441 13829712.490 0.233 0.233
## V1 1 82865.118 3321083.232 14714894.698 0.184 0.184
## V2 1 83221.425 2651063.397 15384914.533 0.147 0.147
## V15 1 84144.678 769530.179 17266447.752 0.043 0.043
## V20 1 84153.770 749900.071 17286077.859 0.042 0.041
## V6 1 84154.325 748700.329 17287277.602 0.042 0.041
## V16 1 84159.500 737517.834 17298460.097 0.041 0.041
## V7 1 84161.983 732148.507 17303829.424 0.041 0.040
## V14 1 84163.207 729501.909 17306476.022 0.040 0.040
## V18 1 84166.860 721598.640 17314379.291 0.040 0.040
## V13 1 84167.183 720899.728 17315078.202 0.040 0.040
## V17 1 84174.172 705771.314 17330206.616 0.039 0.039
## V4 1 84187.707 676433.210 17359544.720 0.038 0.037
## V10 1 84191.704 667759.306 17368218.625 0.037 0.037
## V12 1 84191.901 667330.745 17368647.186 0.037 0.037
## V3 1 84196.721 656867.497 17379110.434 0.036 0.036
## V11 1 84198.112 653846.071 17382131.859 0.036 0.036
## V19 1 84200.465 648733.850 17387244.080 0.036 0.036
## V5 1 84211.017 625789.235 17410188.696 0.035 0.035
## V9 1 84220.328 605520.927 17430457.003 0.034 0.033
## V8 1 84233.859 576020.624 17459957.307 0.032 0.032
## V30 1 84489.813 8515.745 18027462.185 0.000 0.000
## V35 1 84490.528 6902.791 18029075.140 0.000 0.000
## V21 1 84491.282 5203.917 18030774.014 0.000 0.000
## V45 1 84491.322 5115.268 18030862.662 0.000 0.000
## V28 1 84492.227 3074.682 18032903.249 0.000 0.000
## V31 1 84492.244 3037.811 18032940.119 0.000 0.000
## V34 1 84492.275 2968.010 18033009.921 0.000 0.000
## V49 1 84492.289 2936.172 18033041.759 0.000 0.000
## V40 1 84492.375 2742.962 18033234.969 0.000 0.000
## V39 1 84492.648 2126.704 18033851.227 0.000 0.000
## V25 1 84492.675 2065.292 18033912.639 0.000 0.000
## V22 1 84492.723 1957.432 18034020.499 0.000 0.000
## V33 1 84492.797 1791.240 18034186.691 0.000 0.000
## V41 1 84492.965 1413.326 18034564.605 0.000 0.000
## V23 1 84492.975 1388.988 18034588.943 0.000 0.000
## V46 1 84493.010 1310.046 18034667.885 0.000 0.000
## V50 1 84493.120 1062.993 18034914.937 0.000 0.000
## V47 1 84493.173 943.103 18035034.827 0.000 0.000
## V52 1 84493.221 834.715 18035143.216 0.000 0.000
## V48 1 84493.313 627.880 18035350.050 0.000 0.000
## V32 1 84493.326 598.339 18035379.592 0.000 0.000
## V27 1 84493.416 394.817 18035583.114 0.000 0.000
## V44 1 84493.423 379.845 18035598.085 0.000 0.000
## V29 1 84493.482 247.283 18035730.648 0.000 0.000
## V38 1 84493.521 159.066 18035818.865 0.000 0.000
## V37 1 84493.556 79.197 18035898.734 0.000 0.000
## V42 1 84493.570 49.048 18035928.883 0.000 0.000
## V43 1 84493.576 36.236 18035941.694 0.000 0.000
## V24 1 84493.584 17.499 18035960.431 0.000 0.000
## V36 1 84493.588 6.981 18035970.950 0.000 0.000
## V26 1 84493.590 4.167 18035973.763 0.000 0.000
## ---------------------------------------------------------------------------------
##
##
## - V51
##
##
## Step 1 : AIC = 82368.67
## Y ~ V51
##
## ---------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------------
## V52 1 81673.595 1153754.618 12675957.872 0.297 0.297
## V1 1 81875.537 829788.284 12999924.206 0.279 0.279
## V15 1 81894.799 798456.836 13031255.654 0.277 0.277
## V18 1 81924.634 749780.456 13079932.034 0.275 0.275
## V14 1 81933.469 735331.484 13094381.006 0.274 0.274
## V20 1 81934.513 733622.523 13096089.967 0.274 0.274
## V16 1 81936.837 729818.829 13099893.661 0.274 0.273
## V7 1 81938.451 727175.634 13102536.855 0.274 0.273
## V6 1 81943.901 718248.736 13111463.754 0.273 0.273
## V12 1 81953.821 701984.248 13127728.242 0.272 0.272
## V5 1 81965.718 682452.786 13147259.704 0.271 0.271
## V4 1 81968.383 678072.378 13151640.112 0.271 0.271
## V10 1 81970.795 674108.172 13155604.318 0.271 0.270
## V17 1 81973.986 668861.760 13160850.730 0.270 0.270
## V9 1 81977.683 662778.657 13166933.832 0.270 0.270
## V19 1 81980.021 658932.418 13170780.072 0.270 0.270
## V3 1 81983.114 653839.312 13175873.178 0.269 0.269
## V13 1 81989.382 643514.476 13186198.014 0.269 0.269
## V11 1 82003.489 620248.770 13209463.720 0.268 0.267
## V8 1 82014.339 602324.952 13227387.538 0.267 0.266
## V2 1 82052.910 538412.808 13291299.681 0.263 0.263
## V35 1 82364.940 9893.964 13819818.525 0.234 0.234
## V28 1 82368.545 3667.729 13826044.761 0.233 0.233
## V30 1 82368.634 3513.216 13826199.273 0.233 0.233
## V21 1 82368.829 3175.932 13826536.558 0.233 0.233
## V47 1 82368.988 2901.108 13826811.382 0.233 0.233
## V22 1 82369.066 2767.138 13826945.352 0.233 0.233
## V34 1 82369.072 2755.785 13826956.704 0.233 0.233
## V33 1 82369.450 2102.398 13827610.092 0.233 0.233
## V50 1 82369.537 1952.226 13827760.263 0.233 0.233
## V36 1 82369.579 1881.057 13827831.433 0.233 0.233
## V41 1 82369.689 1690.950 13828021.540 0.233 0.233
## V40 1 82369.732 1616.073 13828096.417 0.233 0.233
## V45 1 82369.848 1415.579 13828296.911 0.233 0.233
## V44 1 82369.860 1394.229 13828318.261 0.233 0.233
## V39 1 82369.987 1175.861 13828536.629 0.233 0.233
## V25 1 82370.115 953.868 13828758.622 0.233 0.233
## V29 1 82370.227 760.911 13828951.579 0.233 0.233
## V32 1 82370.260 702.795 13829009.695 0.233 0.233
## V48 1 82370.320 599.168 13829113.321 0.233 0.233
## V27 1 82370.437 397.388 13829315.102 0.233 0.233
## V49 1 82370.440 393.134 13829319.356 0.233 0.233
## V31 1 82370.509 273.961 13829438.528 0.233 0.233
## V24 1 82370.513 266.095 13829446.394 0.233 0.233
## V42 1 82370.537 224.385 13829488.105 0.233 0.233
## V46 1 82370.591 131.520 13829580.970 0.233 0.233
## V23 1 82370.615 90.570 13829621.919 0.233 0.233
## V26 1 82370.617 85.986 13829626.504 0.233 0.233
## V43 1 82370.623 75.503 13829636.987 0.233 0.233
## V38 1 82370.659 13.329 13829699.161 0.233 0.233
## V37 1 82370.664 4.647 13829707.842 0.233 0.233
## ---------------------------------------------------------------------------------
##
## - V52
##
##
## Step 2 : AIC = 81673.59
## Y ~ V51 + V52
##
## --------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## --------------------------------------------------------------------------------
## V15 1 81164.271 784651.204 11891306.668 0.341 0.340
## V20 1 81189.050 747770.984 11928186.887 0.339 0.338
## V14 1 81190.307 745897.732 11930060.140 0.339 0.338
## V16 1 81190.933 744963.751 11930994.121 0.338 0.338
## V6 1 81195.608 737992.092 11937965.780 0.338 0.338
## V18 1 81203.001 726956.774 11949001.098 0.337 0.337
## V7 1 81212.339 713005.515 11962952.357 0.337 0.336
## V10 1 81220.839 700290.732 11975667.140 0.336 0.336
## V12 1 81232.237 683220.691 11992737.181 0.335 0.335
## V5 1 81232.380 683006.962 11992950.910 0.335 0.335
## V4 1 81235.431 678432.235 11997525.637 0.335 0.335
## V17 1 81238.154 674349.741 12001608.131 0.335 0.334
## V19 1 81258.781 643372.991 12032584.881 0.333 0.333
## V3 1 81263.060 636936.388 12039021.484 0.332 0.332
## V9 1 81264.394 634929.863 12041028.009 0.332 0.332
## V13 1 81284.413 604768.405 12071189.467 0.331 0.330
## V11 1 81285.240 603520.344 12072437.528 0.331 0.330
## V8 1 81297.403 585156.708 12090801.164 0.330 0.329
## V2 1 81666.825 13885.208 12662072.664 0.298 0.298
## V35 1 81671.958 5760.033 12670197.839 0.298 0.297
## V1 1 81672.133 5482.107 12670475.765 0.297 0.297
## V28 1 81672.479 4934.912 12671022.960 0.297 0.297
## V22 1 81673.750 2922.491 12673035.381 0.297 0.297
## V21 1 81673.870 2732.697 12673225.175 0.297 0.297
## V34 1 81673.917 2657.613 12673300.259 0.297 0.297
## V30 1 81674.124 2329.999 12673627.873 0.297 0.297
## V41 1 81674.306 2040.952 12673916.920 0.297 0.297
## V45 1 81674.349 1973.149 12673984.723 0.297 0.297
## V40 1 81674.420 1860.422 12674097.450 0.297 0.297
## V47 1 81674.640 1512.176 12674445.696 0.297 0.297
## V29 1 81674.787 1279.512 12674678.360 0.297 0.297
## V32 1 81674.794 1269.230 12674688.642 0.297 0.297
## V48 1 81674.843 1191.153 12674766.719 0.297 0.297
## V25 1 81674.920 1069.325 12674888.547 0.297 0.297
## V49 1 81674.937 1042.011 12674915.861 0.297 0.297
## V36 1 81674.940 1038.018 12674919.854 0.297 0.297
## V46 1 81674.997 947.280 12675010.592 0.297 0.297
## V24 1 81675.004 935.889 12675021.983 0.297 0.297
## V33 1 81675.045 870.813 12675087.059 0.297 0.297
## V39 1 81675.051 861.193 12675096.679 0.297 0.297
## V26 1 81675.068 834.607 12675123.265 0.297 0.297
## V42 1 81675.151 703.640 12675254.232 0.297 0.297
## V31 1 81675.245 554.785 12675403.087 0.297 0.297
## V44 1 81675.286 489.924 12675467.947 0.297 0.297
## V27 1 81675.498 153.680 12675804.192 0.297 0.297
## V50 1 81675.513 129.658 12675828.214 0.297 0.297
## V37 1 81675.557 59.877 12675897.995 0.297 0.297
## V23 1 81675.587 12.939 12675944.933 0.297 0.297
## V38 1 81675.587 12.540 12675945.332 0.297 0.297
## V43 1 81675.594 0.705 12675957.167 0.297 0.297
## --------------------------------------------------------------------------------
##
## - V15
##
##
## Step 3 : AIC = 81164.27
## Y ~ V51 + V52 + V15
##
## --------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## --------------------------------------------------------------------------------
## V20 1 80643.109 752571.190 11138735.478 0.382 0.382
## V16 1 80652.902 738931.175 11152375.492 0.382 0.381
## V14 1 80653.285 738397.346 11152909.321 0.382 0.381
## V18 1 80662.614 725387.404 11165919.264 0.381 0.381
## V7 1 80670.499 714379.966 11176926.702 0.380 0.380
## V6 1 80673.942 709569.518 11181737.150 0.380 0.380
## V10 1 80687.794 690195.769 11201110.899 0.379 0.379
## V4 1 80697.005 677295.053 11214011.615 0.378 0.378
## V5 1 80697.782 676206.043 11215100.625 0.378 0.378
## V3 1 80699.136 674309.104 11216997.563 0.378 0.378
## V12 1 80706.878 663451.352 11227855.316 0.377 0.377
## V17 1 80713.221 654546.774 11236759.894 0.377 0.377
## V19 1 80719.269 646051.086 11245255.581 0.377 0.376
## V9 1 80729.713 631363.752 11259942.915 0.376 0.375
## V11 1 80740.292 616468.338 11274838.330 0.375 0.375
## V13 1 80740.937 615560.247 11275746.421 0.375 0.375
## V8 1 80775.483 566775.477 11324531.190 0.372 0.372
## V2 1 81156.765 14118.433 11877188.235 0.341 0.341
## V1 1 81162.765 5209.525 11886097.143 0.341 0.341
## V35 1 81163.025 4822.654 11886484.013 0.341 0.341
## V34 1 81164.296 2934.251 11888372.417 0.341 0.341
## V28 1 81164.310 2913.436 11888393.232 0.341 0.341
## V41 1 81164.408 2768.849 11888537.819 0.341 0.341
## V40 1 81164.525 2593.802 11888712.865 0.341 0.341
## V30 1 81164.541 2571.066 11888735.602 0.341 0.341
## V21 1 81164.804 2179.757 11889126.910 0.341 0.340
## V47 1 81165.069 1786.025 11889520.642 0.341 0.340
## V45 1 81165.138 1683.271 11889623.396 0.341 0.340
## V22 1 81165.181 1619.752 11889686.916 0.341 0.340
## V42 1 81165.349 1369.950 11889936.718 0.341 0.340
## V49 1 81165.354 1361.949 11889944.719 0.341 0.340
## V26 1 81165.382 1320.597 11889986.070 0.341 0.340
## V32 1 81165.432 1246.338 11890060.330 0.341 0.340
## V25 1 81165.537 1090.143 11890216.525 0.341 0.340
## V24 1 81165.659 909.456 11890397.212 0.341 0.340
## V44 1 81165.710 834.089 11890472.579 0.341 0.340
## V29 1 81165.736 794.871 11890511.796 0.341 0.340
## V31 1 81165.768 746.873 11890559.794 0.341 0.340
## V48 1 81165.769 746.470 11890560.198 0.341 0.340
## V36 1 81165.887 570.637 11890736.030 0.341 0.340
## V33 1 81165.901 549.267 11890757.401 0.341 0.340
## V39 1 81165.918 524.132 11890782.536 0.341 0.340
## V46 1 81166.053 324.359 11890982.308 0.341 0.340
## V43 1 81166.145 186.958 11891119.710 0.341 0.340
## V50 1 81166.183 130.660 11891176.007 0.341 0.340
## V38 1 81166.192 117.332 11891189.335 0.341 0.340
## V37 1 81166.212 87.033 11891219.635 0.341 0.340
## V27 1 81166.219 77.789 11891228.879 0.341 0.340
## V23 1 81166.243 41.998 11891264.669 0.341 0.340
## --------------------------------------------------------------------------------
##
## - V20
##
##
## Step 4 : AIC = 80643.11
## Y ~ V51 + V52 + V15 + V20
##
## --------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## --------------------------------------------------------------------------------
## V16 1 80091.127 745052.154 10393683.324 0.424 0.423
## V14 1 80097.445 736842.434 10401893.044 0.423 0.423
## V18 1 80113.318 716188.694 10422546.784 0.422 0.422
## V6 1 80124.650 701417.870 10437317.608 0.421 0.421
## V7 1 80129.728 694792.454 10443943.024 0.421 0.421
## V4 1 80136.615 685799.656 10452935.822 0.420 0.420
## V3 1 80145.004 674835.712 10463899.766 0.420 0.419
## V17 1 80152.004 665678.731 10473056.747 0.419 0.419
## V5 1 80152.376 665191.517 10473543.961 0.419 0.419
## V10 1 80152.792 664647.430 10474088.048 0.419 0.419
## V12 1 80156.629 659623.069 10479112.409 0.419 0.419
## V19 1 80166.056 647270.895 10491464.582 0.418 0.418
## V9 1 80167.322 645610.463 10493125.014 0.418 0.418
## V11 1 80188.050 618395.067 10520340.411 0.417 0.416
## V13 1 80192.690 612292.791 10526442.687 0.416 0.416
## V8 1 80218.268 578591.241 10560144.236 0.414 0.414
## V2 1 80632.629 17358.797 11121376.681 0.383 0.383
## V41 1 80642.511 3615.994 11135119.483 0.383 0.382
## V35 1 80642.629 3452.035 11135283.442 0.383 0.382
## V28 1 80642.980 2962.695 11135772.783 0.383 0.382
## V1 1 80643.172 2696.630 11136038.847 0.383 0.382
## V21 1 80643.233 2611.144 11136124.334 0.383 0.382
## V47 1 80643.255 2581.073 11136154.404 0.383 0.382
## V40 1 80643.308 2507.408 11136228.069 0.383 0.382
## V30 1 80643.376 2412.324 11136323.154 0.383 0.382
## V26 1 80644.108 1393.902 11137341.575 0.382 0.382
## V31 1 80644.152 1331.610 11137403.868 0.382 0.382
## V44 1 80644.241 1208.133 11137527.344 0.382 0.382
## V34 1 80644.252 1193.359 11137542.119 0.382 0.382
## V42 1 80644.316 1103.567 11137631.911 0.382 0.382
## V36 1 80644.456 909.177 11137826.301 0.382 0.382
## V29 1 80644.530 806.689 11137928.789 0.382 0.382
## V45 1 80644.582 733.968 11138001.509 0.382 0.382
## V49 1 80644.609 695.580 11138039.897 0.382 0.382
## V32 1 80644.697 573.949 11138161.528 0.382 0.382
## V24 1 80644.705 561.949 11138173.529 0.382 0.382
## V22 1 80644.732 524.894 11138210.583 0.382 0.382
## V43 1 80644.809 417.798 11138317.680 0.382 0.382
## V25 1 80644.838 377.212 11138358.266 0.382 0.382
## V39 1 80644.891 303.320 11138432.157 0.382 0.382
## V50 1 80644.917 267.094 11138468.384 0.382 0.382
## V37 1 80644.920 263.941 11138471.537 0.382 0.382
## V48 1 80644.954 216.011 11138519.467 0.382 0.382
## V33 1 80645.018 127.046 11138608.432 0.382 0.382
## V46 1 80645.067 59.123 11138676.354 0.382 0.382
## V23 1 80645.088 29.575 11138705.903 0.382 0.382
## V38 1 80645.096 18.971 11138716.506 0.382 0.382
## V27 1 80645.109 0.271 11138735.207 0.382 0.382
## --------------------------------------------------------------------------------
##
## - V16
##
##
## Step 5 : AIC = 80091.13
## Y ~ V51 + V52 + V15 + V20 + V16
##
## --------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## --------------------------------------------------------------------------------
## V14 1 79524.715 712689.802 9680993.521 0.463 0.463
## V18 1 79525.395 711866.910 9681816.413 0.463 0.463
## V6 1 79535.436 699711.387 9693971.937 0.463 0.462
## V7 1 79539.536 694743.102 9698940.222 0.462 0.462
## V5 1 79549.892 682182.413 9711500.911 0.462 0.461
## V4 1 79552.326 679227.902 9714455.422 0.461 0.461
## V10 1 79554.667 676385.961 9717297.363 0.461 0.461
## V12 1 79560.467 669339.574 9724343.749 0.461 0.460
## V3 1 79567.480 660813.324 9732869.999 0.460 0.460
## V17 1 79571.694 655686.758 9737996.566 0.460 0.460
## V19 1 79573.630 653330.768 9740352.556 0.460 0.460
## V11 1 79590.788 632422.634 9761260.689 0.459 0.458
## V9 1 79597.230 624560.868 9769122.456 0.458 0.458
## V13 1 79608.368 610954.373 9782728.951 0.458 0.457
## V8 1 79625.616 589845.114 9803838.210 0.456 0.456
## V2 1 80078.715 18702.583 10374980.741 0.425 0.424
## V41 1 80088.379 6165.531 10387517.793 0.424 0.424
## V1 1 80091.207 2493.670 10391189.653 0.424 0.423
## V35 1 80091.260 2424.678 10391258.646 0.424 0.423
## V21 1 80091.533 2069.912 10391613.412 0.424 0.423
## V47 1 80091.538 2063.291 10391620.032 0.424 0.423
## V28 1 80091.609 1971.586 10391711.737 0.424 0.423
## V40 1 80091.632 1941.392 10391741.932 0.424 0.423
## V30 1 80091.666 1897.676 10391785.647 0.424 0.423
## V29 1 80092.136 1286.511 10392396.813 0.424 0.423
## V25 1 80092.270 1112.848 10392570.476 0.424 0.423
## V44 1 80092.272 1110.262 10392573.062 0.424 0.423
## V26 1 80092.351 1008.005 10392675.318 0.424 0.423
## V42 1 80092.551 747.869 10392935.455 0.424 0.423
## V36 1 80092.560 735.729 10392947.595 0.424 0.423
## V45 1 80092.576 715.574 10392967.750 0.424 0.423
## V22 1 80092.592 695.332 10392987.991 0.424 0.423
## V48 1 80092.599 685.798 10392997.526 0.424 0.423
## V31 1 80092.611 670.548 10393012.776 0.424 0.423
## V46 1 80092.672 590.781 10393092.543 0.424 0.423
## V50 1 80092.733 512.104 10393171.219 0.424 0.423
## V34 1 80092.753 485.757 10393197.567 0.424 0.423
## V24 1 80092.761 474.710 10393208.614 0.424 0.423
## V32 1 80092.824 393.624 10393289.700 0.424 0.423
## V27 1 80092.868 335.951 10393347.373 0.424 0.423
## V39 1 80092.900 294.687 10393388.637 0.424 0.423
## V49 1 80092.967 207.781 10393475.542 0.424 0.423
## V43 1 80093.048 102.234 10393581.090 0.424 0.423
## V23 1 80093.055 92.880 10393590.443 0.424 0.423
## V33 1 80093.087 51.483 10393631.841 0.424 0.423
## V38 1 80093.096 40.655 10393642.669 0.424 0.423
## V37 1 80093.096 40.508 10393642.816 0.424 0.423
## --------------------------------------------------------------------------------
##
## - V14
##
##
## Step 6 : AIC = 79524.72
## Y ~ V51 + V52 + V15 + V20 + V16 + V14
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V7 1 78907.750 720608.166 8960385.356 0.503 0.503
## V12 1 78928.079 697815.000 8983178.521 0.502 0.501
## V3 1 78931.684 693767.898 8987225.623 0.502 0.501
## V6 1 78933.817 691372.079 8989621.443 0.502 0.501
## V5 1 78938.506 686102.225 8994891.297 0.501 0.501
## V18 1 78949.893 673293.733 9007699.788 0.501 0.500
## V10 1 78951.907 671025.581 9009967.940 0.500 0.500
## V19 1 78957.432 664802.926 9016190.595 0.500 0.500
## V4 1 78964.197 657177.137 9023816.385 0.500 0.499
## V17 1 78972.383 647941.455 9033052.067 0.499 0.499
## V9 1 78984.311 634465.896 9046527.626 0.498 0.498
## V11 1 78997.550 619487.030 9061506.491 0.498 0.497
## V8 1 79006.792 609015.512 9071978.009 0.497 0.497
## V13 1 79018.271 595991.896 9085001.626 0.496 0.496
## V2 1 79514.228 15095.800 9665897.722 0.464 0.464
## V41 1 79522.444 5166.044 9675827.477 0.464 0.463
## V1 1 79523.565 3810.609 9677182.912 0.463 0.463
## V40 1 79524.658 2488.049 9678505.472 0.463 0.463
## V35 1 79524.742 2386.455 9678607.067 0.463 0.463
## V47 1 79524.810 2305.203 9678688.319 0.463 0.463
## V21 1 79525.231 1794.839 9679198.682 0.463 0.463
## V26 1 79525.370 1626.722 9679366.800 0.463 0.463
## V30 1 79525.471 1504.973 9679488.549 0.463 0.463
## V25 1 79525.591 1360.446 9679633.075 0.463 0.463
## V48 1 79525.597 1352.751 9679640.770 0.463 0.463
## V42 1 79525.609 1337.951 9679655.570 0.463 0.463
## V44 1 79525.685 1245.735 9679747.787 0.463 0.463
## V24 1 79525.954 921.070 9680072.451 0.463 0.463
## V28 1 79525.969 902.360 9680091.162 0.463 0.463
## V50 1 79525.995 871.676 9680121.846 0.463 0.463
## V45 1 79526.016 845.732 9680147.790 0.463 0.463
## V46 1 79526.131 706.998 9680286.523 0.463 0.463
## V27 1 79526.182 644.524 9680348.997 0.463 0.463
## V29 1 79526.208 613.970 9680379.551 0.463 0.463
## V31 1 79526.241 573.393 9680420.128 0.463 0.463
## V36 1 79526.246 567.201 9680426.321 0.463 0.463
## V34 1 79526.358 431.822 9680561.700 0.463 0.463
## V38 1 79526.402 378.369 9680615.153 0.463 0.463
## V22 1 79526.444 327.485 9680666.036 0.463 0.463
## V37 1 79526.528 226.820 9680766.702 0.463 0.463
## V43 1 79526.545 205.973 9680787.548 0.463 0.463
## V32 1 79526.571 174.922 9680818.599 0.463 0.463
## V39 1 79526.637 94.370 9680899.151 0.463 0.463
## V49 1 79526.694 25.563 9680967.958 0.463 0.463
## V23 1 79526.700 18.013 9680975.508 0.463 0.463
## V33 1 79526.713 3.165 9680990.357 0.463 0.463
## -------------------------------------------------------------------------------
##
## - V7
##
##
## Step 7 : AIC = 78907.75
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V6 1 78258.066 700811.169 8259574.187 0.542 0.542
