pca1
2024-01-31
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## ℹ Use the ]8;;http://conflicted.r-lib.org/conflicted package]8;; to force all conflicts to become errors###Principal Component Regression
Temel Bilesenler Analizi olan PCA tanima, siniflandirma, goruntu sikistirma alanlarinda kullanilan yararlı bir istatistiksel tekniktir. Temel amaci cok sayida birbiri ile iliskili degiskenler iceren veri setinin boyutlarini veri icerisinde var olan degisimlerin mumkun oldugunca korunarak daha az boyuta indirgenmesini saglayan bir donusum teknigidir. Eldeki veriyi daha az sayida degiskenle ifade edebilecek en iyi donusumu belirlemeyi amaclar. Donusum sonrasinda elde edilen degiskenler ilk degiskenlerin temel bilesenleri olarak adlandirilir.
Ilk temel bilesen varyans degeri en buyuk olandır ve diger temel bilesenler varyans degerleri azalacak sekilde siralanir.
Daha aciklayici bir degisle temel bilesen analizi, istatistikte cok boyutlu uzaydaki bir verinin daha dusuk boyutlu bir uzaya izdusumunu, varyansı maksimize edecek sekilde bulma yontemidir. Amac aralarinda korelasyon yapisi bulunmayan degiskenler olusturmaktir.
Temel Bilesenler Analizi;
- Veri kumelerinin boyutunu azaltmak(indirgemek),
- Yorumlanabilirligi arttirmak,
- Bilgi kaybini en aza indirmek icin kullanilir.
Modelde kullanilacak veri train ve test olarak ikiye ayrilir. Train seti ile model kurulur ve test seti uzerinden modelin performansi degerlendirilir.
Bu analizde kullanacagimiz veriyi gorelim;
Factor.Hair.Revised <- read.csv("C:/Users/90555/Downloads/Factor-Hair-Revised.csv")
View(Factor.Hair.Revised)df<- Factor.Hair.Revised
View(df)
df<-na.omit(df)
glimpse(df)## Rows: 100
## Columns: 13
## $ ID <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17…
## $ ProdQual <dbl> 8.5, 8.2, 9.2, 6.4, 9.0, 6.5, 6.9, 6.2, 5.8, 6.4, 8.7, 6.…
## $ Ecom <dbl> 3.9, 2.7, 3.4, 3.3, 3.4, 2.8, 3.7, 3.3, 3.6, 4.5, 3.2, 4.…
## $ TechSup <dbl> 2.5, 5.1, 5.6, 7.0, 5.2, 3.1, 5.0, 3.9, 5.1, 5.1, 4.6, 6.…
## $ CompRes <dbl> 5.9, 7.2, 5.6, 3.7, 4.6, 4.1, 2.6, 4.8, 6.7, 6.1, 4.8, 3.…
## $ Advertising <dbl> 4.8, 3.4, 5.4, 4.7, 2.2, 4.0, 2.1, 4.6, 3.7, 4.7, 2.7, 4.…
## $ ProdLine <dbl> 4.9, 7.9, 7.4, 4.7, 6.0, 4.3, 2.3, 3.6, 5.9, 5.7, 6.8, 3.…
## $ SalesFImage <dbl> 6.0, 3.1, 5.8, 4.5, 4.5, 3.7, 5.4, 5.1, 5.8, 5.7, 4.6, 6.…
## $ ComPricing <dbl> 6.8, 5.3, 4.5, 8.8, 6.8, 8.5, 8.9, 6.9, 9.3, 8.4, 6.8, 8.…
## $ WartyClaim <dbl> 4.7, 5.5, 6.2, 7.0, 6.1, 5.1, 4.8, 5.4, 5.9, 5.4, 5.8, 5.…
## $ OrdBilling <dbl> 5.0, 3.9, 5.4, 4.3, 4.5, 3.6, 2.1, 4.3, 4.4, 4.1, 3.8, 3.…
## $ DelSpeed <dbl> 3.7, 4.9, 4.5, 3.0, 3.5, 3.3, 2.0, 3.7, 4.6, 4.4, 4.0, 3.…
## $ Satisfaction <dbl> 8.2, 5.7, 8.9, 4.8, 7.1, 4.7, 5.7, 6.3, 7.0, 5.5, 7.4, 6.…ID kismi bizim isimize yaramadigi icin onu verimzdemn cikaracagiz
df <- df[, -1]
view(df)Veriden kisaca bahsedecek olursak: 100 musteri icin urun musteri anketi verisini ele alacagiz. Burada bagimli degiskenimiz satisfaction degeridir. Yani biz burada memnuniyeti tahmin etmeye calisacagiz.