## V5 1 78269.684 688809.603 8271575.752 0.541 0.541
## V10 1 78273.558 684804.372 8275580.984 0.541 0.541
## V19 1 78275.617 682675.068 8277710.288 0.541 0.541
## V12 1 78276.716 681538.319 8278847.037 0.541 0.541
## V3 1 78281.913 676159.041 8284226.314 0.541 0.540
## V18 1 78285.854 672078.322 8288307.033 0.540 0.540
## V17 1 78293.037 664635.273 8295750.083 0.540 0.540
## V9 1 78309.702 647340.229 8313045.126 0.539 0.539
## V4 1 78312.759 644163.536 8316221.820 0.539 0.538
## V13 1 78344.831 610765.853 8349619.503 0.537 0.537
## V11 1 78352.650 602602.750 8357782.606 0.537 0.536
## V8 1 78360.477 594424.084 8365961.272 0.536 0.536
## V2 1 78895.498 15945.304 8944440.052 0.504 0.504
## V47 1 78906.640 3482.297 8956903.058 0.503 0.503
## V41 1 78906.849 3248.053 8957137.302 0.503 0.503
## V35 1 78907.239 2811.860 8957573.496 0.503 0.503
## V26 1 78907.281 2764.020 8957621.335 0.503 0.503
## V1 1 78907.369 2666.018 8957719.337 0.503 0.503
## V25 1 78907.684 2313.120 8958072.235 0.503 0.503
## V48 1 78907.948 2017.384 8958367.971 0.503 0.503
## V40 1 78907.981 1980.716 8958404.640 0.503 0.503
## V44 1 78908.423 1485.654 8958899.701 0.503 0.503
## V30 1 78908.647 1234.580 8959150.776 0.503 0.503
## V45 1 78908.712 1162.632 8959222.724 0.503 0.503
## V21 1 78908.954 891.589 8959493.767 0.503 0.503
## V50 1 78909.019 818.560 8959566.796 0.503 0.503
## V28 1 78909.082 747.937 8959637.419 0.503 0.503
## V49 1 78909.117 708.651 8959676.705 0.503 0.503
## V24 1 78909.128 697.042 8959688.314 0.503 0.503
## V31 1 78909.165 654.826 8959730.530 0.503 0.503
## V22 1 78909.303 500.484 8959884.872 0.503 0.503
## V36 1 78909.348 450.377 8959934.979 0.503 0.503
## V34 1 78909.356 441.091 8959944.265 0.503 0.503
## V32 1 78909.398 394.122 8959991.234 0.503 0.503
## V27 1 78909.468 315.980 8960069.376 0.503 0.503
## V43 1 78909.486 296.040 8960089.315 0.503 0.503
## V46 1 78909.577 193.870 8960191.485 0.503 0.503
## V39 1 78909.615 151.310 8960234.046 0.503 0.503
## V42 1 78909.621 144.513 8960240.843 0.503 0.503
## V38 1 78909.625 140.365 8960244.991 0.503 0.503
## V29 1 78909.686 71.206 8960314.150 0.503 0.503
## V23 1 78909.705 50.929 8960334.426 0.503 0.503
## V37 1 78909.744 6.239 8960379.116 0.503 0.503
## V33 1 78909.749 1.496 8960383.859 0.503 0.503
## -------------------------------------------------------------------------------
##
## - V6
##
##
## Step 8 : AIC = 78258.07
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V5 1 77566.468 685774.022 7573800.165 0.580 0.580
## V10 1 77569.411 682987.404 7576586.783 0.580 0.579
## V19 1 77576.798 675990.207 7583583.980 0.580 0.579
## V12 1 77578.043 674810.171 7584764.016 0.579 0.579
## V3 1 77578.455 674419.477 7585154.710 0.579 0.579
## V9 1 77588.600 664796.819 7594777.368 0.579 0.578
## V4 1 77598.912 655003.305 7604570.882 0.578 0.578
## V17 1 77601.520 652524.336 7607049.851 0.578 0.578
## V18 1 77608.923 645483.533 7614090.654 0.578 0.577
## V13 1 77635.870 619799.848 7639774.339 0.576 0.576
## V11 1 77639.743 616100.820 7643473.367 0.576 0.576
## V8 1 77642.948 613039.155 7646535.032 0.576 0.576
## V2 1 78237.947 22798.924 8236775.263 0.543 0.543
## V35 1 78256.107 4084.521 8255489.666 0.542 0.542
## V41 1 78256.864 3304.208 8256269.979 0.542 0.542
## V26 1 78257.571 2574.407 8256999.780 0.542 0.542
## V47 1 78257.652 2490.704 8257083.483 0.542 0.542
## V48 1 78258.656 1454.589 8258119.598 0.542 0.542
## V25 1 78258.712 1397.390 8258176.797 0.542 0.542
## V30 1 78258.730 1378.418 8258195.769 0.542 0.542
## V50 1 78258.805 1300.927 8258273.260 0.542 0.542
## V44 1 78258.896 1207.620 8258366.567 0.542 0.542
## V1 1 78258.987 1113.190 8258460.996 0.542 0.542
## V36 1 78259.313 776.390 8258797.797 0.542 0.542
## V21 1 78259.326 762.866 8258811.321 0.542 0.542
## V32 1 78259.340 748.795 8258825.392 0.542 0.542
## V40 1 78259.461 623.631 8258950.556 0.542 0.542
## V28 1 78259.550 532.635 8259041.552 0.542 0.542
## V24 1 78259.674 404.209 8259169.978 0.542 0.542
## V22 1 78259.682 395.703 8259178.484 0.542 0.542
## V42 1 78259.820 253.005 8259321.182 0.542 0.542
## V38 1 78259.842 231.261 8259342.926 0.542 0.542
## V45 1 78259.885 186.784 8259387.403 0.542 0.542
## V49 1 78259.892 179.151 8259395.036 0.542 0.542
## V46 1 78259.906 164.269 8259409.918 0.542 0.542
## V23 1 78259.911 159.529 8259414.658 0.542 0.542
## V34 1 78259.924 146.483 8259427.704 0.542 0.542
## V39 1 78259.935 135.229 8259438.958 0.542 0.542
## V31 1 78259.980 88.671 8259485.516 0.542 0.542
## V43 1 78259.987 81.540 8259492.647 0.542 0.542
## V27 1 78259.994 74.342 8259499.845 0.542 0.542
## V29 1 78260.040 26.186 8259548.001 0.542 0.542
## V33 1 78260.062 3.192 8259570.995 0.542 0.542
## V37 1 78260.065 0.967 8259573.220 0.542 0.542
## -------------------------------------------------------------------------------
##
## - V5
##
##
## Step 9 : AIC = 77566.47
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V12 1 76819.889 676389.679 6897410.486 0.618 0.617
## V19 1 76820.964 675463.240 6898336.925 0.618 0.617
## V3 1 76821.214 675247.850 6898552.315 0.618 0.617
## V10 1 76823.981 672861.621 6900938.544 0.617 0.617
## V9 1 76834.870 663464.636 6910335.528 0.617 0.616
## V18 1 76838.245 660549.477 6913250.688 0.617 0.616
## V17 1 76842.972 656464.214 6917335.951 0.616 0.616
## V4 1 76849.470 650845.220 6922954.945 0.616 0.616
## V8 1 76864.411 637906.878 6935893.287 0.615 0.615
## V13 1 76875.366 628404.484 6945395.681 0.615 0.614
## V11 1 76880.374 624056.236 6949743.929 0.615 0.614
## V2 1 77543.403 23686.537 7550113.628 0.581 0.581
## V41 1 77565.289 3007.825 7570792.340 0.580 0.580
## V35 1 77565.309 2988.782 7570811.383 0.580 0.580
## V48 1 77565.767 2555.706 7571244.459 0.580 0.580
## V32 1 77566.030 2306.766 7571493.399 0.580 0.580
## V21 1 77566.429 1929.224 7571870.940 0.580 0.580
## V25 1 77566.464 1895.753 7571904.412 0.580 0.580
## V30 1 77566.637 1732.180 7572067.985 0.580 0.580
## V1 1 77567.213 1186.856 7572613.309 0.580 0.580
## V26 1 77567.384 1025.630 7572774.534 0.580 0.580
## V47 1 77567.456 956.873 7572843.292 0.580 0.580
## V24 1 77567.505 910.538 7572889.627 0.580 0.580
## V36 1 77567.517 899.577 7572900.588 0.580 0.580
## V40 1 77567.586 834.089 7572966.076 0.580 0.580
## V50 1 77567.677 747.939 7573052.225 0.580 0.580
## V43 1 77567.758 671.267 7573128.898 0.580 0.580
## V31 1 77567.779 651.740 7573148.425 0.580 0.580
## V44 1 77567.926 512.593 7573287.572 0.580 0.580
## V28 1 77567.944 495.386 7573304.779 0.580 0.580
## V49 1 77568.081 365.426 7573434.739 0.580 0.580
## V34 1 77568.097 351.095 7573449.070 0.580 0.580
## V27 1 77568.248 208.098 7573592.067 0.580 0.580
## V22 1 77568.321 138.237 7573661.928 0.580 0.580
## V45 1 77568.351 110.168 7573689.997 0.580 0.580
## V38 1 77568.358 103.703 7573696.462 0.580 0.580
## V46 1 77568.373 89.140 7573711.025 0.580 0.580
## V23 1 77568.389 74.639 7573725.526 0.580 0.580
## V29 1 77568.399 64.840 7573735.325 0.580 0.580
## V39 1 77568.415 50.031 7573750.134 0.580 0.580
## V42 1 77568.434 31.652 7573768.513 0.580 0.580
## V33 1 77568.439 26.717 7573773.448 0.580 0.580
## V37 1 77568.467 0.124 7573800.040 0.580 0.580
## -------------------------------------------------------------------------------
##
## - V12
##
##
## Step 10 : AIC = 76819.89
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V19 1 75959.278 704862.597 6192547.889 0.657 0.656
## V10 1 75992.842 678833.555 6218576.931 0.655 0.655
## V3 1 75995.749 676574.240 6220836.246 0.655 0.655
## V18 1 76001.665 671973.673 6225436.813 0.655 0.654
## V4 1 76016.967 660057.346 6237353.140 0.654 0.654
## V13 1 76027.468 651866.787 6245543.699 0.654 0.653
## V9 1 76037.520 644016.504 6253393.982 0.653 0.653
## V17 1 76042.349 640241.455 6257169.031 0.653 0.653
## V8 1 76050.149 634139.350 6263271.136 0.653 0.652
## V11 1 76075.185 614512.812 6282897.674 0.652 0.651
## V2 1 76790.502 27001.405 6870409.081 0.619 0.619
## V41 1 76817.957 3388.636 6894021.850 0.618 0.617
## V48 1 76818.645 2796.260 6894614.225 0.618 0.617
## V35 1 76819.271 2256.570 6895153.916 0.618 0.617
## V32 1 76819.384 2158.760 6895251.726 0.618 0.617
## V30 1 76819.669 1913.879 6895496.607 0.618 0.617
## V28 1 76820.292 1376.484 6896034.002 0.618 0.617
## V25 1 76820.663 1057.291 6896353.195 0.618 0.617
## V40 1 76820.668 1052.862 6896357.624 0.618 0.617
## V21 1 76820.671 1050.183 6896360.303 0.618 0.617
## V26 1 76820.785 951.586 6896458.900 0.618 0.617
## V24 1 76820.799 939.913 6896470.573 0.618 0.617
## V43 1 76820.984 780.623 6896629.863 0.618 0.617
## V31 1 76821.115 667.651 6896742.835 0.618 0.617
## V47 1 76821.121 662.341 6896748.145 0.618 0.617
## V36 1 76821.214 581.712 6896828.774 0.618 0.617
## V1 1 76821.311 498.408 6896912.077 0.618 0.617
## V27 1 76821.461 369.517 6897040.969 0.618 0.617
## V44 1 76821.463 367.632 6897042.853 0.618 0.617
## V34 1 76821.521 317.473 6897093.013 0.618 0.617
## V22 1 76821.582 265.126 6897145.360 0.618 0.617
## V39 1 76821.602 247.958 6897162.528 0.618 0.617
## V49 1 76821.608 242.335 6897168.151 0.618 0.617
## V29 1 76821.714 151.131 6897259.355 0.618 0.617
## V42 1 76821.737 131.431 6897279.055 0.618 0.617
## V46 1 76821.746 123.178 6897287.308 0.618 0.617
## V45 1 76821.812 66.999 6897343.486 0.618 0.617
## V38 1 76821.820 59.724 6897350.762 0.618 0.617
## V50 1 76821.831 50.033 6897360.453 0.618 0.617
## V33 1 76821.874 13.498 6897396.987 0.618 0.617
## V23 1 76821.875 12.163 6897398.323 0.618 0.617
## V37 1 76821.889 0.427 6897410.059 0.618 0.617
## -------------------------------------------------------------------------------
##
## - V19
##
##
## Step 11 : AIC = 75959.28
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V10 1 75009.700 694302.121 5498245.768 0.695 0.695
## V3 1 75020.152 687115.682 5505432.207 0.695 0.694
## V18 1 75037.388 675244.848 5517303.041 0.694 0.694
## V4 1 75052.746 664645.522 5527902.367 0.694 0.693
## V13 1 75065.610 655751.774 5536796.115 0.693 0.693
## V17 1 75071.940 651369.856 5541178.032 0.693 0.692
## V9 1 75102.044 630484.484 5562063.405 0.692 0.691
## V8 1 75114.037 622141.879 5570406.010 0.691 0.691
## V11 1 75135.921 606886.855 5585661.034 0.690 0.690
## V2 1 75923.842 28903.590 6163644.299 0.658 0.658
## V30 1 75957.592 2852.061 6189695.828 0.657 0.656
## V41 1 75958.177 2399.737 6190148.152 0.657 0.656
## V21 1 75959.089 1693.562 6190854.326 0.657 0.656
## V48 1 75959.218 1593.852 6190954.037 0.657 0.656
## V32 1 75959.438 1424.214 6191123.675 0.657 0.656
## V25 1 75959.601 1297.748 6191250.141 0.657 0.656
## V35 1 75959.993 994.143 6191553.746 0.657 0.656
## V40 1 75960.084 923.761 6191624.128 0.657 0.656
## V26 1 75960.325 737.614 6191810.275 0.657 0.656
## V28 1 75960.394 684.165 6191863.724 0.657 0.656
## V44 1 75960.411 670.871 6191877.018 0.657 0.656
## V36 1 75960.516 589.656 6191958.233 0.657 0.656
## V24 1 75960.518 588.399 6191959.489 0.657 0.656
## V34 1 75960.575 543.856 6192004.032 0.657 0.656
## V49 1 75960.701 446.877 6192101.012 0.657 0.656
## V45 1 75960.727 426.442 6192121.447 0.657 0.656
## V43 1 75960.757 402.937 6192144.952 0.657 0.656
## V38 1 75960.779 386.517 6192161.372 0.657 0.656
## V37 1 75960.842 337.693 6192210.196 0.657 0.656
## V31 1 75960.886 303.456 6192244.432 0.657 0.656
## V27 1 75960.986 226.080 6192321.809 0.657 0.656
## V39 1 75961.057 170.956 6192376.933 0.657 0.656
## V1 1 75961.062 167.573 6192380.316 0.657 0.656
## V29 1 75961.068 162.817 6192385.072 0.657 0.656
## V50 1 75961.081 152.278 6192395.611 0.657 0.656
## V23 1 75961.117 124.792 6192423.097 0.657 0.656
## V42 1 75961.124 119.642 6192428.247 0.657 0.656
## V47 1 75961.154 95.963 6192451.926 0.657 0.656
## V22 1 75961.213 50.165 6192497.723 0.657 0.656
## V46 1 75961.251 21.036 6192526.853 0.657 0.656
## V33 1 75961.256 17.477 6192530.412 0.657 0.656
## -------------------------------------------------------------------------------
##
## - V10
##
##
## Step 12 : AIC = 75009.7
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V3 1 73942.448 687721.767 4810524.001 0.733 0.733
## V4 1 73955.988 679575.487 4818670.281 0.733 0.732
## V13 1 73969.143 671647.184 4826598.584 0.732 0.732
## V18 1 73997.403 654571.383 4843674.385 0.731 0.731
## V17 1 74001.450 652120.970 4846124.798 0.731 0.731
## V9 1 74016.068 643259.784 4854985.984 0.731 0.730
## V8 1 74019.928 640917.552 4857328.216 0.731 0.730
## V11 1 74104.523 589294.725 4908951.043 0.728 0.727
## V2 1 74975.006 25155.419 5473090.349 0.697 0.696
## V41 1 75009.160 1744.948 5496500.820 0.695 0.695
## V30 1 75009.337 1623.647 5496622.121 0.695 0.695
## V48 1 75009.565 1466.681 5496779.087 0.695 0.695
## V21 1 75009.902 1235.060 5497010.708 0.695 0.695
## V44 1 75010.347 929.536 5497316.232 0.695 0.695
## V36 1 75010.392 899.028 5497346.739 0.695 0.695
## V32 1 75010.447 860.938 5497384.829 0.695 0.695
## V35 1 75010.531 803.152 5497442.615 0.695 0.695
## V28 1 75010.610 749.129 5497496.639 0.695 0.695
## V42 1 75010.732 665.282 5497580.486 0.695 0.695
## V49 1 75010.824 601.858 5497643.910 0.695 0.695
## V40 1 75010.919 536.967 5497708.801 0.695 0.695
## V29 1 75010.928 530.510 5497715.258 0.695 0.695
## V45 1 75011.033 458.429 5497787.339 0.695 0.695
## V27 1 75011.098 413.602 5497832.166 0.695 0.695
## V31 1 75011.152 376.733 5497869.035 0.695 0.695
## V37 1 75011.201 343.190 5497902.578 0.695 0.695
## V26 1 75011.226 325.451 5497920.317 0.695 0.695
## V38 1 75011.275 292.314 5497953.454 0.695 0.695
## V34 1 75011.357 235.562 5498010.206 0.695 0.695
## V39 1 75011.430 185.829 5498059.938 0.695 0.695
## V1 1 75011.433 183.608 5498062.160 0.695 0.695
## V24 1 75011.444 176.068 5498069.700 0.695 0.695
## V25 1 75011.514 127.787 5498117.981 0.695 0.695
## V22 1 75011.673 18.934 5498226.834 0.695 0.695
## V50 1 75011.683 11.901 5498233.866 0.695 0.695
## V43 1 75011.696 2.978 5498242.789 0.695 0.695
## V47 1 75011.696 2.859 5498242.909 0.695 0.695
## V33 1 75011.697 2.171 5498243.596 0.695 0.695
## V46 1 75011.698 1.809 5498243.959 0.695 0.695
## V23 1 75011.700 0.301 5498245.466 0.695 0.695
## -------------------------------------------------------------------------------
##
## - V3
##
##
## Step 13 : AIC = 73942.45
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V13 1 72717.194 683991.100 4126532.901 0.771 0.771
## V4 1 72725.311 679802.895 4130721.105 0.771 0.771
## V8 1 72751.526 666248.269 4144275.731 0.770 0.770
## V18 1 72757.896 662948.094 4147575.907 0.770 0.770
## V17 1 72790.475 646027.425 4164496.576 0.769 0.769
## V9 1 72798.935 641621.968 4168902.033 0.769 0.768
## V11 1 72913.693 581404.293 4229119.707 0.766 0.765
## V2 1 73897.555 28108.473 4782415.528 0.735 0.734
## V30 1 73940.448 2404.116 4808119.884 0.733 0.733
## V48 1 73941.307 1888.304 4808635.697 0.733 0.733
## V42 1 73942.051 1441.072 4809082.929 0.733 0.733
## V21 1 73942.057 1437.459 4809086.542 0.733 0.733
## V28 1 73942.553 1138.973 4809385.027 0.733 0.733
## V40 1 73942.976 885.101 4809638.900 0.733 0.733
## V1 1 73943.007 866.143 4809657.858 0.733 0.733
## V27 1 73943.072 827.167 4809696.834 0.733 0.733
## V49 1 73943.279 703.031 4809820.970 0.733 0.733
## V38 1 73943.312 682.942 4809841.059 0.733 0.733
## V26 1 73943.424 615.813 4809908.187 0.733 0.733
## V41 1 73943.590 515.752 4810008.248 0.733 0.733
## V29 1 73943.672 466.531 4810057.469 0.733 0.733
## V44 1 73943.676 464.287 4810059.713 0.733 0.733
## V45 1 73943.756 416.228 4810107.772 0.733 0.733
## V35 1 73943.871 346.908 4810177.092 0.733 0.733
## V36 1 73943.904 327.395 4810196.605 0.733 0.733
## V24 1 73944.083 219.595 4810304.405 0.733 0.733
## V33 1 73944.148 180.377 4810343.623 0.733 0.733
## V34 1 73944.173 165.558 4810358.443 0.733 0.733
## V32 1 73944.179 161.799 4810362.201 0.733 0.733
## V37 1 73944.187 157.111 4810366.890 0.733 0.733
## V31 1 73944.269 107.977 4810416.024 0.733 0.733
## V46 1 73944.320 77.140 4810446.860 0.733 0.733
## V23 1 73944.343 63.555 4810460.446 0.733 0.733
## V22 1 73944.403 27.388 4810496.612 0.733 0.733
## V39 1 73944.414 20.794 4810503.206 0.733 0.733
## V50 1 73944.435 8.038 4810515.962 0.733 0.733
## V47 1 73944.436 7.307 4810516.694 0.733 0.733
## V43 1 73944.439 5.467 4810518.533 0.733 0.733
## V25 1 73944.448 0.218 4810523.783 0.733 0.733
## -------------------------------------------------------------------------------
##
## - V13
##
##
## Step 14 : AIC = 72717.19
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V8 1 71273.942 681869.204 3444663.697 0.809 0.809
## V4 1 71279.303 679560.704 3446972.197 0.809 0.809
## V18 1 71299.960 670651.133 3455881.767 0.808 0.808
## V17 1 71359.552 644818.500 3481714.401 0.807 0.807
## V9 1 71370.342 640120.433 3486412.468 0.807 0.806
## V11 1 71456.971 602171.937 3524360.964 0.805 0.804
## V2 1 72664.969 27868.600 4098664.301 0.773 0.772
## V42 1 72713.970 2692.993 4123839.908 0.771 0.771
## V48 1 72715.246 2035.212 4124497.688 0.771 0.771
## V1 1 72715.429 1941.138 4124591.762 0.771 0.771
## V30 1 72716.545 1365.885 4125167.015 0.771 0.771
## V27 1 72716.654 1309.703 4125223.197 0.771 0.771
## V28 1 72717.573 835.780 4125697.120 0.771 0.771
## V45 1 72717.587 828.586 4125704.314 0.771 0.771
## V35 1 72718.313 454.284 4126078.616 0.771 0.771
## V40 1 72718.428 395.113 4126137.788 0.771 0.771
## V26 1 72718.445 386.078 4126146.823 0.771 0.771
## V44 1 72718.446 385.774 4126147.127 0.771 0.771
## V46 1 72718.486 364.924 4126167.977 0.771 0.771
## V31 1 72718.496 360.133 4126172.767 0.771 0.771
## V49 1 72718.564 325.072 4126207.829 0.771 0.771
## V37 1 72718.829 188.146 4126344.755 0.771 0.771
## V32 1 72718.912 145.525 4126387.375 0.771 0.771
## V29 1 72718.928 136.995 4126395.906 0.771 0.771
## V41 1 72718.978 111.504 4126421.397 0.771 0.771
## V21 1 72718.987 106.488 4126426.413 0.771 0.771
## V43 1 72719.025 87.290 4126445.611 0.771 0.771
## V23 1 72719.043 77.955 4126454.946 0.771 0.771
## V38 1 72719.055 71.402 4126461.499 0.771 0.771
## V36 1 72719.127 34.607 4126498.294 0.771 0.771
## V39 1 72719.136 29.653 4126503.248 0.771 0.771
## V22 1 72719.138 28.734 4126504.167 0.771 0.771
## V25 1 72719.142 26.882 4126506.019 0.771 0.771
## V33 1 72719.155 20.012 4126512.889 0.771 0.771
## V24 1 72719.164 15.362 4126517.539 0.771 0.771
## V47 1 72719.182 6.036 4126526.865 0.771 0.771
## V50 1 72719.185 4.680 4126528.220 0.771 0.771
## V34 1 72719.188 2.942 4126529.959 0.771 0.771
## -------------------------------------------------------------------------------
##
## - V8
##
##
## Step 15 : AIC = 71273.94
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V4 1 69508.379 682715.971 2761947.726 0.847 0.847
## V18 1 69537.613 672607.429 2772056.268 0.846 0.846
## V9 1 69554.485 666756.354 2777907.343 0.846 0.846
## V17 1 69612.039 646704.398 2797959.299 0.845 0.845
## V11 1 69717.379 609628.000 2835035.697 0.843 0.842
## V2 1 71209.342 28550.796 3416112.901 0.811 0.810
## V42 1 71270.831 2199.624 3442464.073 0.809 0.809
## V1 1 71270.889 2174.669 3442489.028 0.809 0.809
## V48 1 71272.760 1369.791 3443293.906 0.809 0.809
## V40 1 71272.971 1279.014 3443384.683 0.809 0.809
## V28 1 71274.210 745.695 3443918.002 0.809 0.809
## V49 1 71274.292 710.464 3443953.233 0.809 0.809
## V32 1 71274.378 673.455 3443990.242 0.809 0.809
## V45 1 71274.545 601.672 3444062.025 0.809 0.809
## V44 1 71274.618 570.276 3444093.421 0.809 0.809
## V27 1 71274.654 554.435 3444109.262 0.809 0.809
## V24 1 71274.698 535.782 3444127.915 0.809 0.809
## V26 1 71274.915 442.364 3444221.333 0.809 0.809
## V41 1 71275.195 321.866 3444341.831 0.809 0.809
## V46 1 71275.198 320.525 3444343.172 0.809 0.809
## V35 1 71275.314 270.652 3444393.045 0.809 0.809
## V30 1 71275.326 265.551 3444398.146 0.809 0.809
## V29 1 71275.465 205.341 3444458.356 0.809 0.809
## V23 1 71275.499 191.081 3444472.616 0.809 0.809
## V36 1 71275.518 182.761 3444480.936 0.809 0.809
## V37 1 71275.555 166.958 3444496.739 0.809 0.809
## V38 1 71275.597 148.871 3444514.826 0.809 0.809
## V39 1 71275.761 77.991 3444585.706 0.809 0.809
## V47 1 71275.762 77.673 3444586.024 0.809 0.809
## V21 1 71275.834 46.678 3444617.019 0.809 0.809
## V33 1 71275.873 29.968 3444633.729 0.809 0.809
## V50 1 71275.915 11.798 3444651.899 0.809 0.809
## V43 1 71275.918 10.376 3444653.321 0.809 0.809
## V22 1 71275.937 2.150 3444661.547 0.809 0.809
## V31 1 71275.938 1.823 3444661.874 0.809 0.809
## V34 1 71275.940 1.266 3444662.431 0.809 0.809
## V25 1 71275.942 0.002 3444663.695 0.809 0.809
## -------------------------------------------------------------------------------
##
## - V4
##
##
## Step 16 : AIC = 69508.38
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V18 1 67262.095 676526.525 2085421.201 0.884 0.884
## V9 1 67285.194 670497.941 2091449.785 0.884 0.884
## V17 1 67386.735 643789.603 2118158.123 0.883 0.882
## V11 1 67451.364 626612.736 2135334.990 0.882 0.881
## V2 1 69427.104 28594.131 2733353.595 0.848 0.848
## V40 1 69506.044 1495.839 2760451.887 0.847 0.847
## V42 1 69507.003 1165.196 2760782.531 0.847 0.847
## V1 1 69507.594 961.293 2760986.434 0.847 0.847
## V27 1 69508.298 718.236 2761229.490 0.847 0.847
## V44 1 69508.468 659.666 2761288.060 0.847 0.847
## V48 1 69508.501 648.424 2761299.302 0.847 0.847
## V24 1 69508.589 617.894 2761329.833 0.847 0.847
## V45 1 69508.629 604.080 2761343.646 0.847 0.847
## V26 1 69508.778 552.633 2761395.093 0.847 0.847
## V21 1 69509.093 444.041 2761503.686 0.847 0.847
## V41 1 69509.101 441.330 2761506.396 0.847 0.847
## V39 1 69509.163 419.945 2761527.782 0.847 0.847
## V49 1 69509.346 356.670 2761591.056 0.847 0.847
## V34 1 69509.526 294.548 2761653.178 0.847 0.847
## V33 1 69509.955 146.417 2761801.310 0.847 0.847
## V37 1 69509.980 137.973 2761809.753 0.847 0.847
## V32 1 69510.032 119.856 2761827.870 0.847 0.847
## V28 1 69510.040 117.078 2761830.649 0.847 0.847
## V50 1 69510.102 95.716 2761852.011 0.847 0.847
## V43 1 69510.193 64.361 2761883.365 0.847 0.847
## V23 1 69510.224 53.540 2761894.187 0.847 0.847
## V29 1 69510.265 39.452 2761908.275 0.847 0.847
## V30 1 69510.283 33.225 2761914.501 0.847 0.847
## V22 1 69510.311 23.673 2761924.053 0.847 0.847
## V35 1 69510.333 16.048 2761931.679 0.847 0.847
## V47 1 69510.353 9.240 2761938.487 0.847 0.847
## V36 1 69510.363 5.684 2761942.042 0.847 0.847
## V25 1 69510.375 1.430 2761946.296 0.847 0.847
## V46 1 69510.379 0.268 2761947.459 0.847 0.847
## V31 1 69510.379 0.139 2761947.587 0.847 0.847
## V38 1 69510.379 0.113 2761947.613 0.847 0.847
## -------------------------------------------------------------------------------
##
## - V18
##
##
## Step 17 : AIC = 67262.1
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V9 1 64128.980 675999.702 1409421.499 0.922 0.922
## V17 1 64228.065 658438.965 1426982.236 0.921 0.921
## V11 1 64398.119 627789.014 1457632.187 0.919 0.919
## V2 1 67138.363 32511.337 2052909.865 0.886 0.886
## V40 1 67257.256 1781.752 2083639.450 0.884 0.884
## V1 1 67260.751 871.379 2084549.822 0.884 0.884
## V26 1 67261.729 616.682 2084804.519 0.884 0.884
## V24 1 67261.997 546.686 2084874.515 0.884 0.884
## V27 1 67262.201 493.743 2084927.459 0.884 0.884
## V45 1 67262.493 417.505 2085003.696 0.884 0.884
## V23 1 67262.576 395.996 2085025.205 0.884 0.884
## V34 1 67262.763 347.145 2085074.056 0.884 0.884
## V39 1 67262.871 318.935 2085102.267 0.884 0.884
## V48 1 67263.156 244.785 2085176.416 0.884 0.884
## V21 1 67263.212 230.130 2085191.072 0.884 0.884
## V37 1 67263.265 216.254 2085204.947 0.884 0.884
## V49 1 67263.467 163.802 2085257.400 0.884 0.884
## V42 1 67263.482 159.748 2085261.453 0.884 0.884
## V25 1 67263.515 151.282 2085269.920 0.884 0.884
## V41 1 67263.720 97.850 2085323.352 0.884 0.884
## V44 1 67263.758 87.871 2085333.331 0.884 0.884
## V35 1 67263.764 86.434 2085334.767 0.884 0.884
## V31 1 67263.765 86.004 2085335.197 0.884 0.884
## V50 1 67263.777 82.921 2085338.281 0.884 0.884
## V30 1 67263.805 75.687 2085345.515 0.884 0.884
## V47 1 67263.877 56.771 2085364.431 0.884 0.884
## V28 1 67263.945 39.130 2085382.071 0.884 0.884
## V43 1 67263.982 29.591 2085391.610 0.884 0.884
## V29 1 67264.040 14.462 2085406.739 0.884 0.884
## V46 1 67264.054 10.850 2085410.351 0.884 0.884
## V38 1 67264.059 9.374 2085411.827 0.884 0.884
## V32 1 67264.075 5.274 2085415.927 0.884 0.884
## V36 1 67264.090 1.265 2085419.937 0.884 0.884
## V33 1 67264.092 0.981 2085420.220 0.884 0.884
## V22 1 67264.095 0.090 2085421.111 0.884 0.884
## -------------------------------------------------------------------------------
##
## - V9
##
##
## Step 18 : AIC = 64128.98
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9
##
## -------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## -------------------------------------------------------------------------------
## V17 1 58972.904 669653.731 739767.768 0.959 0.959
## V11 1 58973.772 669573.491 739848.007 0.959 0.959
## V2 1 63951.273 31299.535 1378121.964 0.924 0.923
## V1 1 64123.939 1239.488 1408182.011 0.922 0.922
## V24 1 64126.096 859.985 1408561.514 0.922 0.922
## V27 1 64127.531 607.306 1408814.193 0.922 0.922
## V45 1 64127.745 569.634 1408851.864 0.922 0.922
## V40 1 64127.792 561.325 1408860.174 0.922 0.922
## V34 1 64128.066 513.028 1408908.471 0.922 0.922
## V37 1 64129.057 338.593 1409082.906 0.922 0.922
## V26 1 64129.380 281.736 1409139.763 0.922 0.922
## V31 1 64129.711 223.420 1409198.078 0.922 0.922
## V49 1 64129.844 199.956 1409221.542 0.922 0.922
## V47 1 64129.893 191.372 1409230.127 0.922 0.922
## V50 1 64130.310 118.010 1409303.489 0.922 0.922
## V21 1 64130.428 97.194 1409324.305 0.922 0.922
## V41 1 64130.471 89.539 1409331.960 0.922 0.922
## V38 1 64130.477 88.586 1409332.913 0.922 0.922
## V39 1 64130.599 67.003 1409354.496 0.922 0.922
## V43 1 64130.674 53.825 1409367.674 0.922 0.922
## V30 1 64130.686 51.699 1409369.799 0.922 0.922
## V32 1 64130.694 50.229 1409371.270 0.922 0.922
## V36 1 64130.785 34.265 1409387.234 0.922 0.922
## V23 1 64130.859 21.291 1409400.208 0.922 0.922
## V35 1 64130.860 21.066 1409400.433 0.922 0.922
## V44 1 64130.868 19.656 1409401.843 0.922 0.922
## V42 1 64130.886 16.552 1409404.947 0.922 0.922
## V25 1 64130.894 15.165 1409406.334 0.922 0.922
## V48 1 64130.896 14.684 1409406.815 0.922 0.922
## V28 1 64130.899 14.253 1409407.245 0.922 0.922
## V29 1 64130.955 4.304 1409417.195 0.922 0.922
## V46 1 64130.965 2.489 1409419.010 0.922 0.922
## V22 1 64130.978 0.351 1409421.148 0.922 0.922
## V33 1 64130.979 0.019 1409421.480 0.922 0.922
## -------------------------------------------------------------------------------
##
## - V17
##
##
## Step 19 : AIC = 58972.9
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V11 1 37293.052 690524.032 49243.736 0.997 0.997
## V2 1 58656.589 28849.958 710917.810 0.961 0.960
## V1 1 58953.931 1936.351 737831.417 0.959 0.959
## V45 1 58967.389 694.427 739073.341 0.959 0.959
## V24 1 58969.378 510.643 739257.125 0.959 0.959
## V40 1 58971.356 327.952 739439.816 0.959 0.959
## V31 1 58971.698 296.332 739471.436 0.959 0.959
## V33 1 58972.577 215.111 739552.657 0.959 0.959
## V46 1 58972.881 186.980 739580.788 0.959 0.959
## V21 1 58972.928 182.611 739585.157 0.959 0.959
## V37 1 58973.035 172.762 739595.006 0.959 0.959
## V41 1 58973.158 161.429 739606.339 0.959 0.959
## V22 1 58973.646 116.273 739651.495 0.959 0.959
## V34 1 58973.730 108.551 739659.217 0.959 0.959
## V25 1 58974.125 71.980 739695.788 0.959 0.959
## V35 1 58974.235 61.843 739705.925 0.959 0.959
## V27 1 58974.306 55.324 739712.444 0.959 0.959
## V38 1 58974.501 37.297 739730.471 0.959 0.959
## V29 1 58974.504 37.001 739730.767 0.959 0.959
## V28 1 58974.637 24.715 739743.053 0.959 0.959
## V48 1 58974.655 22.991 739744.777 0.959 0.959
## V44 1 58974.679 20.808 739746.960 0.959 0.959
## V23 1 58974.686 20.106 739747.662 0.959 0.959
## V39 1 58974.835 6.347 739761.421 0.959 0.959
## V43 1 58974.840 5.902 739761.866 0.959 0.959
## V42 1 58974.850 4.999 739762.769 0.959 0.959
## V36 1 58974.859 4.143 739763.625 0.959 0.959
## V26 1 58974.867 3.437 739764.331 0.959 0.959
## V49 1 58974.874 2.780 739764.988 0.959 0.959
## V32 1 58974.884 1.858 739765.910 0.959 0.959
## V47 1 58974.901 0.277 739767.491 0.959 0.959
## V30 1 58974.903 0.080 739767.688 0.959 0.959
## V50 1 58974.904 0.011 739767.757 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V11
##
##
## Step 20 : AIC = 37293.05
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11
##
## ----------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ----------------------------------------------------------------------------
## V2 1 28850.433 32102.815 17140.921 0.999 0.999
## V1 1 36712.859 3455.543 45788.193 0.997 0.997
## V39 1 37290.095 30.495 49213.241 0.997 0.997
## V38 1 37293.478 9.686 49234.050 0.997 0.997
## V47 1 37293.579 9.064 49234.672 0.997 0.997
## V26 1 37293.811 7.633 49236.104 0.997 0.997
## V46 1 37293.922 6.955 49236.782 0.997 0.997
## V50 1 37294.233 5.038 49238.699 0.997 0.997
## V28 1 37294.275 4.778 49238.958 0.997 0.997
## V24 1 37294.307 4.584 49239.153 0.997 0.997
## V43 1 37294.341 4.373 49239.363 0.997 0.997
## V35 1 37294.372 4.182 49239.555 0.997 0.997
## V41 1 37294.391 4.069 49239.667 0.997 0.997
## V42 1 37294.475 3.552 49240.185 0.997 0.997
## V49 1 37294.533 3.191 49240.546 0.997 0.997
## V44 1 37294.820 1.425 49242.312 0.997 0.997
## V34 1 37294.841 1.300 49242.436 0.997 0.997
## V25 1 37294.854 1.219 49242.517 0.997 0.997
## V22 1 37294.867 1.138 49242.599 0.997 0.997
## V31 1 37294.882 1.044 49242.692 0.997 0.997
## V45 1 37294.885 1.025 49242.711 0.997 0.997
## V27 1 37294.894 0.969 49242.767 0.997 0.997
## V21 1 37294.977 0.462 49243.274 0.997 0.997
## V33 1 37294.987 0.401 49243.335 0.997 0.997
## V40 1 37294.992 0.365 49243.371 0.997 0.997
## V23 1 37295.019 0.200 49243.536 0.997 0.997
## V29 1 37295.019 0.199 49243.537 0.997 0.997
## V37 1 37295.027 0.155 49243.582 0.997 0.997
## V30 1 37295.029 0.142 49243.594 0.997 0.997
## V36 1 37295.040 0.070 49243.666 0.997 0.997
## V32 1 37295.050 0.013 49243.723 0.997 0.997
## V48 1 37295.051 0.004 49243.733 0.997 0.997
## ----------------------------------------------------------------------------
##
## - V2
##
##
## Step 21 : AIC = 28850.43
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11 + V2
##
## ---------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------
## V1 1 22088.480 9779.994 7360.927 1.000 1.000
## V33 1 28849.418 6.456 17134.465 0.999 0.999
## V49 1 28850.280 4.610 17136.311 0.999 0.999
## V37 1 28850.319 4.527 17136.394 0.999 0.999
## V38 1 28850.458 4.230 17136.691 0.999 0.999
## V39 1 28851.393 2.227 17138.694 0.999 0.999
## V23 1 28851.465 2.072 17138.849 0.999 0.999
## V22 1 28851.469 2.064 17138.857 0.999 0.999
## V24 1 28851.719 1.530 17139.391 0.999 0.999
## V34 1 28851.811 1.333 17139.588 0.999 0.999
## V50 1 28851.930 1.077 17139.844 0.999 0.999
## V45 1 28851.936 1.064 17139.856 0.999 0.999
## V40 1 28851.963 1.006 17139.915 0.999 0.999
## V42 1 28852.139 0.629 17140.292 0.999 0.999
## V47 1 28852.185 0.530 17140.391 0.999 0.999
## V36 1 28852.211 0.475 17140.446 0.999 0.999
## V35 1 28852.218 0.461 17140.460 0.999 0.999
## V27 1 28852.240 0.414 17140.507 0.999 0.999
## V21 1 28852.250 0.391 17140.530 0.999 0.999
## V44 1 28852.275 0.339 17140.582 0.999 0.999
## V43 1 28852.290 0.307 17140.614 0.999 0.999
## V29 1 28852.326 0.229 17140.692 0.999 0.999
## V26 1 28852.366 0.142 17140.779 0.999 0.999
## V32 1 28852.406 0.059 17140.862 0.999 0.999
## V28 1 28852.407 0.056 17140.864 0.999 0.999
## V25 1 28852.418 0.031 17140.890 0.999 0.999
## V48 1 28852.420 0.028 17140.893 0.999 0.999
## V46 1 28852.429 0.008 17140.913 0.999 0.999
## V41 1 28852.432 0.003 17140.918 0.999 0.999
## V31 1 28852.432 0.002 17140.919 0.999 0.999
## V30 1 28852.433 0.000 17140.921 0.999 0.999
## ---------------------------------------------------------------------------
##
## - V1
##
##
## Step 22 : AIC = 22088.48
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11 + V2 + V1
##
## ------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------
## V37 1 22084.832 5.194 7355.733 1.000 1.000
## V27 1 22085.352 4.715 7356.212 1.000 1.000
## V24 1 22088.302 2.003 7358.924 1.000 1.000
## V42 1 22088.372 1.939 7358.988 1.000 1.000
## V33 1 22088.974 1.385 7359.542 1.000 1.000
## V47 1 22089.427 0.969 7359.958 1.000 1.000
## V36 1 22089.480 0.920 7360.007 1.000 1.000
## V50 1 22089.650 0.764 7360.163 1.000 1.000
## V44 1 22089.777 0.646 7360.280 1.000 1.000
## V49 1 22089.832 0.596 7360.331 1.000 1.000
## V22 1 22089.937 0.499 7360.428 1.000 1.000
## V29 1 22089.995 0.446 7360.481 1.000 1.000
## V21 1 22090.030 0.414 7360.513 1.000 1.000
## V35 1 22090.073 0.375 7360.552 1.000 1.000
## V45 1 22090.201 0.257 7360.670 1.000 1.000
## V30 1 22090.242 0.219 7360.708 1.000 1.000
## V25 1 22090.293 0.172 7360.754 1.000 1.000
## V43 1 22090.332 0.136 7360.791 1.000 1.000
## V23 1 22090.335 0.134 7360.793 1.000 1.000
## V39 1 22090.342 0.127 7360.800 1.000 1.000
## V48 1 22090.344 0.125 7360.802 1.000 1.000
## V38 1 22090.366 0.105 7360.822 1.000 1.000
## V34 1 22090.385 0.087 7360.840 1.000 1.000
## V28 1 22090.411 0.063 7360.864 1.000 1.000
## V41 1 22090.414 0.061 7360.866 1.000 1.000
## V46 1 22090.418 0.057 7360.870 1.000 1.000
## V31 1 22090.436 0.040 7360.887 1.000 1.000
## V26 1 22090.473 0.007 7360.920 1.000 1.000
## V32 1 22090.475 0.005 7360.922 1.000 1.000
## V40 1 22090.474 0.005 7360.922 1.000 1.000
## ------------------------------------------------------------------------
##
## - V37
##
##
## Step 23 : AIC = 22084.83
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11 + V2 + V1 + V37
##
## ------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------
## V27 1 22081.609 4.800 7350.934 1.000 1.000
## V24 1 22084.597 2.054 7353.679 1.000 1.000
## V42 1 22084.667 1.990 7353.743 1.000 1.000
## V33 1 22085.237 1.466 7354.267 1.000 1.000
## V36 1 22085.801 0.947 7354.786 1.000 1.000
## V47 1 22085.814 0.936 7354.797 1.000 1.000
## V50 1 22086.011 0.755 7354.978 1.000 1.000
## V44 1 22086.156 0.622 7355.112 1.000 1.000
## V49 1 22086.229 0.554 7355.179 1.000 1.000
## V22 1 22086.284 0.504 7355.229 1.000 1.000
## V29 1 22086.346 0.446 7355.287 1.000 1.000
## V21 1 22086.359 0.435 7355.298 1.000 1.000
## V35 1 22086.422 0.377 7355.357 1.000 1.000
## V45 1 22086.500 0.305 7355.428 1.000 1.000
## V30 1 22086.600 0.213 7355.520 1.000 1.000
## V25 1 22086.633 0.183 7355.550 1.000 1.000
## V48 1 22086.655 0.163 7355.570 1.000 1.000
## V43 1 22086.677 0.143 7355.590 1.000 1.000
## V39 1 22086.678 0.142 7355.592 1.000 1.000
## V23 1 22086.709 0.113 7355.620 1.000 1.000
## V38 1 22086.718 0.105 7355.629 1.000 1.000
## V34 1 22086.743 0.082 7355.651 1.000 1.000
## V46 1 22086.768 0.059 7355.674 1.000 1.000
## V31 1 22086.778 0.050 7355.684 1.000 1.000
## V41 1 22086.778 0.050 7355.683 1.000 1.000
## V28 1 22086.788 0.040 7355.693 1.000 1.000
## V26 1 22086.818 0.013 7355.721 1.000 1.000
## V40 1 22086.822 0.009 7355.724 1.000 1.000
## V32 1 22086.832 0.000 7355.733 1.000 1.000
## ------------------------------------------------------------------------
##
## - V27
##
##
## Step 24 : AIC = 22081.61
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11 + V2 + V1 + V37 + V27
##
## ------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------
## V42 1 22081.466 1.969 7348.965 1.000 1.000
## V24 1 22081.467 1.968 7348.966 1.000 1.000
## V33 1 22081.925 1.547 7349.386 1.000 1.000
## V36 1 22082.531 0.991 7349.943 1.000 1.000
## V47 1 22082.633 0.897 7350.037 1.000 1.000
## V50 1 22082.769 0.771 7350.162 1.000 1.000
## V44 1 22082.931 0.623 7350.311 1.000 1.000
## V49 1 22083.024 0.537 7350.396 1.000 1.000
## V22 1 22083.063 0.502 7350.432 1.000 1.000
## V29 1 22083.114 0.455 7350.479 1.000 1.000
## V21 1 22083.134 0.436 7350.497 1.000 1.000
## V35 1 22083.192 0.383 7350.551 1.000 1.000
## V45 1 22083.253 0.327 7350.607 1.000 1.000
## V30 1 22083.380 0.211 7350.723 1.000 1.000
## V25 1 22083.418 0.176 7350.758 1.000 1.000
## V43 1 22083.426 0.168 7350.766 1.000 1.000
## V39 1 22083.439 0.157 7350.777 1.000 1.000
## V48 1 22083.442 0.154 7350.780 1.000 1.000
## V23 1 22083.488 0.111 7350.823 1.000 1.000
## V38 1 22083.489 0.110 7350.823 1.000 1.000
## V34 1 22083.533 0.069 7350.864 1.000 1.000
## V31 1 22083.548 0.056 7350.877 1.000 1.000
## V41 1 22083.551 0.053 7350.880 1.000 1.000
## V28 1 22083.560 0.045 7350.889 1.000 1.000
## V46 1 22083.563 0.042 7350.891 1.000 1.000
## V40 1 22083.592 0.016 7350.917 1.000 1.000
## V26 1 22083.607 0.002 7350.931 1.000 1.000
## V32 1 22083.609 0.000 7350.933 1.000 1.000
## ------------------------------------------------------------------------
##
## - V42
##
##
## Step 25 : AIC = 22081.47
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11 + V2 + V1 + V37 + V27 + V42
##
## ------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------
## V24 1 22081.363 1.931 7347.034 1.000 1.000
## V33 1 22081.818 1.513 7347.452 1.000 1.000
## V36 1 22082.383 0.994 7347.971 1.000 1.000
## V47 1 22082.473 0.912 7348.053 1.000 1.000
## V50 1 22082.620 0.777 7348.188 1.000 1.000
## V44 1 22082.758 0.650 7348.315 1.000 1.000
## V49 1 22082.888 0.531 7348.434 1.000 1.000
## V22 1 22082.922 0.499 7348.466 1.000 1.000
## V21 1 22082.981 0.445 7348.520 1.000 1.000
## V29 1 22082.989 0.438 7348.527 1.000 1.000
## V35 1 22083.044 0.387 7348.578 1.000 1.000
## V45 1 22083.113 0.324 7348.641 1.000 1.000
## V30 1 22083.226 0.220 7348.745 1.000 1.000
## V43 1 22083.280 0.170 7348.795 1.000 1.000
## V25 1 22083.285 0.166 7348.799 1.000 1.000
## V48 1 22083.302 0.151 7348.814 1.000 1.000
## V39 1 22083.305 0.148 7348.817 1.000 1.000
## V38 1 22083.344 0.111 7348.854 1.000 1.000
## V23 1 22083.348 0.108 7348.857 1.000 1.000
## V34 1 22083.386 0.073 7348.892 1.000 1.000
## V31 1 22083.400 0.060 7348.905 1.000 1.000
## V41 1 22083.405 0.056 7348.909 1.000 1.000
## V28 1 22083.408 0.053 7348.912 1.000 1.000
## V46 1 22083.432 0.031 7348.934 1.000 1.000
## V40 1 22083.451 0.013 7348.952 1.000 1.000
## V26 1 22083.463 0.002 7348.963 1.000 1.000
## V32 1 22083.466 0.000 7348.965 1.000 1.000
## ------------------------------------------------------------------------
##
## - V24
##
##
## Step 26 : AIC = 22081.36
## Y ~ V51 + V52 + V15 + V20 + V16 + V14 + V7 + V6 + V5 + V12 + V19 + V10 + V3 + V13 + V8 + V4 + V18 + V9 + V17 + V11 + V2 + V1 + V37 + V27 + V42 + V24