Ilk olarak verimizde eksik veri olup olmadigini kontrol etmekle baslayalim; Verimde eksik veri yok ama bu hatayi aldigim icin ve cozemedigim icin maalesef burayi silmek zorunda kaldim.
library(mice)## Warning: package 'mice' was built under R version 4.2.3##
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## ProdQual Ecom TechSup CompRes Advertising ProdLine SalesFImage ComPricing
## 100 1 1 1 1 1 1 1 1
## 0 0 0 0 0 0 0 0
## WartyClaim OrdBilling DelSpeed Satisfaction
## 100 1 1 1 1 0
## 0 0 0 0 0Eksik verimizin olmadigini gozlemliyoruz.
##VERİMİZİ TEST VE TRAİN OLARAK İKİYE AYIRMAKLA DEVAM EDECEGİZ
Veriyi ikiye ayirirkan belirli bir oran kullaniyoruz.
set.seed(145)
sampleIndex<-sample(1:nrow(df),size=0.8*nrow(df))
trainset<-df[sampleIndex,]
testset<-df[-sampleIndex,]
train_x<-trainset %>% dplyr::select(-Satisfaction)
train_y<-trainset$Satisfaction
test_x<-testset %>% dplyr::select(-Satisfaction)
test_y<-testset$Satisfaction
names(df)## [1] "ProdQual" "Ecom" "TechSup" "CompRes" "Advertising"
## [6] "ProdLine" "SalesFImage" "ComPricing" "WartyClaim" "OrdBilling"
## [11] "DelSpeed" "Satisfaction"Ayirdigimiz testset ve trainset icin ayri ayrı satisfactionlu ve satisfactionsuz veri olusturuyoruz.
Bagimsiz degiskenlerimizin birbiriyle olan iliskini gormek icin hisgorgam grafigi olusturalim;
chart.Correlation(df%>%dplyr::select(-c("Advertising","ComPricing","WartyClaim")),histogram=TRUE,pch=19) ## Warning in par(usr): argument 1 does not name a graphical parameter
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Grafigi inceledigimiz zaman alt tarafta yogun koyulasmis olan grafikleri
goruyor olacaktik. Bu koyuluk baska degisle cizgi etrafindaki yogunluk
bize bagimsiz degiskenlerin birbirleriyle olan iliskisinin fazla
oldugunu gostermektedir.
Veri icerisindeki bagimsiz degiskenlerin bazilarinin birbiriyle onemli derecede iliskisi gorulmektedir. Bu da bize multicolinearty problemiini isaret etmektedir.
##MODEL OLUSTURMA
Ilk olarak ham verimizden modelimizi trainset uzerinden inceleyelim;
model1<-lm(Satisfaction~.,data=trainset)
summary(model1)##
## Call:
## lm(formula = Satisfaction ~ ., data = trainset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.22353 -0.27473 0.05019 0.40582 0.87436
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -0.859480 0.914554 -0.940 0.35066
## ProdQual 0.363873 0.060193 6.045 7.09e-08 ***
## Ecom -0.534750 0.169156 -3.161 0.00235 **
## TechSup 0.078205 0.078778 0.993 0.32436
## CompRes 0.136438 0.118606 1.150 0.25403
## Advertising -0.006205 0.069877 -0.089 0.92950
## ProdLine 0.207972 0.096500 2.155 0.03469 *
## SalesFImage 0.907490 0.122567 7.404 2.64e-10 ***
## ComPricing -0.010125 0.054905 -0.184 0.85423
## WartyClaim -0.190195 0.144723 -1.314 0.19320
## OrdBilling 0.221016 0.125085 1.767 0.08173 .
## DelSpeed 0.052662 0.234841 0.224 0.82324
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5763 on 68 degrees of freedom
## Multiple R-squared: 0.8145, Adjusted R-squared: 0.7845
## F-statistic: 27.14 on 11 and 68 DF, p-value: < 2.2e-16Yanlarinda * olan degiskenlerin anlamli oldugunu gozlemliyoruz. Cunku onlar icin p 0.05 den kucuktur. Estimate sutunundaki degerler regresyon modelinde degiskenlerin katsayilarini ifade eder. Katsayinin (-) olmasi bagimsiz degisken ile bagimli degisken arasindaki iliskinin negatif oldugunu gosterir. R-Squared değerinin 0.7148 oldugunu goruyoruz. Bu sayinin 1 e yakin olması bizim istedigimiz seydir. Bu bize modelimizde bagimsiz degiskenlerin bagimli degiskeni aciklama yuzdesini verir. Degiskenlerimiz memnuniyet puanini %71 oraninda etkiler. Degiskenler memnuniyet puanini arttirmaktadir diye de yorumlayabiliriz. RSe yi de inceleyecek olursak bu bagimli degiskenin gercek dogrusal modelden ortalama ne kadar saptigi hakkinda bilgi verir. Bu da 0.7094 dir.