##
## ------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------
## V33 1 22081.708 1.519 7345.514 1.000 1.000
## V36 1 22082.283 0.992 7346.042 1.000 1.000
## V47 1 22082.340 0.939 7346.095 1.000 1.000
## V50 1 22082.476 0.814 7346.220 1.000 1.000
## V44 1 22082.616 0.686 7346.348 1.000 1.000
## V22 1 22082.790 0.526 7346.508 1.000 1.000
## V49 1 22082.827 0.492 7346.542 1.000 1.000
## V21 1 22082.874 0.449 7346.585 1.000 1.000
## V29 1 22082.875 0.448 7346.586 1.000 1.000
## V35 1 22082.951 0.378 7346.656 1.000 1.000
## V45 1 22083.010 0.324 7346.710 1.000 1.000
## V43 1 22083.135 0.209 7346.824 1.000 1.000
## V30 1 22083.162 0.185 7346.849 1.000 1.000
## V25 1 22083.192 0.157 7346.877 1.000 1.000
## V39 1 22083.201 0.148 7346.885 1.000 1.000
## V48 1 22083.206 0.144 7346.890 1.000 1.000
## V23 1 22083.229 0.123 7346.911 1.000 1.000
## V38 1 22083.250 0.103 7346.930 1.000 1.000
## V34 1 22083.280 0.076 7346.958 1.000 1.000
## V28 1 22083.298 0.060 7346.974 1.000 1.000
## V31 1 22083.302 0.056 7346.978 1.000 1.000
## V41 1 22083.319 0.041 7346.993 1.000 1.000
## V46 1 22083.331 0.029 7347.005 1.000 1.000
## V40 1 22083.349 0.012 7347.022 1.000 1.000
## V26 1 22083.355 0.007 7347.027 1.000 1.000
## V32 1 22083.363 0.000 7347.034 1.000 1.000
## ------------------------------------------------------------------------
##
##
## No more variables to be added.
##
## Variables Entered:
##
## - V51
## - V52
## - V15
## - V20
## - V16
## - V14
## - V7
## - V6
## - V5
## - V12
## - V19
## - V10
## - V3
## - V13
## - V8
## - V4
## - V18
## - V9
## - V17
## - V11
## - V2
## - V1
## - V37
## - V27
## - V42
## - V24
##
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------
## R 1.000 RMSE 0.960
## R-Squared 1.000 Coef. Var 0.190
## Adj. R-Squared 1.000 MSE 0.921
## Pred R-Squared 1.000 MAE 0.697
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------------
## Regression 18028630.897 26 693408.881 752675.962 0.0000
## Residual 7347.034 7975 0.921
## Total 18035977.931 8001
## ------------------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------
## (Intercept) 2.601 0.185 14.073 0.000 2.238 2.963
## V51 -4.488 0.010 -0.914 -462.952 0.000 -4.507 -4.469
## V52 -4.517 0.012 -0.193 -380.731 0.000 -4.540 -4.493
## V15 3.502 0.004 0.201 890.173 0.000 3.494 3.510
## V20 3.495 0.004 0.201 887.889 0.000 3.488 3.503
## V16 3.501 0.004 0.202 891.642 0.000 3.494 3.509
## V14 3.501 0.004 0.201 889.322 0.000 3.493 3.508
## V7 3.506 0.004 0.201 887.362 0.000 3.498 3.513
## V6 3.500 0.004 0.200 883.180 0.000 3.493 3.508
## V5 3.502 0.004 0.202 894.446 0.000 3.495 3.510
## V12 3.509 0.004 0.199 876.929 0.000 3.501 3.516
## V19 3.502 0.004 0.200 883.324 0.000 3.495 3.510
## V10 3.496 0.004 0.199 880.979 0.000 3.488 3.504
## V3 3.493 0.004 0.201 887.386 0.000 3.485 3.501
## V13 3.499 0.004 0.201 890.018 0.000 3.492 3.507
## V8 3.498 0.004 0.201 887.750 0.000 3.490 3.506
## V4 3.494 0.004 0.197 872.963 0.000 3.487 3.502
## V18 3.505 0.004 0.198 873.053 0.000 3.497 3.513
## V9 3.500 0.004 0.202 890.071 0.000 3.492 3.507
## V17 3.491 0.004 0.196 864.819 0.000 3.483 3.499
## V11 3.501 0.004 0.197 869.336 0.000 3.493 3.509
## V2 3.496 0.017 0.157 204.239 0.000 3.462 3.529
## V1 3.449 0.033 0.199 103.069 0.000 3.383 3.514
## V37 -0.009 0.004 -0.001 -2.416 0.016 -0.017 -0.002
## V27 -0.009 0.004 -0.001 -2.257 0.024 -0.017 -0.001
## V42 -0.006 0.004 0.000 -1.448 0.148 -0.014 0.002
## V24 -0.006 0.004 0.000 -1.448 0.148 -0.014 0.002
## ------------------------------------------------------------------------------------------mod_forwd##
## Selection Summary
## ------------------------------------------------------------------------------
## Variable AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V51 82368.667 4206265.441 13829712.490 0.23322 0.23312
## V52 81673.595 5360020.059 12675957.872 0.29718 0.29701
## V15 81164.271 6144671.263 11891306.668 0.34069 0.34044
## V20 80643.109 6897242.453 11138735.478 0.38242 0.38211
## V16 80091.127 7642294.607 10393683.324 0.42372 0.42336
## V14 79524.715 8354984.409 9680993.521 0.46324 0.46284
## V7 78907.750 9075592.575 8960385.356 0.50319 0.50276
## V6 78258.066 9776403.744 8259574.187 0.54205 0.54159
## V5 77566.468 10462177.766 7573800.165 0.58007 0.57960
## V12 76819.889 11138567.445 6897410.486 0.61757 0.61710
## V19 75959.278 11843430.042 6192547.889 0.65666 0.65618
## V10 75009.700 12537732.163 5498245.768 0.69515 0.69469
## V3 73942.448 13225453.930 4810524.001 0.73328 0.73285
## V13 72717.194 13909445.030 4126532.901 0.77121 0.77080
## V8 71273.942 14591314.234 3444663.697 0.80901 0.80865
## V4 69508.379 15274030.204 2761947.726 0.84686 0.84656
## V18 67262.095 15950556.729 2085421.201 0.88437 0.88413
## V9 64128.980 16626556.432 1409421.499 0.92185 0.92168
## V17 58972.904 17296210.163 739767.768 0.95898 0.95889
## V11 37293.052 17986734.194 49243.736 0.99727 0.99726
## V2 28850.433 18018837.010 17140.921 0.99905 0.99905
## V1 22088.480 18028617.004 7360.927 0.99959 0.99959
## V37 22084.832 18028622.197 7355.733 0.99959 0.99959
## V27 22081.609 18028626.997 7350.934 0.99959 0.99959
## V42 22081.466 18028628.966 7348.965 0.99959 0.99959
## V24 22081.363 18028630.897 7347.034 0.99959 0.99959
## ------------------------------------------------------------------------------mod_forwd$model##
## Call:
## lm(formula = paste(response, "~", paste(preds, collapse = " + ")),
## data = l)
##
## Coefficients:
## (Intercept) V51 V52 V15 V20 V16
## 2.600549 -4.487634 -4.516698 3.501821 3.495246 3.501314
## V14 V7 V6 V5 V12 V19
## 3.500580 3.505625 3.500391 3.502448 3.508631 3.502441
## V10 V3 V13 V8 V4 V18
## 3.495768 3.493128 3.499304 3.497991 3.494456 3.505106
## V9 V17 V11 V2 V1 V37
## 3.499672 3.491392 3.501190 3.495759 3.448787 -0.009406
## V27 V42 V24
## -0.008911 -0.005739 -0.005822#Backward Selection
mod_bcwd<- ols_step_backward_aic(Mod_best, prem = 0.1, details = T )## Backward Elimination Method
## ---------------------------
##
## Candidate Terms:
##
## 1 . V1
## 2 . V2
## 3 . V3
## 4 . V4
## 5 . V5
## 6 . V6
## 7 . V7
## 8 . V8
## 9 . V9
## 10 . V10
## 11 . V11
## 12 . V12
## 13 . V13
## 14 . V14
## 15 . V15
## 16 . V16
## 17 . V17
## 18 . V18
## 19 . V19
## 20 . V20
## 21 . V21
## 22 . V22
## 23 . V23
## 24 . V24
## 25 . V25
## 26 . V26
## 27 . V27
## 28 . V28
## 29 . V29
## 30 . V30
## 31 . V31
## 32 . V32
## 33 . V33
## 34 . V34
## 35 . V35
## 36 . V36
## 37 . V37
## 38 . V38
## 39 . V39
## 40 . V40
## 41 . V41
## 42 . V42
## 43 . V43
## 44 . V44
## 45 . V45
## 46 . V46
## 47 . V47
## 48 . V48
## 49 . V49
## 50 . V50
## 51 . V51
## 52 . V52
##
## Step 0: AIC = 22123.58
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V32 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V32 1 22121.582 0.001 7338.059 1.000 1.000
## V26 1 22121.585 0.003 7338.062 1.000 1.000
## V40 1 22121.599 0.015 7338.074 1.000 1.000
## V46 1 22121.610 0.026 7338.085 1.000 1.000
## V41 1 22121.633 0.047 7338.106 1.000 1.000
## V28 1 22121.637 0.051 7338.110 1.000 1.000
## V31 1 22121.642 0.056 7338.114 1.000 1.000
## V34 1 22121.644 0.057 7338.116 1.000 1.000
## V39 1 22121.718 0.125 7338.184 1.000 1.000
## V38 1 22121.719 0.126 7338.185 1.000 1.000
## V23 1 22121.726 0.132 7338.191 1.000 1.000
## V48 1 22121.740 0.145 7338.204 1.000 1.000
## V25 1 22121.814 0.213 7338.272 1.000 1.000
## V30 1 22121.818 0.217 7338.276 1.000 1.000
## V43 1 22121.854 0.249 7338.308 1.000 1.000
## V45 1 22121.904 0.296 7338.355 1.000 1.000
## V29 1 22122.010 0.393 7338.452 1.000 1.000
## V35 1 22122.043 0.423 7338.482 1.000 1.000
## V21 1 22122.052 0.431 7338.490 1.000 1.000
## V49 1 22122.134 0.506 7338.565 1.000 1.000
## V22 1 22122.150 0.521 7338.580 1.000 1.000
## V44 1 22122.264 0.625 7338.684 1.000 1.000
## V47 1 22122.539 0.878 7338.937 1.000 1.000
## V50 1 22122.553 0.891 7338.950 1.000 1.000
## V36 1 22122.763 1.084 7339.142 1.000 1.000
## V33 1 22123.234 1.515 7339.574 1.000 1.000
## V42 1 22123.681 1.925 7339.984 1.000 1.000
## V24 1 22123.768 2.005 7340.064 1.000 1.000
## V27 1 22126.845 4.828 7342.887 1.000 1.000
## V37 1 22127.556 5.481 7343.539 1.000 1.000
## V1 1 28893.224 9766.039 17104.098 0.999 0.999
## V2 1 36751.035 38325.424 45663.483 0.997 0.997
## V52 1 45748.430 133230.069 140568.128 0.992 0.992
## V51 1 48744.162 197059.123 204397.182 0.989 0.989
## V17 1 58525.256 686609.454 693947.513 0.962 0.961
## V11 1 58606.753 693713.118 701051.177 0.961 0.961
## V4 1 58673.698 699602.753 706940.812 0.961 0.961
## V18 1 58686.140 700702.743 708040.802 0.961 0.960
## V12 1 58748.440 706236.807 713574.865 0.960 0.960
## V10 1 58821.987 712825.515 720163.574 0.960 0.960
## V6 1 58858.816 716147.696 723485.755 0.960 0.960
## V19 1 58867.300 716915.148 724253.207 0.960 0.960
## V20 1 58923.778 722044.992 729383.051 0.960 0.959
## V3 1 58935.524 723116.470 730454.528 0.960 0.959
## V7 1 58938.896 723424.373 730762.432 0.959 0.959
## V8 1 58944.847 723968.049 731306.108 0.959 0.959
## V14 1 58977.658 726972.766 734310.824 0.959 0.959
## V13 1 58980.185 727204.703 734542.762 0.959 0.959
## V9 1 58986.738 727806.453 735144.511 0.959 0.959
## V15 1 58995.168 728581.322 735919.381 0.959 0.959
## V16 1 59016.061 730505.288 737843.346 0.959 0.959
## V5 1 59054.804 734086.375 741424.434 0.959 0.959
## ------------------------------------------------------------------------------
##
##
## Variables Removed:
##
## - V32
##
##
## Step 1 : AIC = 22121.58
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V26 + V27 + V28 + V29 + V30 + V31 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V26 1 22119.585 0.003 7338.062 1.000 1.000
## V40 1 22119.599 0.016 7338.075 1.000 1.000
## V46 1 22119.611 0.026 7338.086 1.000 1.000
## V41 1 22119.634 0.047 7338.107 1.000 1.000
## V28 1 22119.638 0.051 7338.111 1.000 1.000
## V31 1 22119.643 0.056 7338.115 1.000 1.000
## V34 1 22119.645 0.057 7338.117 1.000 1.000
## V39 1 22119.719 0.125 7338.184 1.000 1.000
## V38 1 22119.720 0.126 7338.186 1.000 1.000
## V23 1 22119.726 0.132 7338.191 1.000 1.000
## V48 1 22119.740 0.145 7338.204 1.000 1.000
## V25 1 22119.814 0.213 7338.272 1.000 1.000
## V30 1 22119.820 0.218 7338.277 1.000 1.000
## V43 1 22119.854 0.249 7338.309 1.000 1.000
## V45 1 22119.905 0.296 7338.355 1.000 1.000
## V29 1 22120.010 0.393 7338.452 1.000 1.000
## V35 1 22120.044 0.423 7338.483 1.000 1.000
## V21 1 22120.052 0.430 7338.490 1.000 1.000
## V49 1 22120.135 0.507 7338.566 1.000 1.000
## V22 1 22120.150 0.521 7338.580 1.000 1.000
## V44 1 22120.264 0.625 7338.685 1.000 1.000
## V47 1 22120.539 0.878 7338.937 1.000 1.000
## V50 1 22120.554 0.891 7338.950 1.000 1.000
## V36 1 22120.763 1.083 7339.143 1.000 1.000
## V33 1 22121.236 1.517 7339.576 1.000 1.000
## V42 1 22121.683 1.926 7339.986 1.000 1.000
## V24 1 22121.769 2.005 7340.065 1.000 1.000
## V27 1 22124.845 4.828 7342.887 1.000 1.000
## V37 1 22125.557 5.481 7343.541 1.000 1.000
## V1 1 28891.252 9766.098 17104.158 0.999 0.999
## V2 1 36749.041 38325.459 45663.518 0.997 0.997
## V52 1 45746.698 133234.766 140572.826 0.992 0.992
## V51 1 48742.179 197059.573 204397.633 0.989 0.989
## V17 1 58523.646 686643.290 693981.350 0.962 0.961
## V11 1 58604.781 693715.538 701053.597 0.961 0.961
## V4 1 58674.120 699816.751 707154.811 0.961 0.961
## V18 1 58686.056 700872.370 708210.430 0.961 0.960
## V12 1 58746.522 706244.124 713582.184 0.960 0.960
## V10 1 58820.771 712896.098 720234.157 0.960 0.960
## V6 1 58857.607 716219.201 723557.261 0.960 0.960
## V19 1 58866.163 716993.297 724331.357 0.960 0.960
## V20 1 58923.283 722182.203 729520.263 0.960 0.959
## V3 1 58936.939 723428.282 730766.341 0.959 0.959
## V7 1 58937.477 723477.407 730815.466 0.959 0.959
## V8 1 58944.945 724159.742 731497.801 0.959 0.959
## V14 1 58976.039 727007.694 734345.754 0.959 0.959
## V13 1 58978.186 727204.799 734542.858 0.959 0.959
## V9 1 58984.924 727823.532 735161.592 0.959 0.959
## V15 1 58993.179 728582.399 735920.459 0.959 0.959
## V16 1 59014.160 730514.465 737852.525 0.959 0.959
## V5 1 59057.835 734552.645 741890.704 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V26
##
##
## Step 2 : AIC = 22119.59
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V28 + V29 + V30 + V31 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V40 + V41 + V42 + V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V40 1 22117.602 0.016 7338.078 1.000 1.000
## V46 1 22117.614 0.026 7338.089 1.000 1.000
## V41 1 22117.636 0.047 7338.109 1.000 1.000
## V28 1 22117.641 0.051 7338.113 1.000 1.000
## V31 1 22117.646 0.055 7338.118 1.000 1.000
## V34 1 22117.648 0.058 7338.120 1.000 1.000
## V39 1 22117.722 0.125 7338.188 1.000 1.000
## V38 1 22117.723 0.126 7338.188 1.000 1.000
## V23 1 22117.729 0.132 7338.194 1.000 1.000
## V48 1 22117.744 0.145 7338.208 1.000 1.000
## V25 1 22117.819 0.214 7338.276 1.000 1.000
## V30 1 22117.823 0.218 7338.280 1.000 1.000
## V43 1 22117.857 0.249 7338.311 1.000 1.000
## V45 1 22117.910 0.298 7338.360 1.000 1.000
## V29 1 22118.014 0.393 7338.456 1.000 1.000
## V35 1 22118.047 0.423 7338.485 1.000 1.000
## V21 1 22118.053 0.429 7338.491 1.000 1.000
## V49 1 22118.138 0.506 7338.569 1.000 1.000
## V22 1 22118.155 0.523 7338.585 1.000 1.000
## V44 1 22118.266 0.624 7338.686 1.000 1.000
## V47 1 22118.543 0.878 7338.940 1.000 1.000
## V50 1 22118.556 0.890 7338.952 1.000 1.000
## V36 1 22118.767 1.084 7339.146 1.000 1.000
## V33 1 22119.240 1.518 7339.580 1.000 1.000
## V42 1 22119.685 1.926 7339.988 1.000 1.000
## V24 1 22119.769 2.003 7340.065 1.000 1.000
## V27 1 22122.860 4.839 7342.901 1.000 1.000
## V37 1 22123.558 5.479 7343.541 1.000 1.000
## V1 1 28889.313 9766.226 17104.289 0.999 0.999
## V2 1 36748.358 38332.974 45671.036 0.997 0.997
## V52 1 45746.759 133270.975 140609.037 0.992 0.992
## V51 1 48740.407 197065.393 204403.456 0.989 0.989
## V17 1 58525.278 686958.278 694296.340 0.962 0.961
## V11 1 58602.984 693733.321 701071.384 0.961 0.961
## V4 1 58672.171 699821.231 707159.294 0.961 0.961
## V18 1 58684.063 700872.978 708211.040 0.961 0.960
## V12 1 58744.538 706245.543 713583.606 0.960 0.960
## V10 1 58820.034 713009.786 720347.848 0.960 0.960
## V6 1 58855.641 716222.284 723560.346 0.960 0.960
## V19 1 58864.477 717021.755 724359.817 0.960 0.960
## V20 1 58921.285 722182.425 729520.487 0.960 0.959
## V3 1 58935.312 723462.332 730800.395 0.959 0.959
## V7 1 58936.862 723603.913 730941.976 0.959 0.959
## V8 1 58942.989 724163.749 731501.811 0.959 0.959
## V14 1 58974.990 727095.010 734433.073 0.959 0.959
## V13 1 58976.535 727236.869 734574.931 0.959 0.959
## V9 1 58983.801 727904.156 735242.218 0.959 0.959
## V15 1 58991.882 728647.052 735985.114 0.959 0.959
## V16 1 59012.458 730541.928 737879.990 0.959 0.959
## V5 1 59060.056 734944.076 742282.138 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V40
##
##
## Step 3 : AIC = 22117.6
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V28 + V29 + V30 + V31 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V41 + V42 + V43 + V44 + V45 + V46 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V46 1 22115.632 0.027 7338.105 1.000 1.000
## V41 1 22115.654 0.048 7338.125 1.000 1.000
## V28 1 22115.658 0.051 7338.129 1.000 1.000
## V31 1 22115.662 0.055 7338.133 1.000 1.000
## V34 1 22115.666 0.058 7338.136 1.000 1.000
## V38 1 22115.738 0.125 7338.203 1.000 1.000
## V39 1 22115.740 0.126 7338.204 1.000 1.000
## V23 1 22115.745 0.131 7338.209 1.000 1.000
## V48 1 22115.762 0.146 7338.224 1.000 1.000
## V25 1 22115.836 0.214 7338.292 1.000 1.000
## V30 1 22115.839 0.217 7338.295 1.000 1.000
## V43 1 22115.875 0.250 7338.328 1.000 1.000
## V45 1 22115.929 0.299 7338.377 1.000 1.000
## V29 1 22116.031 0.393 7338.471 1.000 1.000
## V35 1 22116.065 0.425 7338.502 1.000 1.000
## V21 1 22116.071 0.430 7338.507 1.000 1.000
## V49 1 22116.154 0.506 7338.584 1.000 1.000
## V22 1 22116.173 0.523 7338.601 1.000 1.000
## V44 1 22116.281 0.622 7338.700 1.000 1.000
## V47 1 22116.558 0.876 7338.954 1.000 1.000
## V50 1 22116.572 0.889 7338.967 1.000 1.000
## V36 1 22116.783 1.083 7339.160 1.000 1.000
## V33 1 22117.256 1.516 7339.594 1.000 1.000
## V42 1 22117.705 1.929 7340.006 1.000 1.000
## V24 1 22117.787 2.004 7340.082 1.000 1.000
## V27 1 22120.870 4.832 7342.910 1.000 1.000
## V37 1 22121.569 5.474 7343.552 1.000 1.000
## V1 1 28887.822 9767.299 17105.377 0.999 0.999
## V2 1 36746.654 38334.643 45672.721 0.997 0.997
## V52 1 45744.791 133271.517 140609.595 0.992 0.992
## V51 1 48738.650 197071.586 204409.664 0.989 0.989
## V17 1 58523.725 686997.087 694335.165 0.962 0.961
## V11 1 58604.418 694034.215 701372.293 0.961 0.961
## V4 1 58670.276 699830.492 707168.570 0.961 0.961
## V18 1 58682.226 700887.386 708225.464 0.961 0.960
## V12 1 58742.649 706255.407 713593.485 0.960 0.960
## V10 1 58818.615 713062.115 720400.193 0.960 0.960
## V6 1 58858.038 716619.945 723958.023 0.960 0.960
## V19 1 58862.515 717025.143 724363.221 0.960 0.960
## V20 1 58919.285 722182.410 729520.488 0.960 0.959
## V3 1 58933.888 723514.913 730852.991 0.959 0.959
## V7 1 58935.364 723649.721 730987.798 0.959 0.959
## V8 1 58944.050 724443.690 731781.768 0.959 0.959
## V14 1 58973.514 727143.135 734481.213 0.959 0.959
## V13 1 58975.644 727338.628 734676.705 0.959 0.959
## V9 1 58985.785 728270.264 735608.342 0.959 0.959
## V15 1 58990.595 728712.542 736050.620 0.959 0.959
## V16 1 59010.772 730570.885 737908.963 0.959 0.959
## V5 1 59058.197 734957.211 742295.289 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V46
##
##
## Step 4 : AIC = 22115.63
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V28 + V29 + V30 + V31 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V41 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V41 1 22113.684 0.048 7338.153 1.000 1.000
## V28 1 22113.687 0.051 7338.155 1.000 1.000
## V31 1 22113.690 0.053 7338.158 1.000 1.000
## V34 1 22113.696 0.059 7338.163 1.000 1.000
## V38 1 22113.768 0.125 7338.229 1.000 1.000
## V39 1 22113.770 0.127 7338.231 1.000 1.000
## V23 1 22113.773 0.130 7338.235 1.000 1.000
## V48 1 22113.793 0.147 7338.252 1.000 1.000
## V25 1 22113.861 0.210 7338.315 1.000 1.000
## V30 1 22113.869 0.217 7338.322 1.000 1.000
## V43 1 22113.902 0.248 7338.353 1.000 1.000
## V45 1 22113.958 0.299 7338.404 1.000 1.000
## V29 1 22114.062 0.394 7338.499 1.000 1.000
## V35 1 22114.094 0.424 7338.529 1.000 1.000
## V21 1 22114.104 0.433 7338.537 1.000 1.000
## V49 1 22114.183 0.505 7338.610 1.000 1.000
## V22 1 22114.200 0.521 7338.626 1.000 1.000
## V44 1 22114.315 0.626 7338.731 1.000 1.000
## V47 1 22114.590 0.879 7338.984 1.000 1.000
## V50 1 22114.602 0.890 7338.995 1.000 1.000
## V36 1 22114.815 1.085 7339.190 1.000 1.000
## V33 1 22115.282 1.513 7339.618 1.000 1.000
## V42 1 22115.746 1.939 7340.044 1.000 1.000
## V24 1 22115.819 2.006 7340.110 1.000 1.000
## V27 1 22118.914 4.846 7342.950 1.000 1.000
## V37 1 22119.597 5.472 7343.577 1.000 1.000
## V1 1 28885.830 9767.288 17105.392 0.999 0.999
## V2 1 36746.176 38343.306 45681.411 0.997 0.997
## V52 1 45743.070 133276.403 140614.507 0.992 0.992
## V51 1 48736.690 197072.585 204410.690 0.989 0.989
## V17 1 58524.339 687223.911 694562.016 0.961 0.961
## V11 1 58605.442 694299.357 701637.461 0.961 0.961
## V4 1 58671.951 700155.355 707493.460 0.961 0.961
## V18 1 58680.276 700891.771 708229.876 0.961 0.961
## V12 1 58740.690 706258.988 713597.093 0.960 0.960
## V10 1 58816.920 713089.545 720427.650 0.960 0.960
## V6 1 58856.066 716622.454 723960.559 0.960 0.960
## V19 1 58861.075 717075.782 724413.887 0.960 0.960
## V20 1 58924.500 722840.401 730178.506 0.960 0.959
## V3 1 58933.115 723626.978 730965.083 0.959 0.959
## V7 1 58935.226 723819.837 731157.942 0.959 0.959
## V8 1 58942.081 724446.418 731784.523 0.959 0.959
## V14 1 58971.561 727147.371 734485.476 0.959 0.959
## V13 1 58974.899 727453.875 734791.979 0.959 0.959
## V9 1 58983.799 728271.543 735609.647 0.959 0.959
## V15 1 58990.394 728878.012 736216.117 0.959 0.959
## V16 1 59011.517 730824.015 738162.120 0.959 0.959
## V5 1 59056.288 734965.638 742303.743 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V41
##
##
## Step 5 : AIC = 22113.68
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V28 + V29 + V30 + V31 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V28 1 22111.738 0.050 7338.202 1.000 1.000
## V31 1 22111.744 0.055 7338.207 1.000 1.000
## V34 1 22111.747 0.058 7338.210 1.000 1.000
## V38 1 22111.820 0.125 7338.278 1.000 1.000
## V39 1 22111.822 0.126 7338.279 1.000 1.000
## V23 1 22111.825 0.129 7338.282 1.000 1.000
## V48 1 22111.842 0.145 7338.298 1.000 1.000
## V25 1 22111.916 0.213 7338.366 1.000 1.000
## V30 1 22111.922 0.218 7338.371 1.000 1.000
## V43 1 22111.956 0.249 7338.402 1.000 1.000
## V45 1 22112.014 0.303 7338.455 1.000 1.000
## V29 1 22112.118 0.398 7338.550 1.000 1.000
## V35 1 22112.148 0.425 7338.578 1.000 1.000
## V21 1 22112.152 0.429 7338.581 1.000 1.000
## V49 1 22112.228 0.499 7338.652 1.000 1.000
## V22 1 22112.248 0.517 7338.670 1.000 1.000
## V44 1 22112.364 0.624 7338.776 1.000 1.000
## V47 1 22112.641 0.878 7339.031 1.000 1.000
## V50 1 22112.660 0.895 7339.047 1.000 1.000
## V36 1 22112.864 1.082 7339.234 1.000 1.000
## V33 1 22113.336 1.515 7339.668 1.000 1.000
## V42 1 22113.795 1.936 7340.089 1.000 1.000
## V24 1 22113.889 2.023 7340.175 1.000 1.000
## V27 1 22116.963 4.843 7342.995 1.000 1.000
## V37 1 22117.662 5.484 7343.637 1.000 1.000
## V1 1 28883.831 9767.242 17105.395 0.999 0.999
## V2 1 36744.987 38347.888 45686.041 0.997 0.997
## V52 1 45741.202 133278.678 140616.830 0.992 0.992
## V51 1 48734.710 197073.033 204411.186 0.989 0.989
## V17 1 58522.423 687231.193 694569.346 0.961 0.961
## V11 1 58604.649 694405.163 701743.316 0.961 0.961
## V4 1 58670.038 700162.938 707501.091 0.961 0.961
## V18 1 58679.769 701023.852 708362.005 0.961 0.960
## V12 1 58738.754 706264.699 713602.851 0.960 0.960
## V10 1 58815.460 713138.062 720476.215 0.960 0.960
## V6 1 58854.066 716622.487 723960.640 0.960 0.960
## V19 1 58859.974 717157.112 724495.265 0.960 0.960
## V20 1 58923.121 722897.064 730235.217 0.960 0.959
## V7 1 58935.601 724036.781 731374.933 0.959 0.959
## V3 1 58935.653 724041.551 731379.703 0.959 0.959
## V8 1 58940.676 724500.834 731838.986 0.959 0.959
## V14 1 58970.158 727202.166 734540.319 0.959 0.959
## V13 1 58974.715 727620.526 734958.679 0.959 0.959
## V9 1 58981.811 728272.561 735610.714 0.959 0.959
## V15 1 58988.877 728922.399 736260.552 0.959 0.959
## V16 1 59013.085 731153.174 738491.326 0.959 0.959
## V5 1 59054.412 734977.089 742315.241 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V28
##
##
## Step 6 : AIC = 22111.74
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V29 + V30 + V31 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V31 1 22109.797 0.054 7338.256 1.000 1.000
## V34 1 22109.802 0.059 7338.261 1.000 1.000
## V39 1 22109.872 0.123 7338.325 1.000 1.000
## V23 1 22109.877 0.127 7338.329 1.000 1.000
## V38 1 22109.877 0.127 7338.329 1.000 1.000
## V48 1 22109.895 0.144 7338.346 1.000 1.000
## V25 1 22109.973 0.215 7338.417 1.000 1.000
## V30 1 22109.982 0.223 7338.425 1.000 1.000
## V43 1 22110.008 0.247 7338.449 1.000 1.000
## V45 1 22110.070 0.304 7338.507 1.000 1.000
## V29 1 22110.178 0.403 7338.605 1.000 1.000
## V35 1 22110.201 0.425 7338.627 1.000 1.000
## V21 1 22110.204 0.427 7338.630 1.000 1.000
## V49 1 22110.277 0.494 7338.697 1.000 1.000
## V22 1 22110.306 0.520 7338.723 1.000 1.000
## V44 1 22110.418 0.623 7338.826 1.000 1.000
## V47 1 22110.700 0.882 7339.084 1.000 1.000
## V50 1 22110.714 0.895 7339.097 1.000 1.000
## V36 1 22110.923 1.087 7339.289 1.000 1.000
## V33 1 22111.391 1.516 7339.718 1.000 1.000
## V42 1 22111.841 1.928 7340.131 1.000 1.000
## V24 1 22111.936 2.016 7340.218 1.000 1.000
## V27 1 22115.012 4.838 7343.040 1.000 1.000
## V37 1 22115.745 5.510 7343.713 1.000 1.000
## V1 1 28881.856 9767.245 17105.448 0.999 0.999
## V2 1 36743.949 38353.329 45691.532 0.997 0.997
## V52 1 45739.208 133278.723 140616.926 0.992 0.992
## V51 1 48732.887 197077.507 204415.709 0.989 0.989
## V17 1 58521.237 687301.774 694639.976 0.961 0.961
## V11 1 58602.827 694420.670 701758.872 0.961 0.961
## V4 1 58671.129 700436.260 707774.463 0.961 0.961
## V18 1 58678.020 701046.031 708384.233 0.961 0.961
## V12 1 58739.551 706514.110 713852.313 0.960 0.960
## V10 1 58813.491 713140.823 720479.026 0.960 0.960
## V6 1 58852.175 716632.222 723970.425 0.960 0.960
## V19 1 58859.363 717282.901 724621.104 0.960 0.960
## V20 1 58921.121 722897.020 730235.222 0.960 0.959
## V7 1 58933.705 724046.321 731384.524 0.959 0.959
## V3 1 58934.170 724088.745 731426.947 0.959 0.959
## V8 1 58938.703 724503.242 731841.445 0.959 0.959
## V14 1 58970.060 727376.658 734714.861 0.959 0.959
## V13 1 58972.931 727640.310 734978.513 0.959 0.959
## V9 1 58979.890 728279.810 735618.013 0.959 0.959
## V15 1 58989.483 729162.163 736500.366 0.959 0.959
## V16 1 59012.053 731242.470 738580.673 0.959 0.959
## V5 1 59052.414 734977.174 742315.377 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V31
##
##
## Step 7 : AIC = 22109.8
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V29 + V30 + V33 + V34 + V35 + V36 + V37 + V38 + V39 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V34 1 22107.861 0.059 7338.315 1.000 1.000
## V38 1 22107.934 0.125 7338.381 1.000 1.000
## V39 1 22107.934 0.125 7338.382 1.000 1.000
## V23 1 22107.938 0.130 7338.386 1.000 1.000
## V48 1 22107.956 0.146 7338.402 1.000 1.000
## V25 1 22108.030 0.213 7338.469 1.000 1.000
## V30 1 22108.038 0.221 7338.478 1.000 1.000
## V43 1 22108.071 0.251 7338.507 1.000 1.000
## V45 1 22108.125 0.301 7338.557 1.000 1.000
## V29 1 22108.238 0.405 7338.661 1.000 1.000
## V35 1 22108.254 0.420 7338.676 1.000 1.000
## V21 1 22108.261 0.426 7338.682 1.000 1.000
## V49 1 22108.337 0.495 7338.751 1.000 1.000
## V22 1 22108.365 0.521 7338.777 1.000 1.000
## V44 1 22108.476 0.623 7338.879 1.000 1.000
## V47 1 22108.755 0.879 7339.135 1.000 1.000
## V50 1 22108.776 0.898 7339.155 1.000 1.000
## V36 1 22108.978 1.084 7339.340 1.000 1.000
## V33 1 22109.454 1.520 7339.776 1.000 1.000
## V42 1 22109.895 1.925 7340.181 1.000 1.000
## V24 1 22110.000 2.021 7340.277 1.000 1.000
## V27 1 22113.063 4.831 7343.087 1.000 1.000
## V37 1 22113.792 5.500 7343.756 1.000 1.000
## V1 1 28879.857 9767.195 17105.451 0.999 0.999
## V2 1 36742.168 38354.532 45692.788 0.997 0.997
## V52 1 45737.215 133278.798 140617.054 0.992 0.992
## V51 1 48730.904 197077.895 204416.151 0.989 0.989
## V17 1 58519.277 687305.170 694643.427 0.961 0.961
## V11 1 58604.680 694758.622 702096.878 0.961 0.961
## V4 1 58669.191 700441.731 707779.987 0.961 0.961
## V18 1 58677.037 701136.006 708474.262 0.961 0.961
## V12 1 58737.563 706515.158 713853.414 0.960 0.960
## V10 1 58811.538 713145.037 720483.293 0.960 0.960
## V6 1 58853.456 716929.134 724267.390 0.960 0.960
## V19 1 58858.178 717356.598 724694.854 0.960 0.960
## V20 1 58919.771 722956.302 730294.558 0.960 0.959
## V7 1 58931.731 724048.614 731386.870 0.959 0.959
## V3 1 58933.070 724171.009 731509.265 0.959 0.959
## V8 1 58940.513 724851.691 732189.947 0.959 0.959
## V14 1 58968.133 727383.347 734721.603 0.959 0.959
## V13 1 58971.687 727709.756 735048.012 0.959 0.959
## V9 1 58978.141 728302.860 735641.116 0.959 0.959
## V15 1 58987.609 729173.716 736511.972 0.959 0.959
## V16 1 59011.301 731357.629 738695.885 0.959 0.959
## V5 1 59053.413 735255.364 742593.620 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V34
##
##
## Step 8 : AIC = 22107.86
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V29 + V30 + V33 + V35 + V36 + V37 + V38 + V39 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V38 1 22105.995 0.123 7338.438 1.000 1.000
## V23 1 22105.997 0.125 7338.440 1.000 1.000
## V39 1 22105.997 0.125 7338.440 1.000 1.000
## V48 1 22106.023 0.149 7338.464 1.000 1.000
## V25 1 22106.095 0.214 7338.529 1.000 1.000
## V30 1 22106.106 0.225 7338.540 1.000 1.000
## V43 1 22106.134 0.250 7338.565 1.000 1.000
## V45 1 22106.188 0.300 7338.615 1.000 1.000
## V29 1 22106.306 0.409 7338.723 1.000 1.000
## V35 1 22106.317 0.418 7338.733 1.000 1.000
## V21 1 22106.317 0.418 7338.733 1.000 1.000
## V49 1 22106.396 0.491 7338.806 1.000 1.000
## V22 1 22106.429 0.521 7338.836 1.000 1.000
## V44 1 22106.551 0.633 7338.948 1.000 1.000
## V47 1 22106.831 0.890 7339.205 1.000 1.000
## V50 1 22106.844 0.901 7339.216 1.000 1.000
## V36 1 22107.043 1.084 7339.399 1.000 1.000
## V33 1 22107.523 1.524 7339.839 1.000 1.000
## V42 1 22107.956 1.922 7340.236 1.000 1.000
## V24 1 22108.062 2.018 7340.333 1.000 1.000
## V27 1 22111.140 4.843 7343.158 1.000 1.000
## V37 1 22111.862 5.505 7343.820 1.000 1.000
## V1 1 28878.494 9768.498 17106.813 0.999 0.999
## V2 1 36740.212 38354.720 45693.035 0.997 0.997
## V52 1 45735.516 133284.025 140622.340 0.992 0.992
## V51 1 48729.545 197094.213 204432.528 0.989 0.989
## V17 1 58519.236 687475.239 694813.554 0.961 0.961
## V11 1 58603.781 694855.117 702193.432 0.961 0.961
## V4 1 58669.816 700673.844 708012.159 0.961 0.961
## V18 1 58675.057 701137.691 708476.006 0.961 0.961
## V12 1 58735.563 706515.099 713853.414 0.960 0.960
## V10 1 58810.422 713224.530 720562.845 0.960 0.960
## V6 1 58852.601 717032.690 724371.004 0.960 0.960
## V19 1 58856.472 717383.221 724721.536 0.960 0.960
## V20 1 58922.046 723346.443 730684.758 0.959 0.959
## V7 1 58929.736 724048.962 731387.277 0.959 0.959
## V3 1 58931.144 724177.735 731516.050 0.959 0.959
## V8 1 58938.517 724852.066 732190.381 0.959 0.959
## V14 1 58966.184 727388.000 734726.315 0.959 0.959
## V13 1 58971.357 727863.062 735201.376 0.959 0.959
## V9 1 58976.322 728319.437 735657.752 0.959 0.959
## V15 1 58985.694 729181.544 736519.859 0.959 0.959
## V16 1 59011.002 731514.590 738852.905 0.959 0.959
## V5 1 59051.867 735297.464 742635.779 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V38
##
##
## Step 9 : AIC = 22105.99
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V29 + V30 + V33 + V35 + V36 + V37 + V39 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V39 1 22104.134 0.128 7338.565 1.000 1.000
## V23 1 22104.137 0.131 7338.568 1.000 1.000
## V48 1 22104.155 0.147 7338.585 1.000 1.000
## V25 1 22104.226 0.212 7338.650 1.000 1.000
## V30 1 22104.242 0.226 7338.664 1.000 1.000
## V43 1 22104.272 0.254 7338.692 1.000 1.000
## V45 1 22104.319 0.297 7338.735 1.000 1.000
## V29 1 22104.441 0.409 7338.847 1.000 1.000
## V35 1 22104.450 0.417 7338.855 1.000 1.000
## V21 1 22104.453 0.420 7338.858 1.000 1.000
## V49 1 22104.525 0.487 7338.924 1.000 1.000
## V22 1 22104.559 0.517 7338.955 1.000 1.000
## V44 1 22104.702 0.649 7339.086 1.000 1.000
## V47 1 22104.959 0.884 7339.322 1.000 1.000
## V50 1 22104.972 0.896 7339.334 1.000 1.000
## V36 1 22105.162 1.071 7339.508 1.000 1.000
## V33 1 22105.643 1.512 7339.950 1.000 1.000
## V42 1 22106.089 1.921 7340.358 1.000 1.000
## V24 1 22106.206 2.028 7340.466 1.000 1.000
## V27 1 22109.267 4.836 7343.274 1.000 1.000
## V37 1 22109.995 5.504 7343.942 1.000 1.000
## V1 1 28878.585 9772.845 17111.282 0.999 0.999
## V2 1 36738.957 38358.851 45697.289 0.997 0.997
## V52 1 45736.011 133327.755 140666.193 0.992 0.992
## V51 1 48730.139 197160.358 204498.796 0.989 0.989
## V17 1 58519.695 687688.594 695027.032 0.961 0.961
## V11 1 58601.898 694865.339 702203.777 0.961 0.961
## V4 1 58669.863 700854.842 708193.279 0.961 0.961
## V18 1 58673.233 701153.217 708491.654 0.961 0.961
## V12 1 58737.099 706830.488 714168.926 0.960 0.960
## V10 1 58808.509 713232.263 720570.701 0.960 0.960
## V6 1 58850.756 717046.577 724385.015 0.960 0.960
## V19 1 58856.072 717528.006 724866.444 0.960 0.960
## V20 1 58920.529 723390.442 730728.880 0.959 0.959
## V7 1 58928.249 724095.795 731434.233 0.959 0.959
## V3 1 58929.900 724246.727 731585.165 0.959 0.959
## V8 1 58936.601 724859.579 732198.016 0.959 0.959
## V14 1 58971.242 728036.192 735374.630 0.959 0.959
## V13 1 58973.238 728219.669 735558.106 0.959 0.959
## V9 1 58976.248 728496.379 735834.816 0.959 0.959
## V15 1 58984.109 729219.616 736558.054 0.959 0.959
## V16 1 59009.048 731518.742 738857.180 0.959 0.959
## V5 1 59050.202 735328.463 742666.900 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V39
##
##
## Step 10 : AIC = 22104.13
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V23 + V24 + V25 + V27 + V29 + V30 + V33 + V35 + V36 + V37 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V23 1 22102.278 0.132 7338.697 1.000 1.000
## V48 1 22102.300 0.152 7338.717 1.000 1.000
## V25 1 22102.364 0.211 7338.776 1.000 1.000
## V30 1 22102.383 0.228 7338.794 1.000 1.000
## V43 1 22102.409 0.252 7338.818 1.000 1.000
## V45 1 22102.465 0.303 7338.869 1.000 1.000
## V29 1 22102.572 0.402 7338.967 1.000 1.000
## V21 1 22102.588 0.416 7338.981 1.000 1.000
## V35 1 22102.588 0.416 7338.982 1.000 1.000
## V49 1 22102.660 0.482 7339.048 1.000 1.000
## V22 1 22102.712 0.530 7339.095 1.000 1.000
## V44 1 22102.839 0.647 7339.212 1.000 1.000
## V47 1 22103.107 0.892 7339.458 1.000 1.000
## V50 1 22103.117 0.901 7339.467 1.000 1.000
## V36 1 22103.291 1.061 7339.627 1.000 1.000
## V33 1 22103.798 1.526 7340.092 1.000 1.000
## V42 1 22104.237 1.929 7340.494 1.000 1.000
## V24 1 22104.345 2.028 7340.593 1.000 1.000
## V27 1 22107.391 4.823 7343.388 1.000 1.000
## V37 1 22108.120 5.491 7344.057 1.000 1.000
## V1 1 28877.549 9774.778 17113.344 0.999 0.999
## V2 1 36741.629 38385.414 45723.979 0.997 0.997
## V52 1 45736.556 133372.377 140710.942 0.992 0.992
## V51 1 48730.431 197218.832 204557.398 0.989 0.989
## V17 1 58518.152 687728.230 695066.796 0.961 0.961
## V11 1 58599.970 694871.517 702210.083 0.961 0.961
## V4 1 58669.294 700981.414 708319.980 0.961 0.961
## V18 1 58671.417 701169.392 708507.957 0.961 0.961
## V12 1 58741.123 707368.141 714706.707 0.960 0.960
## V10 1 58806.512 713232.362 720570.927 0.960 0.960
## V6 1 58848.767 717047.434 724386.000 0.960 0.960
## V19 1 58854.095 717529.948 724868.513 0.960 0.960
## V7 1 58926.328 724102.889 731441.454 0.959 0.959
## V3 1 58928.917 724339.555 731678.120 0.959 0.959
## V20 1 58934.942 724890.666 732229.232 0.959 0.959
## V8 1 58936.792 725059.956 732398.521 0.959 0.959
## V14 1 58969.904 728096.897 735435.463 0.959 0.959
## V13 1 58971.257 728221.215 735559.780 0.959 0.959
## V9 1 58975.463 728607.984 735946.549 0.959 0.959
## V15 1 58982.512 729256.527 736595.092 0.959 0.959
## V16 1 59007.052 731518.995 738857.560 0.959 0.959
## V5 1 59048.504 735356.330 742694.896 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V23
##
##
## Step 11 : AIC = 22102.28
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V25 + V27 + V29 + V30 + V33 + V35 + V36 + V37 + V42 + V43 + V44 + V45 + V47 + V48 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V48 1 22100.451 0.159 7338.856 1.000 1.000
## V25 1 22100.511 0.214 7338.911 1.000 1.000
## V30 1 22100.520 0.222 7338.919 1.000 1.000
## V43 1 22100.553 0.253 7338.950 1.000 1.000
## V45 1 22100.615 0.309 7339.006 1.000 1.000
## V29 1 22100.719 0.404 7339.101 1.000 1.000
## V21 1 22100.725 0.410 7339.107 1.000 1.000
## V35 1 22100.737 0.421 7339.118 1.000 1.000
## V49 1 22100.806 0.485 7339.182 1.000 1.000
## V22 1 22100.867 0.540 7339.238 1.000 1.000
## V44 1 22100.982 0.646 7339.343 1.000 1.000
## V47 1 22101.241 0.884 7339.581 1.000 1.000
## V50 1 22101.248 0.889 7339.587 1.000 1.000
## V36 1 22101.429 1.056 7339.753 1.000 1.000
## V33 1 22101.936 1.521 7340.218 1.000 1.000
## V42 1 22102.384 1.932 7340.629 1.000 1.000
## V24 1 22102.471 2.012 7340.709 1.000 1.000
## V27 1 22105.537 4.825 7343.522 1.000 1.000
## V37 1 22106.290 5.516 7344.213 1.000 1.000
## V1 1 28876.548 9776.785 17115.482 0.999 0.999
## V2 1 36739.753 38385.992 45724.690 0.997 0.997
## V52 1 45735.416 133387.361 140726.058 0.992 0.992
## V51 1 48730.559 197273.108 204611.805 0.989 0.989
## V17 1 58517.096 687810.043 695148.740 0.961 0.961
## V11 1 58598.263 694897.035 702235.732 0.961 0.961
## V4 1 58667.615 701009.669 708348.367 0.961 0.961
## V18 1 58671.392 701344.147 708682.845 0.961 0.961
## V12 1 58740.574 707497.688 714836.385 0.960 0.960
## V10 1 58806.133 713378.219 720716.917 0.960 0.960
## V6 1 58851.302 717458.003 724796.701 0.960 0.960
## V19 1 58852.529 717569.158 724907.856 0.960 0.960
## V7 1 58924.424 724111.478 731450.175 0.959 0.959
## V3 1 58927.678 724408.968 731747.665 0.959 0.959
## V20 1 58932.983 724894.302 732233.000 0.959 0.959
## V8 1 58935.064 725084.716 732423.413 0.959 0.959
## V14 1 58968.136 728118.113 735456.810 0.959 0.959
## V13 1 58969.261 728221.449 735560.146 0.959 0.959
## V9 1 58976.043 728845.181 736183.878 0.959 0.959
## V15 1 58981.334 729332.140 736670.837 0.959 0.959
## V16 1 59005.271 731539.025 738877.722 0.959 0.959
## V5 1 59046.658 735370.460 742709.157 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V48
##
##
## Step 12 : AIC = 22100.45
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V25 + V27 + V29 + V30 + V33 + V35 + V36 + V37 + V42 + V43 + V44 + V45 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V25 1 22098.677 0.208 7339.064 1.000 1.000