Coklu baglantililik kontrolu;
library(car)## Warning: package 'car' was built under R version 4.2.3## Zorunlu paket yükleniyor: carData## Warning: package 'carData' was built under R version 4.2.3##
## Attaching package: 'car'## The following object is masked from 'package:purrr':
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## recodevif(model1)## ProdQual Ecom TechSup CompRes Advertising ProdLine
## 1.514165 3.600209 3.218277 4.997532 1.514776 4.106217
## SalesFImage ComPricing WartyClaim OrdBilling DelSpeed
## 4.073167 1.790959 3.281176 3.093060 7.329510Bu degerler 10 dan buyuk oldugunda coklu baglantililik sorunu ortaya cikar.
Verileri Normallestirme
Normallestirme islemini scale() kullanarak yapacagiz.
Bu bagimsiz degiskenler arasindaki iliskiler ele almak ve bagimli degiskeni tahmin etmek icin kullanılır.
PCR modeli olusturalim;
library(pls) ## Warning: package 'pls' was built under R version 4.2.3##
## Attaching package: 'pls'## The following object is masked from 'package:caret':
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## loadingsmodelpcr<-pcr(Satisfaction~.,data=trainset,scale=TRUE)
summary(modelpcr)## Data: X dimension: 80 11
## Y dimension: 80 1
## Fit method: svdpc
## Number of components considered: 11
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps 7 comps
## X 33.40 56.08 71.92 80.47 85.90 91.25 94.50
## Satisfaction 58.98 59.08 59.11 68.54 71.07 71.75 72.01
## 8 comps 9 comps 10 comps 11 comps
## X 96.54 98.05 99.24 100.00
## Satisfaction 73.44 77.64 80.27 81.45Burada bize her bir bilesenin varyans degerini gostermektedir.
Ilgili temel bilesenlerin x ler cinsinden katsayilarinii bulmak icin;
modelpcr$coefficients## , , 1 comps
##
## Satisfaction
## ProdQual 0.08721716
## Ecom 0.10611214
## TechSup 0.05606388
## CompRes 0.23033452
## Advertising 0.11194258
## ProdLine 0.18951508
## SalesFImage 0.11181017
## ComPricing -0.08216872
## WartyClaim 0.08253388
## OrdBilling 0.21282954
## DelSpeed 0.22908623
##
## , , 2 comps
##
## Satisfaction
## ProdQual 0.07937495
## Ecom 0.11738107
## TechSup 0.04952973
## CompRes 0.22989388
## Advertising 0.12026351
## ProdLine 0.18197960
## SalesFImage 0.12313738
## ComPricing -0.07197740
## WartyClaim 0.07774564
## OrdBilling 0.21390583
## DelSpeed 0.22991425
##
## , , 3 comps
##
## Satisfaction
## ProdQual 0.08092105
## Ecom 0.11422149
## TechSup 0.04048912
## CompRes 0.23235898
## Advertising 0.11916760
## ProdLine 0.18372460
## SalesFImage 0.11951646
## ComPricing -0.07149507
## WartyClaim 0.06866071
## OrdBilling 0.21566965
## DelSpeed 0.23318971
##
## , , 4 comps
##
## Satisfaction
## ProdQual 0.319541360
## Ecom 0.194632101
## TechSup -0.007803581
## CompRes 0.145669332
## Advertising 0.260144039
## ProdLine 0.225044113
## SalesFImage 0.216242937
## ComPricing -0.218827070
## WartyClaim -0.006870847
## OrdBilling 0.097404952
## DelSpeed 0.138037241
##
## , , 5 comps
##
## Satisfaction
## ProdQual 0.414805735
## Ecom 0.295072930
## TechSup -0.006936973
## CompRes 0.146010657
## Advertising 0.070167678
## ProdLine 0.254986813
## SalesFImage 0.267289462
## ComPricing -0.138969288
## WartyClaim -0.016027798
## OrdBilling 0.092099013
## DelSpeed 0.134707824
##
## , , 6 comps
##
## Satisfaction
## ProdQual 0.488182443
## Ecom 0.261685986
## TechSup 0.009235641
## CompRes 0.152758146
## Advertising 0.112601995
## ProdLine 0.228306804
## SalesFImage 0.241229550
## ComPricing -0.053976604
## WartyClaim 0.001302351
## OrdBilling 0.110561011
## DelSpeed 0.132639390
##
## , , 7 comps
##
## Satisfaction
## ProdQual 0.50427277
## Ecom 0.26267308
## TechSup 0.01188492
## CompRes 0.14859333
## Advertising 0.09673984
## ProdLine 0.16712339
## SalesFImage 0.24743923
## ComPricing -0.09062607
## WartyClaim -0.00870250
## OrdBilling 0.18007035
## DelSpeed 0.11081294
##
## , , 8 comps
##
## Satisfaction
## ProdQual 0.51443727
## Ecom 0.21255233
## TechSup 0.15674406
## CompRes 0.31357432
## Advertising 0.07789320
## ProdLine 0.06481775
## SalesFImage 0.30935286
## ComPricing -0.10990678
## WartyClaim -0.14325560
## OrdBilling 0.06332029
## DelSpeed 0.14247843
##
## , , 9 comps
##
## Satisfaction
## ProdQual 0.56451167
## Ecom -0.10990549
## TechSup -0.09583756
## CompRes 0.35480795
## Advertising -0.01363354
## ProdLine -0.03036170
## SalesFImage 0.65988335
## ComPricing -0.14151047
## WartyClaim 0.10433603
## OrdBilling -0.02271774
## DelSpeed 0.22490690
##
## , , 10 comps
##
## Satisfaction
## ProdQual 0.54278702
## Ecom -0.28722486
## TechSup 0.10347668
## CompRes 0.03099156
## Advertising -0.01931026
## ProdLine 0.09381129
## SalesFImage 0.85308150
## ComPricing -0.08537194
## WartyClaim -0.09483309
## OrdBilling 0.09757962
## DelSpeed 0.37800104
##
## , , 11 comps
##
## Satisfaction
## ProdQual 0.482308037
## Ecom -0.388922778
## TechSup 0.115471958
## CompRes 0.166740612
## Advertising -0.007086578
## ProdLine 0.283161658
## SalesFImage 0.968879645
## ComPricing -0.016002319
## WartyClaim -0.154351936
## OrdBilling 0.201488868
## DelSpeed 0.039363748modelpcr$scores## Comp 1 Comp 2 Comp 3 Comp 4 Comp 5 Comp 6
## 2 -1.09621234 -2.53874852 -2.02935858 -0.559374272 0.51758885 -0.38375888
## 54 1.10837574 -1.21192785 0.67691516 0.278491529 0.28683502 -1.29850584
## 92 4.59098621 1.14578785 0.26523609 0.176747747 -1.68584081 0.04554362
## 75 -0.32466398 0.82319487 0.07567640 0.964791069 0.24584264 0.36559216
## 47 -1.16774776 -1.98777227 0.99669197 0.845049071 -0.87945458 -0.30536038
## 64 2.76850465 -2.37417915 0.15229428 -0.422589184 0.28719880 0.10273602
## 20 -1.52552297 2.24371270 -0.56950213 1.103113558 -0.58694753 0.79015360
## 45 -0.89820944 -2.40319927 -2.51581567 -0.580383512 0.85691651 -0.37102836
## 32 2.15495797 -2.47308754 1.16067752 -0.453032015 -0.20765329 0.31464422
## 43 -2.19656304 1.80770124 -0.80843730 1.683123834 -0.43948912 0.36294167
## 80 2.24237833 0.61202872 0.78950073 0.725655273 0.03282150 -0.19326140
## 1 -0.30022279 1.52512669 -2.00841758 1.101477803 0.09110249 0.02822082
## 86 2.13242800 0.47380381 -1.11016815 0.223239439 -0.10147078 -0.02783907
## 21 1.35664437 0.62670324 2.15498363 -1.509903499 0.46036575 -0.15785030
## 53 -1.11476193 -2.06896792 -1.19601692 -0.199586101 -0.21881083 0.52790141
## 51 1.85650837 0.08256858 0.50885458 -0.224665196 0.01048100 -0.35874178
## 57 -3.63123254 2.32208112 -0.25227720 -1.169747208 -1.24862556 0.30535305
## 97 1.31423377 0.97616749 -2.23906584 0.292995442 0.37726904 -0.17899123
## 22 -3.38013017 0.79810980 1.65745600 2.798495323 -0.91568504 -1.21463752
## 69 2.33000604 0.34650756 -1.06352632 -0.005037041 -0.46789444 -0.13766174
## 72 1.92792268 -0.20891115 -1.15320843 1.393731868 1.45724546 -1.40814718
## 38 -2.64688112 -0.72712130 -0.50086855 -0.393655721 -1.81194796 0.52000622
## 81 0.29112219 -2.06388880 0.56210882 1.557653606 0.18083009 0.27584884
## 26 -0.39805399 0.57473322 0.55619754 -1.476013218 0.55027896 0.08892553
## 40 0.84652567 3.35542884 -0.46684558 0.450156331 0.15299190 -0.59492217
## 84 4.35455006 -0.31275221 2.77945476 -0.517222755 -0.58713072 0.04918600
## 76 -0.25412294 -1.88615324 1.45949803 1.712596827 1.15320547 0.83263069
## 18 -1.94079497 0.92683773 -0.30610706 -2.245390779 -0.39102614 -0.34104977
## 15 -2.07087086 1.73115042 -0.55149638 -1.272307569 -0.27724238 -0.26006370
## 83 2.25802219 -1.85907271 0.28884469 0.721757944 -0.22887499 0.02382639
## 16 -1.25924869 -2.12587187 -1.63379290 0.014858084 -0.03530272 -0.62001695
## 58 -1.42545471 -0.43558695 0.42532416 0.773128489 1.54647500 -0.65454132
## 39 -0.60403132 1.49560605 -1.55861454 -0.007110675 0.76652474 1.49771352
## 9 -0.63462029 1.25039591 -0.43507935 -1.863733622 -0.19836925 -0.06870800
## 87 3.94352995 2.04159415 -2.01149803 0.136965112 0.29923270 -1.47641984
## 95 0.48865805 0.37757063 -0.82747589 1.793225304 -0.31191384 0.43807041
## 33 0.93108175 1.05730411 0.59542608 -0.297948669 0.74140309 0.86927984
## 7 5.02392173 1.22216240 0.39739795 0.499163374 -1.28150854 -0.30030599
## 65 1.69075309 0.35243745 1.26522242 0.202377806 1.03967354 0.05654479
## 71 -2.41228571 1.83200135 1.48649137 0.694712376 0.13696387 1.59638318
## 62 0.94792037 0.42810711 0.46800132 1.428109397 -0.01148675 -0.03040104
## 70 0.82906978 1.42466233 -1.54136236 -0.528825357 0.43473828 -0.57163566
## 10 -0.59847766 1.83596986 -0.33727501 -0.456957671 -0.02033296 -0.31182012
## 25 0.21784263 0.87619116 0.60642935 -1.250308384 -0.22819897 -0.46945728
## 3 -2.37286033 -0.87176371 -0.19719710 1.212151667 0.91485156 -0.07340526
## 85 -0.80419268 -2.60048099 -0.19962010 -1.538246085 -0.49855441 -0.44886261
## 34 -0.25141765 0.56258605 -0.07367013 -0.459678533 0.95211593 1.69024479
## 100 1.40605890 1.17544873 -0.49127275 0.243272545 1.17472707 1.92726174
## 12 1.63458019 2.33547939 1.72584901 0.447457546 -0.31269103 -0.67169867
## 82 0.01247446 -1.77180496 0.11589420 -0.321914391 -0.99903597 0.08303498
## 55 0.36839027 0.44802273 -1.68604031 -0.932385568 -0.56237603 0.80099345
## 11 0.46561004 -1.26557907 -0.92016389 0.223284757 -0.83291234 -0.14083198
## 31 0.19546904 -1.64328145 2.86929425 -0.032278395 1.13074319 -0.45617683
## 56 -0.48358345 -0.80722441 1.26443356 0.533810492 -0.90307016 0.75937903
## 88 -1.52623237 -2.43986900 0.68855110 -1.388777293 0.56702414 0.23107107
## 89 -0.42868117 -0.44825114 0.03985027 0.007533453 -0.38528884 1.32953218
## 35 1.66403603 1.19718266 1.09821915 0.254775465 -1.13613372 -0.82396519
## 6 2.73287744 0.41076767 -1.63394175 -0.582248075 0.85276282 0.38212829
## 14 -1.19042482 -1.60768234 0.02788528 -0.073179216 -1.72598264 -0.04318438
## 50 -1.02820309 0.01721419 -1.07581083 1.160002337 0.28809051 -1.35857748
## 44 -2.38585803 2.08327645 2.24848820 -0.915616538 0.04813854 -1.92235205
## 17 -0.58958513 -0.09002468 1.03716953 -1.477657851 0.15780860 -1.21769318
## 28 1.03552837 -0.28816363 0.07249815 -1.752580789 -0.62745098 0.63261283
## 37 0.49072194 -1.11318768 0.40785997 0.623582122 -0.13913603 0.60346890
## 78 -1.31550924 -0.60963597 1.25627687 -0.021269333 -0.34609072 1.73996231
## 4 1.53403052 0.16129556 1.85014803 -0.959361619 0.90903265 0.99842183
## 8 1.27871969 1.13740595 -0.74770831 -0.367060775 1.20585967 -0.30364582
## 23 -1.26212924 -2.30274967 0.98950582 0.507722559 0.10712594 -0.89891549
## 41 0.97853521 1.07921037 -2.53561922 -0.202168743 -1.00225281 0.64841219
## 13 -2.95875477 1.64438144 0.27181555 1.162288621 -1.33368049 0.33485169
## 90 -3.60990475 2.59989091 2.87248177 -0.707146163 0.34780796 -1.30773212
## 36 2.00291036 -2.34632142 0.29237608 0.924129572 0.27208428 0.08699447
## 52 -1.16790606 -2.42128283 -2.92091971 -0.849344004 0.06959445 -0.62585391
## 77 -0.19668199 -0.39781403 2.66991812 -0.716208911 0.66765966 1.02620705
## 29 -1.29097683 -2.65013910 -1.30290171 -0.785765997 -0.38739251 -0.60448759
## 46 -1.72290916 1.51472534 0.32668980 -1.187928376 1.10509990 0.21719751
## 73 -1.32858521 2.90930637 -2.01043554 0.187333276 1.05356945 0.06037649
## 79 -3.33462530 -1.01158261 0.16310416 0.844435610 0.86172931 0.14028264
## 5 0.65891453 -1.38794859 -0.30532285 0.021228020 -1.24412047 0.11651556
## 94 -2.93567004 -1.08981220 -0.40015778 0.779984454 0.25956606 -0.26794287
## Comp 7 Comp 8 Comp 9 Comp 10 Comp 11
## 2 1.011419393 0.63314933 -0.329390535 0.354968235 -0.338096183
## 54 0.455768403 -0.31063422 0.068039284 0.027597918 0.079140429
## 92 0.470274447 -0.32654947 -0.319286098 0.396074714 -0.472619351
## 75 -0.668945726 0.34838215 0.108191484 -0.089695367 0.087178800
## 47 -1.867115897 0.23410335 -0.652535884 1.024341388 -0.305768852
## 64 -0.494305505 0.45392910 0.065611866 0.114427559 0.427811121
## 20 -0.051936151 0.11747368 0.835082198 0.271613254 -0.106126636
## 45 0.572862862 0.54803299 -0.439331098 0.186775653 -0.020887818
## 32 0.086192659 0.40082613 0.302998643 0.094018785 -0.027398732
## 43 0.175975097 0.34418526 -0.806643355 0.308009169 0.158758538
## 80 0.670950228 0.05633955 0.736779117 -0.004964070 0.581896448
## 1 -1.186641227 -0.06069597 0.343611752 0.194737544 0.434332125
## 86 -0.293093925 0.35884269 -0.218992366 0.069600003 -0.329462895
## 21 0.529353189 0.33314050 -0.119156260 0.526532323 0.013060394
## 53 0.130558970 -0.25727491 0.976325164 -0.329463751 -0.041008759
## 51 -0.611781487 -0.06470170 -0.537745633 -0.229344643 0.494359568
## 57 0.645540881 -0.27591873 0.099078097 0.057543991 -0.043910600
## 97 -0.679266824 0.01764825 0.080926357 0.032446190 -0.093469133
## 22 0.387857631 -0.03991376 -0.442229307 -0.322518129 0.069036899
## 69 -0.810967505 -0.48365864 -0.106637443 -0.392960104 -0.472004312
## 72 0.648373770 -0.77128143 0.043399802 -0.021130767 0.194305755
## 38 0.189382287 0.32385731 -0.166167718 -0.158341952 0.086090199
## 81 -0.013869866 0.99808694 -0.038377878 -0.610573067 -0.516964832
## 26 -1.647091332 0.50435871 -0.218016078 -0.130938521 0.128678500
## 40 -0.797376159 -0.48723828 -0.287308957 0.343166994 0.349779383
## 84 0.024966930 0.30087155 0.772774669 0.870422850 0.535272973
## 76 0.424182574 0.12452552 0.657248053 0.283368171 -0.692935061
## 18 -0.075151209 -0.04609442 -0.201967850 -0.009135321 0.308546948
## 15 0.986196072 -0.06635864 -0.125388470 -0.005132520 -0.242219716
## 83 0.378758847 0.01922131 0.085150976 -0.022077195 -0.146094895
## 16 0.426509534 -0.33475794 0.206132838 0.794382248 -0.167989467
## 58 -0.184826930 -0.53510216 0.316049090 0.277501487 0.090390077
## 39 0.007932281 0.20779753 -0.123203637 0.048673459 -0.284962882
## 9 0.779551847 0.51249701 0.404244138 -0.193791615 0.275767598
## 87 0.717218905 -0.53314008 0.230333855 -0.096978225 -0.199694253
## 95 0.443652905 -0.36511727 -0.004094971 -0.223574036 0.342290335
## 33 0.798187698 0.60384628 -0.832687496 -0.118406440 0.405808924
## 7 -0.478348360 0.77880601 -0.033089227 -0.296969712 0.054667737
## 65 0.052342236 -0.43873223 -0.247468857 0.228884596 0.264108471
## 71 -0.478655696 -0.42246503 0.493478259 -0.203797008 -0.143337356
## 62 0.269804493 1.64665203 -0.254612909 -0.471406641 -0.297015488
## 70 -1.072919679 -0.21062825 0.517366129 0.249579645 -0.211846645
## 10 0.636339463 0.44284881 -0.596328985 -0.011683353 -0.142370803
## 25 -0.173373823 -0.79767289 -0.088815262 -0.213220154 -0.228879150
## 3 -0.564518582 -0.51889293 0.300765288 -0.818258884 0.077947716
## 85 -0.036531764 0.39422535 0.385983120 -0.232107110 0.341907384
## 34 -0.237355811 0.37489664 -0.339329978 -0.277896203 -0.269157495
## 100 0.608858634 0.24485483 0.290977439 0.164645053 0.060334726
## 12 0.193863411 0.43590319 -0.581843753 -0.227406064 -0.302376404
## 82 0.050531479 -0.21954319 0.029561929 -0.644162643 -0.075791211
## 55 -0.713777775 0.05536791 0.268859753 -0.005088617 -0.194667092
## 11 0.421358995 -0.37277820 0.310451510 -0.354566513 -0.168008131
## 31 0.353174952 -0.43221026 -0.299387435 -0.233602838 0.049286267
## 56 0.080966023 0.30112313 -0.160990802 -0.054564707 0.557421401
## 88 -0.087247770 0.38495712 -0.035737016 -0.403897085 0.460408842
## 89 0.121015152 -0.61457565 -0.134088472 0.071408558 0.011471373
## 35 1.125316262 0.11829438 0.936674322 -0.553656773 -0.058957688
## 6 0.080187311 -0.45393961 -0.016031264 0.037562244 -0.049008870
## 14 0.711081051 -0.94515502 -0.096249795 -0.158554751 0.140527674
## 50 0.075614854 0.21515913 0.084228273 -0.226129370 -0.039649458
## 44 -0.397037528 0.40132585 0.565488578 0.320298839 -0.005815337
## 17 0.078651671 0.37478680 -0.131961613 0.181422277 -0.637348472
## 28 -0.098755628 -0.17483242 0.124416143 0.395109119 -0.031596278
## 37 0.036833390 -0.40430734 -0.108251223 -0.069563254 -0.100534520
## 78 0.672457255 -0.16201288 -0.100494521 0.380083935 -0.065352428
## 4 -0.076954084 -0.84520806 -0.421774825 -0.438798096 0.298223679
## 8 -0.893575763 0.04670079 0.330087658 -0.026876265 -0.274418967
## 23 -0.599187611 -0.36503490 -0.449775166 -0.468209493 -0.156061189
## 41 -0.710012296 0.55314100 0.005375396 -0.510414891 0.225920792
## 13 0.029158087 -0.62950984 -0.296888505 0.875697574 -0.023022102
## 90 -0.411632606 0.33711053 0.096634904 -0.107004159 -0.148160280
## 36 0.141827276 -0.33623088 -1.021670492 0.644606181 0.280965640
## 52 0.491103061 0.17936620 -0.033181912 0.552963548 -0.152099359
## 77 -0.345556013 -0.67763105 0.308208122 0.060318536 -0.732003289
## 29 -0.900986978 -0.45404391 -0.461174070 -0.455595565 0.125267396
## 46 0.568755061 -0.56510933 -0.449269410 -0.449096801 -0.100054458
## 73 0.839080315 -0.04750873 -0.295661374 0.024025827 0.343213795
## 79 -0.232507890 0.40948864 0.420954386 0.143110974 0.383780078
## 5 -0.645633502 -0.61999115 0.064695191 -0.189463766 0.042628904
## 94 -0.063048937 0.53032791 0.757054113 0.455097598 0.328559960
## attr(,"class")
## [1] "scores"Modelleme fonksiyonlari tarafindan dondurulen nesnelerden uygun degerleri cikarmak icin fitted.values takma adini kullanacagiz.