## V30 1 22098.697 0.226 7339.082 1.000 1.000
## V43 1 22098.726 0.252 7339.108 1.000 1.000
## V45 1 22098.779 0.301 7339.157 1.000 1.000
## V29 1 22098.881 0.395 7339.251 1.000 1.000
## V21 1 22098.904 0.416 7339.272 1.000 1.000
## V35 1 22098.905 0.416 7339.272 1.000 1.000
## V49 1 22098.991 0.495 7339.351 1.000 1.000
## V22 1 22099.036 0.537 7339.393 1.000 1.000
## V44 1 22099.164 0.654 7339.510 1.000 1.000
## V50 1 22099.414 0.883 7339.739 1.000 1.000
## V47 1 22099.432 0.900 7339.756 1.000 1.000
## V36 1 22099.592 1.047 7339.903 1.000 1.000
## V33 1 22100.098 1.510 7340.366 1.000 1.000
## V42 1 22100.561 1.936 7340.792 1.000 1.000
## V24 1 22100.652 2.019 7340.875 1.000 1.000
## V27 1 22103.719 4.833 7343.689 1.000 1.000
## V37 1 22104.420 5.476 7344.332 1.000 1.000
## V1 1 28874.557 9776.644 17115.500 0.999 0.999
## V2 1 36737.763 38385.886 45724.742 0.997 0.997
## V52 1 45734.209 133401.159 140740.015 0.992 0.992
## V51 1 48728.651 197275.294 204614.150 0.989 0.989
## V17 1 58515.860 687876.234 695215.091 0.961 0.961
## V11 1 58596.514 694918.980 702257.836 0.961 0.961
## V4 1 58667.034 701135.114 708473.970 0.961 0.961
## V18 1 58670.507 701442.684 708781.540 0.961 0.961
## V12 1 58738.674 707506.404 714845.260 0.960 0.960
## V10 1 58804.157 713380.277 720719.133 0.960 0.960
## V6 1 58849.785 717501.583 724840.439 0.960 0.960
## V19 1 58852.180 717718.590 725057.446 0.960 0.960
## V7 1 58923.269 724188.583 731527.439 0.959 0.959
## V3 1 58925.971 724435.648 731774.504 0.959 0.959
## V20 1 58932.908 725070.278 732409.134 0.959 0.959
## V8 1 58933.771 725149.288 732488.144 0.959 0.959
## V13 1 58967.307 728225.559 735564.415 0.959 0.959
## V14 1 58967.469 728240.415 735579.271 0.959 0.959
## V9 1 58975.624 728990.439 736329.295 0.959 0.959
## V15 1 58979.756 729370.792 736709.648 0.959 0.959
## V16 1 59004.961 731694.986 739033.843 0.959 0.959
## V5 1 59046.579 735548.660 742887.516 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V25
##
##
## Step 13 : AIC = 22098.68
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V27 + V29 + V30 + V33 + V35 + V36 + V37 + V42 + V43 + V44 + V45 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V30 1 22096.922 0.224 7339.288 1.000 1.000
## V43 1 22096.954 0.254 7339.317 1.000 1.000
## V45 1 22097.015 0.309 7339.373 1.000 1.000
## V29 1 22097.108 0.395 7339.458 1.000 1.000
## V35 1 22097.120 0.406 7339.470 1.000 1.000
## V21 1 22097.138 0.423 7339.486 1.000 1.000
## V49 1 22097.205 0.484 7339.548 1.000 1.000
## V22 1 22097.252 0.527 7339.591 1.000 1.000
## V44 1 22097.388 0.652 7339.716 1.000 1.000
## V50 1 22097.628 0.872 7339.935 1.000 1.000
## V47 1 22097.653 0.895 7339.958 1.000 1.000
## V36 1 22097.806 1.035 7340.099 1.000 1.000
## V33 1 22098.314 1.501 7340.565 1.000 1.000
## V42 1 22098.799 1.947 7341.010 1.000 1.000
## V24 1 22098.890 2.029 7341.093 1.000 1.000
## V27 1 22101.954 4.841 7343.904 1.000 1.000
## V37 1 22102.635 5.466 7344.530 1.000 1.000
## V1 1 28872.566 9776.455 17115.519 0.999 0.999
## V2 1 36736.137 38387.820 45726.884 0.997 0.997
## V52 1 45732.344 133403.328 140742.391 0.992 0.992
## V51 1 48726.675 197275.693 204614.756 0.989 0.989
## V17 1 58514.155 687901.697 695240.761 0.961 0.961
## V11 1 58595.669 695020.126 702359.189 0.961 0.961
## V4 1 58665.067 701137.833 708476.897 0.961 0.961
## V18 1 58670.168 701589.602 708928.666 0.961 0.961
## V12 1 58737.803 707607.076 714946.140 0.960 0.960
## V10 1 58809.226 714016.990 721356.054 0.960 0.960
## V6 1 58849.078 717618.456 724957.520 0.960 0.960
## V19 1 58850.319 717730.922 725069.986 0.960 0.960
## V7 1 58922.812 724329.435 731668.498 0.959 0.959
## V3 1 58925.386 724564.879 731903.943 0.959 0.959
## V8 1 58932.071 725176.590 732515.653 0.959 0.959
## V20 1 58932.875 725250.170 732589.234 0.959 0.959
## V14 1 58965.597 728251.965 735591.028 0.959 0.959
## V13 1 58965.761 728267.065 735606.128 0.959 0.959
## V9 1 58974.379 729059.778 736398.842 0.959 0.959
## V15 1 58977.760 729370.908 736709.972 0.959 0.959
## V16 1 59005.143 731896.299 739235.363 0.959 0.959
## V5 1 59045.015 735588.921 742927.985 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V30
##
##
## Step 14 : AIC = 22096.92
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V27 + V29 + V33 + V35 + V36 + V37 + V42 + V43 + V44 + V45 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V43 1 22095.186 0.242 7339.530 1.000 1.000
## V45 1 22095.265 0.314 7339.602 1.000 1.000
## V29 1 22095.355 0.397 7339.685 1.000 1.000
## V35 1 22095.357 0.399 7339.687 1.000 1.000
## V21 1 22095.387 0.426 7339.714 1.000 1.000
## V49 1 22095.443 0.477 7339.766 1.000 1.000
## V22 1 22095.511 0.540 7339.829 1.000 1.000
## V44 1 22095.635 0.654 7339.942 1.000 1.000
## V50 1 22095.854 0.855 7340.143 1.000 1.000
## V47 1 22095.889 0.887 7340.175 1.000 1.000
## V36 1 22096.037 1.023 7340.311 1.000 1.000
## V33 1 22096.553 1.496 7340.784 1.000 1.000
## V42 1 22097.033 1.937 7341.225 1.000 1.000
## V24 1 22097.177 2.069 7341.357 1.000 1.000
## V27 1 22100.199 4.842 7344.130 1.000 1.000
## V37 1 22100.886 5.472 7344.761 1.000 1.000
## V1 1 28870.568 9776.236 17115.524 0.999 0.999
## V2 1 36734.138 38387.601 45726.890 0.997 0.997
## V52 1 45730.359 133403.360 140742.648 0.992 0.992
## V51 1 48725.058 197285.261 204624.550 0.989 0.989
## V17 1 58512.755 687953.570 695292.858 0.961 0.961
## V11 1 58593.671 695020.015 702359.304 0.961 0.961
## V4 1 58664.202 701238.175 708577.463 0.961 0.961
## V18 1 58668.294 701600.568 708939.856 0.961 0.961
## V12 1 58735.926 707617.853 714957.141 0.960 0.960
## V10 1 58809.414 714214.054 721553.342 0.960 0.960
## V6 1 58847.090 717619.375 724958.664 0.960 0.960
## V19 1 58849.394 717828.161 725167.449 0.960 0.960
## V7 1 58920.910 724338.222 731677.510 0.959 0.959
## V3 1 58924.272 724645.623 731984.911 0.959 0.959
## V20 1 58930.888 725251.109 732590.398 0.959 0.959
## V8 1 58934.814 725610.659 732949.948 0.959 0.959
## V14 1 58963.748 728265.624 735604.912 0.959 0.959
## V13 1 58965.317 728409.913 735749.201 0.959 0.959
## V9 1 58975.261 729324.769 736664.057 0.959 0.959
## V15 1 58975.914 729384.914 736724.202 0.959 0.959
## V16 1 59003.467 731925.995 739265.283 0.959 0.959
## V5 1 59043.331 735618.080 742957.368 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V43
##
##
## Step 15 : AIC = 22095.19
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V27 + V29 + V33 + V35 + V36 + V37 + V42 + V44 + V45 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V45 1 22093.526 0.312 7339.842 1.000 1.000
## V35 1 22093.604 0.383 7339.914 1.000 1.000
## V29 1 22093.621 0.398 7339.929 1.000 1.000
## V21 1 22093.650 0.425 7339.955 1.000 1.000
## V49 1 22093.708 0.478 7340.009 1.000 1.000
## V22 1 22093.777 0.542 7340.072 1.000 1.000
## V44 1 22093.899 0.654 7340.184 1.000 1.000
## V50 1 22094.108 0.846 7340.376 1.000 1.000
## V47 1 22094.164 0.897 7340.427 1.000 1.000
## V36 1 22094.279 1.002 7340.533 1.000 1.000
## V33 1 22094.818 1.497 7341.027 1.000 1.000
## V42 1 22095.295 1.934 7341.464 1.000 1.000
## V24 1 22095.394 2.026 7341.556 1.000 1.000
## V27 1 22098.430 4.812 7344.342 1.000 1.000
## V37 1 22099.139 5.462 7344.992 1.000 1.000
## V1 1 28868.689 9776.253 17115.783 0.999 0.999
## V2 1 36733.582 38395.612 45735.142 0.997 0.997
## V52 1 45728.359 133403.121 140742.651 0.992 0.992
## V51 1 48723.203 197288.736 204628.267 0.989 0.989
## V17 1 58511.167 687989.145 695328.676 0.961 0.961
## V11 1 58591.694 695021.822 702361.352 0.961 0.961
## V4 1 58662.533 701267.211 708606.741 0.961 0.961
## V18 1 58666.329 701603.415 708942.945 0.961 0.961
## V12 1 58734.026 707626.563 714966.094 0.960 0.960
## V10 1 58811.037 714540.533 721880.064 0.960 0.960
## V6 1 58845.616 717666.751 725006.281 0.960 0.960
## V19 1 58847.963 717879.431 725218.962 0.960 0.960
## V7 1 58919.057 724351.398 731690.929 0.959 0.959
## V3 1 58922.279 724646.058 731985.588 0.959 0.959
## V20 1 58929.479 725305.008 732644.539 0.959 0.959
## V8 1 58933.332 725657.799 732997.329 0.959 0.959
## V14 1 58961.912 728280.477 735620.007 0.959 0.959
## V13 1 58964.021 728474.381 735813.911 0.959 0.959
## V9 1 58975.203 729503.364 736842.895 0.959 0.959
## V15 1 58975.836 729561.677 736901.208 0.959 0.959
## V16 1 59002.543 732025.170 739364.701 0.959 0.959
## V5 1 59044.715 735932.037 743271.567 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V45
##
##
## Step 16 : AIC = 22093.53
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V27 + V29 + V33 + V35 + V36 + V37 + V42 + V44 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V35 1 22091.932 0.372 7340.214 1.000 1.000
## V29 1 22091.971 0.408 7340.250 1.000 1.000
## V21 1 22091.998 0.433 7340.275 1.000 1.000
## V49 1 22092.046 0.477 7340.319 1.000 1.000
## V22 1 22092.108 0.534 7340.376 1.000 1.000
## V44 1 22092.270 0.682 7340.525 1.000 1.000
## V50 1 22092.437 0.835 7340.678 1.000 1.000
## V47 1 22092.519 0.911 7340.753 1.000 1.000
## V36 1 22092.621 1.004 7340.847 1.000 1.000
## V33 1 22093.140 1.480 7341.322 1.000 1.000
## V42 1 22093.639 1.938 7341.780 1.000 1.000
## V24 1 22093.735 2.026 7341.868 1.000 1.000
## V27 1 22096.746 4.789 7344.632 1.000 1.000
## V37 1 22097.424 5.411 7345.254 1.000 1.000
## V1 1 28867.279 9777.203 17117.046 0.999 0.999
## V2 1 36731.639 38395.624 45735.466 0.997 0.997
## V52 1 45726.619 133407.385 140747.228 0.992 0.992
## V51 1 48721.668 197300.298 204640.140 0.989 0.989
## V17 1 58509.175 687989.575 695329.418 0.961 0.961
## V11 1 58597.186 695679.467 703019.309 0.961 0.961
## V4 1 58660.540 701267.525 708607.367 0.961 0.961
## V18 1 58664.540 701621.796 708961.639 0.961 0.961
## V12 1 58732.093 707632.259 714972.102 0.960 0.960
## V10 1 58809.043 714540.758 721880.600 0.960 0.960
## V19 1 58847.520 718020.229 725360.072 0.960 0.960
## V6 1 58848.736 718130.541 725470.383 0.960 0.960
## V7 1 58917.267 724370.307 731710.150 0.959 0.959
## V3 1 58920.295 724647.204 731987.047 0.959 0.959
## V20 1 58929.483 725488.178 732828.021 0.959 0.959
## V8 1 58931.616 725683.543 733023.385 0.959 0.959
## V14 1 58959.976 728286.052 735625.894 0.959 0.959
## V13 1 58962.598 728527.138 735866.981 0.959 0.959
## V9 1 58973.276 729509.717 736849.560 0.959 0.959
## V15 1 58973.975 729574.083 736913.926 0.959 0.959
## V16 1 59000.554 732025.935 739365.777 0.959 0.959
## V5 1 59042.846 735943.886 743283.729 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V35
##
##
## Step 17 : AIC = 22091.93
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V27 + V29 + V33 + V36 + V37 + V42 + V44 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V29 1 22090.383 0.413 7340.628 1.000 1.000
## V21 1 22090.402 0.431 7340.645 1.000 1.000
## V49 1 22090.454 0.479 7340.693 1.000 1.000
## V22 1 22090.507 0.527 7340.742 1.000 1.000
## V44 1 22090.689 0.695 7340.909 1.000 1.000
## V50 1 22090.833 0.826 7341.041 1.000 1.000
## V47 1 22090.922 0.908 7341.123 1.000 1.000
## V36 1 22091.045 1.021 7341.235 1.000 1.000
## V33 1 22091.533 1.469 7341.684 1.000 1.000
## V42 1 22092.040 1.934 7342.148 1.000 1.000
## V24 1 22092.151 2.035 7342.250 1.000 1.000
## V27 1 22095.145 4.783 7344.997 1.000 1.000
## V37 1 22095.826 5.409 7345.623 1.000 1.000
## V1 1 28865.472 9777.243 17117.458 0.999 0.999
## V2 1 36729.989 38397.253 45737.467 0.997 0.997
## V52 1 45724.716 133408.722 140748.937 0.992 0.992
## V51 1 48721.046 197335.182 204675.397 0.989 0.989
## V17 1 58507.344 688003.851 695344.066 0.961 0.961
## V11 1 58595.574 695713.130 703053.344 0.961 0.961
## V4 1 58660.131 701408.002 708748.217 0.961 0.961
## V18 1 58662.881 701651.653 708991.867 0.961 0.961
## V12 1 58730.625 707679.409 715019.624 0.960 0.960
## V10 1 58807.128 714548.110 721888.324 0.960 0.960
## V6 1 58848.124 718255.990 725596.204 0.960 0.960
## V19 1 58848.142 718257.633 725597.847 0.960 0.960
## V7 1 58915.594 724399.817 731740.031 0.959 0.959
## V3 1 58919.320 724740.621 732080.835 0.959 0.959
## V20 1 58928.594 725589.559 732929.773 0.959 0.959
## V8 1 58929.817 725701.596 733041.811 0.959 0.959
## V14 1 58957.978 728285.882 735626.096 0.959 0.959
## V13 1 58960.678 728534.110 735874.324 0.959 0.959
## V9 1 58971.503 729530.285 736870.499 0.959 0.959
## V15 1 58972.371 729610.228 736950.442 0.959 0.959
## V16 1 58999.484 732111.414 739451.628 0.959 0.959
## V5 1 59041.735 736026.080 743366.294 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V29
##
##
## Step 18 : AIC = 22090.38
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V21 + V22 + V24 + V27 + V33 + V36 + V37 + V42 + V44 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V21 1 22088.876 0.452 7341.080 1.000 1.000
## V49 1 22088.912 0.486 7341.113 1.000 1.000
## V22 1 22088.939 0.510 7341.138 1.000 1.000
## V44 1 22089.125 0.681 7341.309 1.000 1.000
## V50 1 22089.288 0.830 7341.458 1.000 1.000
## V47 1 22089.378 0.913 7341.541 1.000 1.000
## V36 1 22089.510 1.034 7341.662 1.000 1.000
## V33 1 22090.002 1.485 7342.113 1.000 1.000
## V42 1 22090.508 1.950 7342.578 1.000 1.000
## V24 1 22090.590 2.025 7342.653 1.000 1.000
## V27 1 22093.587 4.776 7345.404 1.000 1.000
## V37 1 22094.278 5.410 7346.038 1.000 1.000
## V1 1 28863.586 9777.074 17117.702 0.999 0.999
## V2 1 36728.231 38398.219 45738.847 0.997 0.997
## V52 1 45724.035 133431.502 140772.130 0.992 0.992
## V51 1 48719.374 197343.169 204683.797 0.989 0.989
## V17 1 58505.555 688021.782 695362.410 0.961 0.961
## V11 1 58593.922 695743.320 703083.948 0.961 0.961
## V4 1 58658.832 701469.738 708810.366 0.961 0.961
## V18 1 58660.899 701652.820 708993.448 0.961 0.961
## V12 1 58728.913 707704.725 715045.352 0.960 0.960
## V10 1 58806.442 714666.197 722006.825 0.960 0.960
## V19 1 58846.152 718258.129 725598.757 0.960 0.960
## V6 1 58846.190 718261.520 725602.148 0.960 0.960
## V7 1 58916.128 724631.125 731971.753 0.959 0.959
## V3 1 58917.336 724741.690 732082.318 0.959 0.959
## V20 1 58926.601 725589.781 732930.409 0.959 0.959
## V8 1 58927.931 725711.625 733052.253 0.959 0.959
## V14 1 58957.234 728400.955 735741.583 0.959 0.959
## V13 1 58959.607 728619.130 735959.757 0.959 0.959
## V9 1 58969.513 729530.774 736871.401 0.959 0.959
## V15 1 58970.914 729659.810 737000.438 0.959 0.959
## V16 1 58998.274 732184.001 739524.629 0.959 0.959
## V5 1 59039.841 736035.519 743376.147 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V21
##
##
## Step 19 : AIC = 22088.88
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V22 + V24 + V27 + V33 + V36 + V37 + V42 + V44 + V47 + V49 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V49 1 22087.397 0.478 7341.558 1.000 1.000
## V22 1 22087.430 0.509 7341.589 1.000 1.000
## V44 1 22087.606 0.670 7341.750 1.000 1.000
## V50 1 22087.806 0.853 7341.933 1.000 1.000
## V47 1 22087.867 0.910 7341.990 1.000 1.000
## V36 1 22087.996 1.028 7342.108 1.000 1.000
## V33 1 22088.499 1.489 7342.569 1.000 1.000
## V42 1 22088.991 1.941 7343.021 1.000 1.000
## V24 1 22089.079 2.022 7343.102 1.000 1.000
## V27 1 22092.079 4.775 7345.855 1.000 1.000
## V37 1 22092.747 5.388 7346.469 1.000 1.000
## V1 1 28861.779 9777.034 17118.114 0.999 0.999
## V2 1 36726.304 38398.189 45739.270 0.997 0.997
## V52 1 45722.037 133431.086 140772.166 0.992 0.992
## V51 1 48717.375 197342.728 204683.808 0.989 0.989
## V17 1 58503.773 688040.266 695381.346 0.961 0.961
## V11 1 58594.004 695925.808 703266.888 0.961 0.961
## V18 1 58659.197 701678.804 709019.884 0.961 0.961
## V4 1 58659.290 701687.000 709028.081 0.961 0.961
## V12 1 58728.377 707835.121 715176.201 0.960 0.960
## V10 1 58804.792 714697.330 722038.410 0.960 0.960
## V6 1 58844.221 718263.904 725604.985 0.960 0.960
## V19 1 58845.181 718350.958 725692.038 0.960 0.960
## V3 1 58915.451 724751.701 732092.781 0.959 0.959
## V7 1 58915.659 724770.723 732111.803 0.959 0.959
## V20 1 58924.919 725618.445 732959.526 0.959 0.959
## V8 1 58926.056 725722.625 733063.705 0.959 0.959
## V14 1 58955.296 728406.227 735747.308 0.959 0.959
## V13 1 58966.008 729391.773 736732.853 0.959 0.959
## V9 1 58967.810 729557.728 736898.808 0.959 0.959
## V15 1 58969.173 729683.199 737024.279 0.959 0.959
## V16 1 58996.500 732204.459 739545.540 0.959 0.959
## V5 1 59040.966 736325.451 743666.531 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V49
##
##
## Step 20 : AIC = 22087.4
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V22 + V24 + V27 + V33 + V36 + V37 + V42 + V44 + V47 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V22 1 22085.964 0.520 7342.078 1.000 1.000
## V44 1 22086.131 0.674 7342.232 1.000 1.000
## V50 1 22086.324 0.850 7342.409 1.000 1.000
## V47 1 22086.395 0.915 7342.474 1.000 1.000
## V36 1 22086.535 1.044 7342.603 1.000 1.000
## V33 1 22086.999 1.469 7343.028 1.000 1.000
## V42 1 22087.519 1.947 7343.506 1.000 1.000
## V24 1 22087.644 2.062 7343.620 1.000 1.000
## V27 1 22090.615 4.789 7346.348 1.000 1.000
## V37 1 22091.312 5.429 7346.987 1.000 1.000
## V1 1 28861.873 9781.036 17122.594 0.999 0.999
## V2 1 36725.787 38406.186 45747.744 0.997 0.997
## V52 1 45720.382 133436.683 140778.242 0.992 0.992
## V51 1 48716.081 197360.307 204701.865 0.989 0.989
## V17 1 58503.869 688221.925 695563.484 0.961 0.961
## V11 1 58592.174 695940.274 703281.832 0.961 0.961
## V18 1 58657.686 701721.675 709063.234 0.961 0.961
## V4 1 58658.091 701757.573 709099.132 0.961 0.961
## V12 1 58726.541 707849.244 715190.803 0.960 0.960
## V10 1 58802.869 714703.841 722045.399 0.960 0.960
## V19 1 58843.466 718376.307 725717.865 0.960 0.960
## V6 1 58844.123 718435.913 725777.471 0.960 0.960
## V3 1 58913.472 724753.134 732094.693 0.959 0.959
## V7 1 58918.709 725232.491 732574.049 0.959 0.959
## V20 1 58924.210 725736.245 733077.803 0.959 0.959
## V8 1 58924.699 725781.049 733122.608 0.959 0.959
## V14 1 58954.334 728501.148 735842.706 0.959 0.959
## V13 1 58964.922 729475.401 736816.959 0.959 0.959
## V9 1 58965.811 729557.288 736898.847 0.959 0.959
## V15 1 58967.359 729699.907 737041.466 0.959 0.959
## V16 1 58996.006 732343.244 739684.802 0.959 0.959
## V5 1 59039.227 736349.285 743690.843 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V22
##
##
## Step 21 : AIC = 22085.96
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V24 + V27 + V33 + V36 + V37 + V42 + V44 + V47 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V44 1 22084.714 0.688 7342.767 1.000 1.000
## V50 1 22084.875 0.837 7342.915 1.000 1.000
## V47 1 22084.961 0.915 7342.994 1.000 1.000
## V36 1 22085.099 1.042 7343.120 1.000 1.000
## V33 1 22085.572 1.476 7343.554 1.000 1.000
## V42 1 22086.089 1.950 7344.029 1.000 1.000
## V24 1 22086.181 2.035 7344.113 1.000 1.000
## V27 1 22089.184 4.792 7346.870 1.000 1.000
## V37 1 22089.872 5.423 7347.501 1.000 1.000
## V1 1 28860.852 9782.611 17124.690 0.999 0.999
## V2 1 36724.248 38408.304 45750.383 0.997 0.997
## V52 1 45718.413 133436.699 140778.777 0.992 0.992
## V51 1 48714.253 197364.202 204706.280 0.989 0.989
## V17 1 58503.599 688371.840 695713.918 0.961 0.961
## V11 1 58591.054 696017.121 703359.199 0.961 0.961
## V18 1 58655.933 701743.034 709085.113 0.961 0.961
## V4 1 58656.268 701772.700 709114.778 0.961 0.961
## V12 1 58724.816 707873.335 715215.414 0.960 0.960
## V10 1 58802.031 714808.195 722150.273 0.960 0.960
## V6 1 58842.185 718441.021 725783.099 0.960 0.960
## V19 1 58842.253 718447.220 725789.298 0.960 0.960
## V3 1 58912.638 724859.313 732201.392 0.959 0.959
## V7 1 58916.964 725255.288 732597.366 0.959 0.959
## V8 1 58922.834 725792.911 733134.989 0.959 0.959
## V20 1 58925.065 725997.278 733339.356 0.959 0.959
## V14 1 58952.881 728550.985 735893.063 0.959 0.959
## V13 1 58962.929 729475.577 736817.655 0.959 0.959
## V9 1 58963.811 729556.776 736898.855 0.959 0.959
## V15 1 58967.020 729852.365 737194.444 0.959 0.959
## V16 1 58994.153 732356.250 739698.328 0.959 0.959
## V5 1 59037.918 736412.997 743755.075 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V44
##
##
## Step 22 : AIC = 22084.71
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V24 + V27 + V33 + V36 + V37 + V42 + V47 + V50 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V50 1 22083.645 0.854 7343.621 1.000 1.000
## V47 1 22083.726 0.928 7343.695 1.000 1.000
## V36 1 22083.835 1.029 7343.796 1.000 1.000
## V33 1 22084.301 1.456 7344.223 1.000 1.000
## V42 1 22084.809 1.923 7344.690 1.000 1.000
## V24 1 22084.892 1.999 7344.766 1.000 1.000
## V27 1 22087.933 4.791 7347.558 1.000 1.000
## V37 1 22088.649 5.448 7348.215 1.000 1.000
## V1 1 28859.027 9782.297 17125.064 0.999 0.999
## V2 1 36722.556 38409.374 45752.141 0.997 0.997
## V52 1 45717.071 133447.597 140790.364 0.992 0.992
## V51 1 48712.255 197363.567 204706.334 0.989 0.989
## V17 1 58502.264 688428.997 695771.764 0.961 0.961
## V11 1 58589.283 696036.543 703379.309 0.961 0.961
## V4 1 58654.276 701772.750 709115.516 0.961 0.961
## V18 1 58657.209 702032.683 709375.450 0.961 0.961
## V12 1 58723.032 707891.952 715234.718 0.960 0.960
## V10 1 58800.197 714822.486 722165.253 0.960 0.960
## V6 1 58840.441 718463.564 725806.331 0.960 0.960
## V19 1 58840.625 718480.247 725823.014 0.960 0.960
## V3 1 58911.809 724965.836 732308.602 0.959 0.959
## V7 1 58915.028 725260.460 732603.227 0.959 0.959
## V8 1 58920.993 725806.748 733149.514 0.959 0.959
## V20 1 58923.330 726020.907 733363.674 0.959 0.959
## V14 1 58950.909 728552.816 735895.583 0.959 0.959
## V13 1 58961.047 729485.776 736828.543 0.959 0.959
## V9 1 58964.178 729774.111 737116.878 0.959 0.959
## V15 1 58965.353 729882.379 737225.146 0.959 0.959
## V16 1 58992.208 732360.635 739703.402 0.959 0.959
## V5 1 59037.880 736594.673 743937.439 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V50
##
##
## Step 23 : AIC = 22083.64
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V24 + V27 + V33 + V36 + V37 + V42 + V47 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V47 1 22082.670 0.941 7344.562 1.000 1.000
## V36 1 22082.687 0.956 7344.577 1.000 1.000
## V33 1 22083.256 1.478 7345.099 1.000 1.000
## V42 1 22083.734 1.917 7345.538 1.000 1.000
## V24 1 22083.782 1.962 7345.583 1.000 1.000
## V27 1 22086.844 4.773 7348.394 1.000 1.000
## V37 1 22087.588 5.456 7349.077 1.000 1.000
## V1 1 28857.503 9782.463 17126.084 0.999 0.999
## V2 1 36721.461 38413.696 45757.317 0.997 0.997
## V52 1 45716.707 133475.521 140819.142 0.992 0.992
## V51 1 48710.546 197370.134 204713.755 0.989 0.989
## V17 1 58501.366 688523.945 695867.566 0.961 0.961
## V11 1 58587.288 696036.166 703379.787 0.961 0.961
## V4 1 58652.949 701831.501 709175.122 0.961 0.961
## V18 1 58655.210 702031.940 709375.561 0.961 0.961
## V12 1 58726.463 708376.692 715720.313 0.960 0.960
## V10 1 58799.318 714922.822 722266.443 0.960 0.960
## V19 1 58838.822 718497.300 725840.921 0.960 0.960
## V6 1 58838.896 718503.998 725847.619 0.960 0.960
## V3 1 58910.489 725027.211 732370.832 0.959 0.959
## V7 1 58913.049 725261.540 732605.161 0.959 0.959
## V8 1 58919.396 725842.859 733186.480 0.959 0.959
## V20 1 58921.515 726037.062 733380.683 0.959 0.959
## V14 1 58949.228 728581.270 735924.891 0.959 0.959
## V13 1 58959.172 729496.443 736840.064 0.959 0.959
## V9 1 58962.230 729778.016 737121.637 0.959 0.959
## V15 1 58963.370 729883.019 737226.640 0.959 0.959
## V16 1 58990.449 732382.087 739725.708 0.959 0.959
## V5 1 59036.931 736691.465 744035.086 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V47
##
##
## Step 24 : AIC = 22082.67
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V24 + V27 + V33 + V36 + V37 + V42 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V36 1 22081.708 0.952 7345.514 1.000 1.000
## V33 1 22082.283 1.480 7346.042 1.000 1.000
## V42 1 22082.742 1.902 7346.464 1.000 1.000
## V24 1 22082.778 1.935 7346.497 1.000 1.000
## V27 1 22085.913 4.814 7349.376 1.000 1.000
## V37 1 22086.649 5.490 7350.052 1.000 1.000
## V1 1 28855.756 9782.063 17126.625 0.999 0.999
## V2 1 36722.643 38430.951 45775.513 0.997 0.997
## V52 1 45714.717 133474.761 140819.323 0.992 0.992
## V51 1 48708.931 197379.063 204723.625 0.989 0.989
## V17 1 58501.271 688688.716 696033.279 0.961 0.961
## V11 1 58585.356 696041.164 703385.726 0.961 0.961
## V4 1 58651.190 701851.902 709196.464 0.961 0.961
## V18 1 58653.549 702060.989 709405.551 0.961 0.961
## V12 1 58724.660 708393.327 715737.889 0.960 0.960
## V10 1 58797.887 714973.166 722317.728 0.960 0.960
## V6 1 58837.471 718555.144 725899.706 0.960 0.960
## V19 1 58839.417 718731.769 726076.331 0.960 0.960
## V3 1 58908.550 725031.788 732376.350 0.959 0.959
## V7 1 58912.539 725397.005 732741.567 0.959 0.959
## V8 1 58919.046 725993.114 733337.676 0.959 0.959
## V20 1 58920.641 726139.278 733483.840 0.959 0.959
## V14 1 58947.361 728592.555 735937.117 0.959 0.959
## V13 1 58957.368 729513.477 736858.039 0.959 0.959
## V9 1 58960.753 729825.321 737169.883 0.959 0.959
## V15 1 58961.599 729903.241 737247.803 0.959 0.959
## V16 1 58988.664 732400.996 739745.558 0.959 0.959
## V5 1 59038.586 737030.456 744375.018 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V36
##
##
## Step 25 : AIC = 22081.71
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V24 + V27 + V33 + V37 + V42 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V33 1 22081.363 1.519 7347.034 1.000 1.000
## V42 1 22081.775 1.898 7347.413 1.000 1.000
## V24 1 22081.818 1.937 7347.452 1.000 1.000
## V27 1 22084.906 4.773 7350.287 1.000 1.000
## V37 1 22085.656 5.462 7350.976 1.000 1.000
## V1 1 28853.992 9781.616 17127.131 0.999 0.999
## V2 1 36720.738 38430.543 45776.057 0.997 0.997
## V52 1 45715.786 133527.824 140873.338 0.992 0.992
## V51 1 48708.705 197423.493 204769.007 0.989 0.989
## V17 1 58500.142 688763.452 696108.966 0.961 0.961
## V11 1 58583.364 696040.943 703386.457 0.961 0.961
## V4 1 58650.905 702002.937 709348.451 0.961 0.961
## V18 1 58651.624 702066.710 709412.225 0.961 0.961
## V12 1 58723.282 708448.041 715793.555 0.960 0.960
## V10 1 58796.124 714993.676 722339.190 0.960 0.960
## V6 1 58835.805 718584.490 725930.004 0.960 0.960
## V19 1 58837.435 718732.463 726077.978 0.960 0.960
## V3 1 58908.255 725186.923 732532.437 0.959 0.959
## V7 1 58910.700 725410.770 732756.284 0.959 0.959
## V8 1 58917.567 726039.848 733385.363 0.959 0.959
## V20 1 58918.865 726158.899 733504.413 0.959 0.959
## V14 1 58945.539 728607.988 735953.502 0.959 0.959
## V13 1 58957.289 729689.484 737034.998 0.959 0.959
## V9 1 58958.933 729840.894 737186.408 0.959 0.959
## V15 1 58960.592 729993.805 737339.319 0.959 0.959
## V16 1 58986.807 732413.334 739758.848 0.959 0.959
## V5 1 59036.602 737031.043 744376.557 0.959 0.959
## ------------------------------------------------------------------------------
##
## - V33
##
##
## Step 26 : AIC = 22081.36
## Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V18 + V19 + V20 + V24 + V27 + V37 + V42 + V51 + V52
##
## ------------------------------------------------------------------------------
## Variable DF AIC Sum Sq RSS R-Sq Adj. R-Sq
## ------------------------------------------------------------------------------
## V24 1 22081.466 1.931 7348.965 1.000 1.000
## V42 1 22081.467 1.932 7348.966 1.000 1.000
## V27 1 22084.473 4.693 7351.727 1.000 1.000
## V37 1 22085.218 5.378 7352.412 1.000 1.000
## V1 1 28855.096 9786.740 17133.774 0.999 0.999
## V2 1 36718.749 38429.085 45776.119 0.997 0.997
## V52 1 45714.676 133541.982 140889.016 0.992 0.992
## V51 1 48707.736 197448.358 204795.392 0.989 0.989
## V17 1 58501.102 689019.511 696366.545 0.961 0.961
## V11 1 58583.608 696236.658 703583.692 0.961 0.961
## V4 1 58649.543 702058.005 709405.039 0.961 0.961
## V18 1 58651.176 702202.779 709549.813 0.961 0.961
## V12 1 58721.332 708451.013 715798.047 0.960 0.960
## V10 1 58794.320 715009.805 722356.839 0.960 0.960
## V6 1 58833.858 718587.792 725934.825 0.960 0.960
## V19 1 58836.440 718822.095 726169.129 0.960 0.960
## V7 1 58908.705 725409.736 732756.770 0.959 0.959
## V3 1 58909.132 725448.877 732795.911 0.959 0.959
## V8 1 58915.631 726044.255 733391.289 0.959 0.959
## V20 1 58918.111 726271.583 733618.616 0.959 0.959
## V14 1 58943.649 728616.588 735963.622 0.959 0.959
## V13 1 58956.047 729757.776 737104.810 0.959 0.959
## V9 1 58956.992 729844.809 737191.843 0.959 0.959
## V15 1 58958.808 730012.154 737359.188 0.959 0.959
## V16 1 58984.936 732423.718 739770.752 0.959 0.959
## V5 1 59034.681 737036.816 744383.850 0.959 0.959
## ------------------------------------------------------------------------------
##
##
## No more variables to be removed.
##
## Variables Removed:
##
## - V32
## - V26
## - V40
## - V46
## - V41
## - V28
## - V31
## - V34
## - V38
## - V39
## - V23
## - V48
## - V25
## - V30
## - V43
## - V45
## - V35
## - V29
## - V21
## - V49
## - V22
## - V44
## - V50
## - V47
## - V36
## - V33
##
##
## Final Model Output
## ------------------
##
## Model Summary
## -------------------------------------------------------------
## R 1.000 RMSE 0.960
## R-Squared 1.000 Coef. Var 0.190
## Adj. R-Squared 1.000 MSE 0.921
## Pred R-Squared 1.000 MAE 0.697
## -------------------------------------------------------------
## RMSE: Root Mean Square Error
## MSE: Mean Square Error
## MAE: Mean Absolute Error
##
## ANOVA
## ------------------------------------------------------------------------------
## Sum of
## Squares DF Mean Square F Sig.
## ------------------------------------------------------------------------------
## Regression 18028630.897 26 693408.881 752675.962 0.0000
## Residual 7347.034 7975 0.921
## Total 18035977.931 8001
## ------------------------------------------------------------------------------
##
## Parameter Estimates
## ------------------------------------------------------------------------------------------
## model Beta Std. Error Std. Beta t Sig lower upper
## ------------------------------------------------------------------------------------------
## (Intercept) 2.601 0.185 14.073 0.000 2.238 2.963
## V1 3.449 0.033 0.199 103.069 0.000 3.383 3.514
## V2 3.496 0.017 0.157 204.239 0.000 3.462 3.529
## V3 3.493 0.004 0.201 887.386 0.000 3.485 3.501
## V4 3.494 0.004 0.197 872.963 0.000 3.487 3.502
## V5 3.502 0.004 0.202 894.446 0.000 3.495 3.510
## V6 3.500 0.004 0.200 883.180 0.000 3.493 3.508
## V7 3.506 0.004 0.201 887.362 0.000 3.498 3.513
## V8 3.498 0.004 0.201 887.750 0.000 3.490 3.506
## V9 3.500 0.004 0.202 890.071 0.000 3.492 3.507
## V10 3.496 0.004 0.199 880.979 0.000 3.488 3.504
## V11 3.501 0.004 0.197 869.336 0.000 3.493 3.509
## V12 3.509 0.004 0.199 876.929 0.000 3.501 3.516
## V13 3.499 0.004 0.201 890.018 0.000 3.492 3.507
## V14 3.501 0.004 0.201 889.322 0.000 3.493 3.508
## V15 3.502 0.004 0.201 890.173 0.000 3.494 3.510
## V16 3.501 0.004 0.202 891.642 0.000 3.494 3.509
## V17 3.491 0.004 0.196 864.819 0.000 3.483 3.499
## V18 3.505 0.004 0.198 873.053 0.000 3.497 3.513
## V19 3.502 0.004 0.200 883.324 0.000 3.495 3.510
## V20 3.495 0.004 0.201 887.889 0.000 3.488 3.503
## V24 -0.006 0.004 0.000 -1.448 0.148 -0.014 0.002
## V27 -0.009 0.004 -0.001 -2.257 0.024 -0.017 -0.001
## V37 -0.009 0.004 -0.001 -2.416 0.016 -0.017 -0.002
## V42 -0.006 0.004 0.000 -1.448 0.148 -0.014 0.002
## V51 -4.488 0.010 -0.914 -462.952 0.000 -4.507 -4.469
## V52 -4.517 0.012 -0.193 -380.731 0.000 -4.540 -4.493
## ------------------------------------------------------------------------------------------mod_bcwd##
##
## Backward Elimination Summary
## ---------------------------------------------------------------------------
## Variable AIC RSS Sum Sq R-Sq Adj. R-Sq
## ---------------------------------------------------------------------------
## Full Model 22123.582 7338.059 18028639.872 0.99959 0.99959
## V32 22121.582 7338.059 18028639.871 0.99959 0.99959
## V26 22119.585 7338.062 18028639.868 0.99959 0.99959
## V40 22117.602 7338.078 18028639.853 0.99959 0.99959
## V46 22115.632 7338.105 18028639.826 0.99959 0.99959
## V41 22113.684 7338.153 18028639.778 0.99959 0.99959
## V28 22111.738 7338.202 18028639.728 0.99959 0.99959
## V31 22109.797 7338.256 18028639.675 0.99959 0.99959
## V34 22107.861 7338.315 18028639.616 0.99959 0.99959
## V38 22105.995 7338.438 18028639.493 0.99959 0.99959
## V39 22104.134 7338.565 18028639.365 0.99959 0.99959
## V23 22102.278 7338.697 18028639.233 0.99959 0.99959
## V48 22100.451 7338.856 18028639.075 0.99959 0.99959
## V25 22098.677 7339.064 18028638.867 0.99959 0.99959
## V30 22096.922 7339.288 18028638.643 0.99959 0.99959
## V43 22095.186 7339.530 18028638.400 0.99959 0.99959
## V45 22093.526 7339.842 18028638.088 0.99959 0.99959
## V35 22091.932 7340.214 18028637.716 0.99959 0.99959
## V29 22090.383 7340.628 18028637.303 0.99959 0.99959
## V21 22088.876 7341.080 18028636.850 0.99959 0.99959
## V49 22087.397 7341.558 18028636.372 0.99959 0.99959
## V22 22085.964 7342.078 18028635.852 0.99959 0.99959
## V44 22084.714 7342.767 18028635.164 0.99959 0.99959
## V50 22083.645 7343.621 18028634.310 0.99959 0.99959
## V47 22082.670 7344.562 18028633.369 0.99959 0.99959
## V36 22081.708 7345.514 18028632.416 0.99959 0.99959
## V33 22081.363 7347.034 18028630.897 0.99959 0.99959
## ---------------------------------------------------------------------------mod_bcwd$model##
## Call:
## lm(formula = paste(response, "~", paste(preds, collapse = " + ")),
## data = l)
##
## Coefficients:
## (Intercept) V1 V2 V3 V4 V5
## 2.600549 3.448787 3.495759 3.493128 3.494456 3.502448
## V6 V7 V8 V9 V10 V11
## 3.500391 3.505625 3.497991 3.499672 3.495768 3.501190
## V12 V13 V14 V15 V16 V17
## 3.508631 3.499304 3.500580 3.501821 3.501314 3.491392
## V18 V19 V20 V24 V27 V37
## 3.505106 3.502441 3.495246 -0.005822 -0.008911 -0.009406
## V42 V51 V52
## -0.005739 -4.487634 -4.516698Model terbaik hasil dari seleksi peubah
#Best Model
best_model<-lm(formula = Y~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V19 + V20 + V29 + V31 + V33 + V34 + V51 + V52, data = train.dataindex)
summary(best_model)##
## Call:
## lm(formula = Y ~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 +
## V10 + V11 + V12 + V13 + V14 + V15 + V16 + V17 + V19 + V20 +
## V29 + V31 + V33 + V34 + V51 + V52, data = train.dataindex)
##
## Residuals:
## Min 1Q Median 3Q Max
## -34.595 -6.107 -0.136 6.130 39.781
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 34.894878 1.769971 19.715 <2e-16 ***
## V1 3.415615 0.328894 10.385 <2e-16 ***
## V2 3.291052 0.168179 19.569 <2e-16 ***
## V3 3.472381 0.038690 89.748 <2e-16 ***
## V4 3.484619 0.039349 88.557 <2e-16 ***
## V5 3.462220 0.038486 89.960 <2e-16 ***
## V6 3.568112 0.038953 91.600 <2e-16 ***
## V7 3.509518 0.038809 90.431 <2e-16 ***
## V8 3.493387 0.038720 90.221 <2e-16 ***
## V9 3.485065 0.038637 90.201 <2e-16 ***
## V10 3.548815 0.038991 91.016 <2e-16 ***
## V11 3.496363 0.039586 88.323 <2e-16 ***
## V12 3.479025 0.039314 88.493 <2e-16 ***
## V13 3.478814 0.038643 90.024 <2e-16 ***
## V14 3.595009 0.038670 92.967 <2e-16 ***
## V15 3.503096 0.038664 90.603 <2e-16 ***
## V16 3.510310 0.038592 90.959 <2e-16 ***
## V17 3.454014 0.039676 87.055 <2e-16 ***
## V19 3.495332 0.038965 89.705 <2e-16 ***
## V20 3.513663 0.038701 90.789 <2e-16 ***
## V29 -0.006534 0.038762 -0.169 0.866
## V31 0.039644 0.038869 1.020 0.308
## V33 -0.049770 0.039045 -1.275 0.202
## V34 -0.003863 0.039004 -0.099 0.921
## V51 -4.440976 0.095262 -46.619 <2e-16 ***
## V52 -4.646754 0.116594 -39.854 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.434 on 7976 degrees of freedom
## Multiple R-squared: 0.9606, Adjusted R-squared: 0.9605
## F-statistic: 7788 on 25 and 7976 DF, p-value: < 2.2e-16Uji Asumsi Regresi
Dalam membangun model regresi linier, metode estimasi yang digunakan adalah dengan metode estimasi kuadrat terkecil (ordinary least square), yaitu dengan meminimumkan jumlah kuadrat residual.
Terdapat asumsi yang harus diuji dalam membangun model regresi linier tersebut. Asumsi model tersebut sering juga disebut sebagai asumsi klasik yang terdiri atas :
- Uji normalitas residual
- Uji asumsi variasi galat yang bersifat konstan (homoskedastisitas)
- Uji asumsi tidak adanya serial korelasi dari galat (autokorelasi)
- Uji multikolinieritas antarvariabel independen.
Uji Kenormalan
Kenormalan sisaan akan diuji dengan Uji Jarque Bera
#Normalitas residual
jarque.bera.test(best_model$residuals)##
## Jarque Bera Test
##
## data: best_model$residuals
## X-squared = 0.56363, df = 2, p-value = 0.7544Hipotesis
H0 : Residual berdistribusi normal H1 : Residual tidak berdistribusi normal
Tingkat signifikansi = 0.05
Statistik Uji : p-value = 0.2272
Keputusan : Karena p-value (0.2272) > alpha (0.05), maka gagal tolak H0
Kesimpulan : Dengan tingkat keyakinan 95%, kita yakin bahwa residual berdistribusi normal.
Uji Homogenitas
Untuk menguji homoskedastisitas akan digunakan uji Breusch Pagan
#Kehomogenan Ragam
bptest(best_model, data=DAT.SIM.01)##
## studentized Breusch-Pagan test
##
## data: best_model
## BP = 22.443, df = 25, p-value = 0.61Hipotesis
H0 : Ragam Homogen H1 : Ragam tidak homogen
Tingkat Signifikansi : 0.05
Statistik Uji : pvalue = 0.2382
Keputusan : Karena p-value (0.2382) > alpha (0.05) maka gagal tolak H0.
Kesimpulan : Dengan tingkat keyakinan 95%, kita yakin bahwa ragam homogen (asumsi homoskedastisitas terpenuhi)
Uji Autokorelasi
Uji autokorelasi akan diuji dengan uji Durbin Watson
#Autokorelasi
dwtest(best_model)##
## Durbin-Watson test
##
## data: best_model
## DW = 2.0156, p-value = 0.7582
## alternative hypothesis: true autocorrelation is greater than 0Hipotesis
H0 : Tidak ada auto korelasi dari galat H1 : Ada auto korelasi dari galat
Tingkat signifikansi : 0.05
Statistik uji : pvalue = 0.8405
Keputusan : Karena nilai pvalue (0.8405) > alpha (0.05) maka gagal tolak H0
Kesimpulan : Dengan tingkat kepercayaan 95%, kita yakin bahwa tidak ada auto korelasi pada galat.
Uji Multikolinieritas
Kolinieritas akan diuji dengan VIF (Variance Inflation Factor). Jika, nilai VIF > 5, maka terjadi multikolinieritas.
#Uji Multikolinieritas
vif(best_model)## V1 V2 V3 V4 V5 V6 V7 V8
## 72.743941 11.632354 1.003192 1.001745 1.001515 1.003058 1.002405 1.003114
## V9 V10 V11 V12 V13 V14 V15 V16
## 1.003211 1.002175 1.004354 1.002672 1.003300 1.003109 1.002121 1.001747
## V17 V19 V20 V29 V31 V33 V34 V51
## 1.001989 1.001678 1.002443 1.001743 1.002903 1.002402 1.002231 76.260358
## V52
## 5.028906Variabel V1,V2,V51,dan V52 memiliki nilai VIF > 5 dan nilainya sangat besar sehingga mengindikasikan bahwa ada multikolinieritas
Cek Korelasi Variabel
Uji multikolinieritas dengan VIF > 5 menunjukkan adanya multikolinieritas. Pada data juga sudah diketahui bahwa ada 4 variabel yang berkorelasi kuat. Akan diuji variabel mana yang berkorelasi dengan menggunakan matrik korelasi
#Cek korelasi
data_kor <- train.dataindex[c(2,3,52,53)]
mk <- cor(data_kor)
round(mk,2) #Membulatkan 2 angka di belakang koma## V1 V2 V51 V52
## V1 1.00 0.94 0.98 -0.59
## V2 0.94 1.00 0.93 -0.62
## V51 0.98 0.93 1.00 -0.45
## V52 -0.59 -0.62 -0.45 1.00corrplot(mk, type="lower",
order = "hclust", # mengurutkan berdasarkan hierarchical clustering
tl.col= "black", # warna tulisan
addCoef.col = "black", # tambahkan koefisien korelasi
diag=FALSE, #menyembunyikan koefisien pada diagonal
tl.srt= 45, # kemiringan tulisan 45 derajat
method = "circle") # Bentuk Visualisasi
Terlihat dalam matriks korelasi bahwa terdapat korelasi yang tinggi antara V1 dan V2, V51 dam V2, V51 dan V1, V52 dam V1, V52 dan V2 yang menyebabkan adanya kolinieritas. Solusi dari masalah ini bisa diselesaikan dengan beberapa cara yaitu menghilangkan variabel yang berkorelasi atau menggunakan metode penyusutan peubah dengan ridge, lasso, dan elastic-net. Pada bahasan kali ini kit akan selesaikan masalah tsb dengan metode ridge, lasso, dan elastic-net.
Prediksi data
Selanjutnya kita akan mencoba model best-subset yang sudah dibuat dengan menggunakan data test.
preds_best <- predict(best_model, test.dataindex)
head(preds_best)## 18 19 30 37 38 40
## 590.4094 518.2193 519.5790 501.0044 483.8206 527.5415Melihat akurasi prediksi dengan menggunakan plot
plot(test.dataindex$Y, preds_best, col = "blue")
cor(test.dataindex$Y, preds_best)## [1] 0.9801524Shrinkage Method
Regresi Shrinkage merupakan model regresi yang menggunakan suatu penalty tertentu saat melakukan estimasi koefisienya. Penalti tersebut berperan untuk seleksi peubah ataupun mengatasi kolinear yang tinggi antar peubah prediktor. Model-model untuk yang termasuk dalam regresi shirnkage antara lain:
Regresi LASSO
Regresi Ridge
Regresi Elastic Net
Regresi Lasso
Metode pertama yang kita coba adalah metode LASSO. Metode ini bisa dijalankan menggunakan package glmnet. Package glmnetUtils merupakan package tambahan dari glmnet yang memungkinkan syntax glmnet bisa dinput menggunakan object data.frame.
Fungsi cv.glmnet digunakan untuk menjalankan menjalankan metode LASSO, asalkan nilai argumen alpha=1. Kemudian, dengan fungsi ini juga dimungkinkan memilih parameter penalty lambda terbaik dengan menggunakan cross-validation (validasi-silang) yang didasarkan pada kriteria tertentu, contohnya saja kriteria “mse” dan “mae”. Proses ini disebut juga sebagai Tuning Parameter. Dimana lambda merupakan parameter yang akan dicari nilai optimalnya berdasarkan nilai kebaikan model “mse” dan “mae”. Argumen nfolds digunakan untuk menentukan jumlah folds/lipatan pada cross-validation.
set.seed(123)
model_lasso_mae <- cv.glmnet(Y~.,data=train.dataindex,alpha = 1,
type.measure="mae",
family="gaussian",
nfolds=5)Melihat jumlah variabel terbaik berdasarkan metode ini
plot(model_lasso_mae)
Informasi penting yang bisa dilihat pada plot diatas adalah banyaknya peubah terpilih yang ditulis diatas plot. Kemudian ada garis vertikal putus-putus yang menandakan nilai lambda optimum berdasarkan kriteria yang dipilih. Nilai lambda optimum dipilih berdasarkan nilai mae terkecil. Selain itu, kriteria lambda optimum juga dipilih berdasarkan lembar selang terkecil dari garis pada setiap titik. Sehingga garis vertikal yang satunya menandakan hal tersebut. Informasi ini akan lebih jelas dengan bantuan package broom.
info_lasso_mae <- broom::glance(model_lasso_mae)
info_lasso_maebroom::tidy(model_lasso_mae)Nilai koefisien dari variable terpilih bisa dikeluarkan dengan bantuan package broom dibawah ini.
broom::tidy(model_lasso_mae$glmnet.fit)coef_mae_min <- broom::tidy(model_lasso_mae$glmnet.fit) %>% filter(lambda==info_lasso_mae$lambda.min)
coef_mae_minMembangun model regresi lasso berdasarkan lambda min.
lasso_model <- glmnet(Y~.,data=train.dataindex, lambda = model_lasso_mae$lambda.min , alpha = 1)
coef(lasso_model)## 53 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 4.3764553
## V1 0.4528286
## V2 2.6493657
## V3 3.4631971
## V4 3.4804307
## V5 3.4800410
## V6 3.4825433
## V7 3.4898556
## V8 3.4743504
## V9 3.4763583
## V10 3.4775971
## V11 3.4713200
## V12 3.4911718
## V13 3.4726461
## V14 3.4785644
## V15 3.4828477
## V16 3.4811897
## V17 3.4687857
## V18 3.4831842
## V19 3.4845621
## V20 3.4809565
## V21 .
## V22 .
## V23 .
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## V48 .
## V49 .
## V50 .
## V51 -3.5661917
## V52 -5.4382644Prediksi data test dengan menggunakan model lasso
preds_lasso <- predict(lasso_model, test.dataindex)
head(preds_lasso)## s0
## [1,] 595.0505
## [2,] 519.1783
## [3,] 533.6368
## [4,] 500.0377
## [5,] 508.8978
## [6,] 526.6427Melihat akurasi prediksi dengan menggunakan plot
plot(test.dataindex$Y, preds_lasso, col = "blue")
cor(test.dataindex$Y, preds_lasso)## s0
## [1,] 0.9995587Regresi Ridge
Metode kedua yang kita coba adalah metode RIDGE. Metode ini bisa dijalankan menggunakan package glmnet. Package glmnetUtils merupakan package tambahan dari glmnet yang memungkinkan syntax glmnet bisa dinput menggunakan object data.frame.
Fungsi cv.glmnet digunakan untuk menjalankan menjalankan metode RIDGE, asalkan nilai argumen alpha=0. Kemudian, dengan fungsi ini juga dimungkinkan memilih parameter penalty lambda terbaik dengan menggunakan cross-validation (validasi-silang) yang didasarkan pada kriteria tertentu, contohnya saja kriteria “mse” dan “mae”. Proses ini disebut juga sebagai Tuning Parameter. Dimana lambda merupakan parameter yang akan dicari nilai optimalnya berdasarkan nilai kebaikan model “mse” dan “mae”. Argumen nfolds digunakan untuk menentukan jumlah folds/lipatan pada cross-validation.
set.seed(123)
model_ridge_mae <- cv.glmnet(Y~.,data=train.dataindex,alpha =0, type.measure="mae",family="gaussian",nfolds=5)plot(model_ridge_mae)
info_ridge_mae <- broom::glance(model_ridge_mae)
info_ridge_maebroom::tidy(model_ridge_mae)broom::tidy(model_ridge_mae$glmnet.fit)ridge_mae_min <- broom::tidy(model_ridge_mae$glmnet.fit) %>% filter(lambda==info_ridge_mae$lambda.min)
ridge_mae_minridge_model <- glmnet(Y~.,data=train.dataindex, lambda = model_ridge_mae$lambda.min , alpha = 0)
coef(ridge_model)## 53 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 2.223285e+01
## V1 -3.507508e+00
## V2 -1.935697e-01
## V3 3.302955e+00
## V4 3.343847e+00
## V5 3.324738e+00
## V6 3.332249e+00
## V7 3.353683e+00
## V8 3.317098e+00
## V9 3.323868e+00
## V10 3.335864e+00
## V11 3.311649e+00
## V12 3.345863e+00
## V13 3.325702e+00
## V14 3.338579e+00
## V15 3.346638e+00
## V16 3.334999e+00
## V17 3.329315e+00
## V18 3.338619e+00
## V19 3.339188e+00
## V20 3.340788e+00
## V21 1.051328e-02
## V22 8.004975e-03
## V23 1.632594e-02
## V24 -4.153250e-03
## V25 -7.018265e-03
## V26 -7.532913e-03
## V27 3.843484e-03
## V28 5.672893e-05
## V29 -4.221685e-03
## V30 2.282977e-02
## V31 -2.983686e-03
## V32 -3.512919e-03
## V33 -2.924336e-03
## V34 1.738675e-02
## V35 3.261770e-02
## V36 -3.663143e-03
## V37 4.760438e-03
## V38 1.504364e-02
## V39 1.506062e-02
## V40 -6.978834e-03
## V41 1.216738e-02
## V42 9.709148e-03
## V43 6.781041e-04
## V44 -9.624483e-03
## V45 -1.602049e-02
## V46 6.368778e-03
## V47 -7.136294e-03
## V48 4.778305e-03
## V49 6.941383e-03
## V50 2.087898e-02
## V51 -1.907352e+00
## V52 -6.582305e+00preds_ridge <- predict(ridge_model, test.dataindex)
head(preds_ridge)## s0
## [1,] 590.4440
## [2,] 519.4716
## [3,] 534.2941
## [4,] 501.1628
## [5,] 506.6590
## [6,] 528.1139plot(test.dataindex$Y, preds_ridge, col = "blue")
cor(test.dataindex$Y, preds_ridge)## s0
## [1,] 0.9977694Regresi Elastic-net
Metode kedua yang kita coba adalah metode ELASTIC-NET. Metode ini bisa dijalankan menggunakan package glmnet. Package glmnetUtils merupakan package tambahan dari glmnet yang memungkinkan syntax glmnet bisa dinput menggunakan object data.frame.
Fungsi cv.glmnet digunakan untuk menjalankan menjalankan metode ELASTIC-NET, asalkan nilai argumen alpha=0-1. Kemudian, dengan fungsi ini juga dimungkinkan memilih parameter penalty lambda terbaik dengan menggunakan cross-validation (validasi-silang) yang didasarkan pada kriteria tertentu, contohnya saja kriteria “mse” dan “mae”. Proses ini disebut juga sebagai Tuning Parameter. Dimana lambda merupakan parameter yang akan dicari nilai optimalnya berdasarkan nilai kebaikan model “mse” dan “mae”. Argumen nfolds digunakan untuk menentukan jumlah folds/lipatan pada cross-validation.
set.seed(123)
model_elastic_mae <- cv.glmnet(Y~.,
data=train.dataindex ,
alpha = 0.8,
type.measure="mae",
family="gaussian",nfolds=5)plot(model_elastic_mae)
info_elastic_mae <- broom::glance(model_elastic_mae)
info_elastic_maebroom::tidy(model_elastic_mae)broom::tidy(model_elastic_mae$glmnet.fit)elastic_mae_min <- broom::tidy(model_elastic_mae$glmnet.fit) %>% filter(lambda==info_elastic_mae$lambda.min)
elastic_mae_minMenghitung nilai mae model elastic-net dengan memasukkan semua nilai alpha yang mungkin.
for (i in 0:10) {
assign(paste("fit", i, sep=""), cv.glmnet(Y~.,data=train.dataindex, type.measure="mae", alpha=i/10))
}
yhat0 <- predict(fit0, s=fit0$lambda.1se, test.dataindex)
yhat1 <- predict(fit1, s=fit1$lambda.1se, test.dataindex)
yhat2 <- predict(fit2, s=fit2$lambda.1se, test.dataindex)
yhat3 <- predict(fit3, s=fit3$lambda.1se, test.dataindex)
yhat4 <- predict(fit4, s=fit4$lambda.1se, test.dataindex)
yhat5 <- predict(fit5, s=fit5$lambda.1se, test.dataindex)
yhat6 <- predict(fit6, s=fit6$lambda.1se, test.dataindex)
yhat7 <- predict(fit7, s=fit7$lambda.1se, test.dataindex)
yhat8 <- predict(fit8, s=fit8$lambda.1se, test.dataindex)
yhat9 <- predict(fit9, s=fit9$lambda.1se, test.dataindex)
yhat10 <- predict(fit10, s=fit10$lambda.1se, test.dataindex)
mae0 <- mean(abs(test.dataindex$Y-yhat0))
mae1 <- mean(abs(test.dataindex$Y-yhat1))
mae2 <- mean(abs(test.dataindex$Y-yhat2))
mae3 <- mean(abs(test.dataindex$Y-yhat3))
mae4 <- mean(abs(test.dataindex$Y-yhat4))
mae5 <- mean(abs(test.dataindex$Y-yhat5))
mae6 <- mean(abs(test.dataindex$Y-yhat6))
mae7 <- mean(abs(test.dataindex$Y-yhat7))
mae8 <- mean(abs(test.dataindex$Y-yhat8))
mae9 <- mean(abs(test.dataindex$Y-yhat9))
mae10 <- mean(abs(test.dataindex$Y-yhat10))
alpha<-seq(0,1,by=0.1)
mae<-c(mae0,mae1,mae2,mae3,mae4,mae5,mae6,mae7,mae8,mae9,mae10)
cbind(alpha,mae)## alpha mae
## [1,] 0.0 3.068943
## [2,] 0.1 1.171934
## [3,] 0.2 1.174604
## [4,] 0.3 1.176776
## [5,] 0.4 1.181179
## [6,] 0.5 1.163554
## [7,] 0.6 1.164347
## [8,] 0.7 1.177716
## [9,] 0.8 1.144676
## [10,] 0.9 1.170801
## [11,] 1.0 1.147450elastic_model <- glmnet(Y~.,data=train.dataindex, lambda = model_elastic_mae$lambda.min , alpha = 0.8)
coef(elastic_model)## 53 x 1 sparse Matrix of class "dgCMatrix"
## s0
## (Intercept) 4.2113828
## V1 0.4621685
## V2 2.6478444
## V3 3.4641305
## V4 3.4813179
## V5 3.4809015
## V6 3.4833821
## V7 3.4907139
## V8 3.4752946
## V9 3.4772633
## V10 3.4784902
## V11 3.4723136
## V12 3.4920355
## V13 3.4736406
## V14 3.4794354
## V15 3.4836613
## V16 3.4820365
## V17 3.4697398
## V18 3.4840439
## V19 3.4854610
## V20 3.4817808
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## V51 -3.5678512
## V52 -5.4362881preds_elastic <- predict(elastic_model, test.dataindex)
head(preds_elastic)## s0
## [1,] 595.0554
## [2,] 519.1799
## [3,] 533.6335
## [4,] 500.0440
## [5,] 508.9137
## [6,] 526.6552plot(test.dataindex$Y, preds_elastic, col = "blue")
cor(test.dataindex$Y, preds_elastic)## s0
## [1,] 0.9995599Komparasi Model
Berikut ini adalah tabel komparasi dari ke-tiga metode shrinkage beserta metode best subset di atas berdasarkan nilai MAE nya.
y_test <- test.dataindex$YMembuat fungsi untuk hitung nilai mae
mae <- function(response,pred){
mean(abs(response-pred),na.rm = TRUE)
}Tabel komparasi model
mae_lasso_fnl<-mae(y_test,preds_lasso)
mae_ridge_fnl<-mae(y_test,preds_ridge)
mae_elastic_fnl<-mae(y_test,preds_elastic)
mae_best_subset<-mae(y_test,preds_best)
komparasi_mae<-as.data.frame(c(mae_ridge_fnl,mae_lasso_fnl,mae_elastic_fnl, mae_best_subset))
colnames(komparasi_mae)## [1] "c(mae_ridge_fnl, mae_lasso_fnl, mae_elastic_fnl, mae_best_subset)"names(komparasi_mae)[names(komparasi_mae) == "c(mae_ridge_fnl, mae_lasso_fnl, mae_elastic_fnl, mae_best_subset)"] <- "Nilai MAE"
Model<-c("Ridge", "Lasso", "Elastic-Net (0.8)", "Best-Subset")
komparasi_mae<- cbind(Model, komparasi_mae)
komparasi_maeKesimpulan
Berdasarkan tabel komparasi di atas, dpat disimpulkan bahwa model yang paling baik adalah model regresi elastic-net dengan nilai alpha = 0.8.
Referensi
Breheny P. (n.d.). Getting started with grpreg. GitHub Pages. https://pbreheny.github.io/grpreg/articles/getting-started.html
Hastie T. (2013, May 9). glmnet: Lasso and elastic-net regularization in R. Revolutions. https://blog.revolutionanalytics.com/2013/05/hastie-glmnet.html
Post J. (2014, September 29). LASSO, Ridge, and Elastic Net. https://www4.stat.ncsu.edu/~post/josh/LASSO_Ridge_Elastic_Net_-_Examples.html
Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., & Knight, K. (2005). Sparsity and smoothness via the fused lasso. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 67(1), 91-108. https://doi.org/10.1111/j.1467-9868.2005.00490.x
Tripathy A. (2013, July 14). Regularization – Predictive Modeling Beyond Ordinary Least Squares Fit. ShatterLine Blog. https://shatterline.com/blog/2013/07/
Xiaotong C., Chen G., & Chong W. (n.d.). Statistical Learning and Data Mining Codes. Biostatistics - Academic Divisions - School of Public Health - University of Minnesota. https://www.biostat.umn.edu/~weip/course/dm/examples/