modelpcr$fitted.values## , , 1 comps
##
## Satisfaction
## 2 7.421447
## 54 6.325004
## 92 4.592942
## 75 7.037720
## 47 7.457024
## 64 5.499346
## 20 7.634962
## 45 7.322971
## 32 5.804491
## 43 7.968701
## 80 5.761013
## 1 7.025565
## 86 5.815696
## 21 6.201529
## 53 7.430672
## 51 5.952923
## 57 8.682228
## 97 6.222621
## 22 8.557344
## 69 5.717431
## 72 5.917406
## 38 8.192665
## 81 6.731462
## 26 7.074220
## 40 6.455234
## 84 4.710533
## 76 7.002637
## 18 7.841496
## 15 7.906189
## 83 5.753232
## 16 7.502532
## 58 7.585194
## 39 7.176662
## 9 7.191876
## 87 4.914952
## 95 6.633218
## 33 6.413180
## 7 4.377624
## 65 6.035361
## 71 8.075990
## 62 6.404806
## 70 6.463916
## 10 7.173900
## 25 6.767907
## 3 8.056382
## 85 7.276212
## 34 7.001292
## 100 6.176953
## 12 6.063298
## 82 6.870046
## 55 6.693033
## 11 6.644681
## 31 6.779034
## 56 7.116758
## 88 7.635315
## 89 7.089453
## 35 6.048649
## 6 5.517065
## 14 7.468303
## 50 7.387622
## 44 8.062846
## 17 7.169478
## 28 6.361234
## 37 6.632192
## 78 7.530513
## 4 6.113306
## 8 6.240284
## 23 7.503965
## 41 6.389580
## 13 8.347774
## 90 8.671621
## 36 5.880111
## 52 7.457103
## 77 6.974069
## 29 7.518312
## 46 7.733132
## 73 7.537016
## 79 8.534712
## 5 6.548542
## 94 8.336293
##
## , , 2 comps
##
## Satisfaction
## 2 7.358522
## 54 6.294965
## 92 4.621342
## 75 7.058124
## 47 7.407756
## 64 5.440500
## 20 7.690575
## 45 7.263405
## 32 5.743193
## 43 8.013507
## 80 5.776182
## 1 7.063366
## 86 5.827440
## 21 6.217062
## 53 7.379391
## 51 5.954970
## 57 8.739783
## 97 6.246817
## 22 8.577125
## 69 5.726020
## 72 5.912228
## 38 8.174643
## 81 6.680306
## 26 7.088466
## 40 6.538401
## 84 4.702781
## 76 6.955887
## 18 7.864469
## 15 7.949097
## 83 5.707153
## 16 7.449840
## 58 7.574398
## 39 7.213732
## 9 7.222868
## 87 4.965555
## 95 6.642576
## 33 6.439387
## 7 4.407916
## 65 6.044097
## 71 8.121398
## 62 6.415417
## 70 6.499227
## 10 7.219406
## 25 6.789624
## 3 8.034775
## 85 7.211757
## 34 7.015236
## 100 6.206087
## 12 6.121185
## 82 6.826130
## 55 6.704137
## 11 6.613312
## 31 6.738304
## 56 7.096750
## 88 7.574841
## 89 7.078342
## 35 6.078322
## 6 5.527246
## 14 7.428455
## 50 7.388049
## 44 8.114482
## 17 7.167246
## 28 6.354092
## 37 6.604600
## 78 7.515403
## 4 6.117304
## 8 6.268476
## 23 7.446889
## 41 6.416329
## 13 8.388532
## 90 8.736062
## 36 5.821955
## 52 7.397090
## 77 6.964209
## 29 7.452626
## 46 7.770675
## 73 7.609126
## 79 8.509639
## 5 6.514140
## 94 8.309281
##
## , , 3 comps
##
## Satisfaction
## 2 7.388219
## 54 6.285059
## 92 4.617460
## 75 7.057016
## 47 7.393170
## 64 5.438271
## 20 7.698909
## 45 7.300221
## 32 5.726208
## 43 8.025337
## 80 5.764629
## 1 7.092757
## 86 5.843686
## 21 6.185526
## 53 7.396893
## 51 5.947523
## 57 8.743475
## 97 6.279583
## 22 8.552871
## 69 5.741583
## 72 5.929104
## 38 8.181972
## 81 6.672081
## 26 7.080326
## 40 6.545233
## 84 4.662107
## 76 6.934529
## 18 7.868948
## 15 7.957167
## 83 5.702927
## 16 7.473749
## 58 7.568173
## 39 7.236541
## 9 7.229235
## 87 4.994990
## 95 6.654686
## 33 6.430673
## 7 4.402101
## 65 6.025582
## 71 8.099645
## 62 6.408568
## 70 6.521783
## 10 7.224342
## 25 6.780750
## 3 8.037660
## 85 7.214678
## 34 7.016314
## 100 6.213276
## 12 6.095930
## 82 6.824434
## 55 6.728810
## 11 6.626778
## 31 6.696315
## 56 7.078247
## 88 7.564765
## 89 7.077759
## 35 6.062251
## 6 5.551157
## 14 7.428047
## 50 7.403792
## 44 8.081578
## 17 7.152069
## 28 6.353031
## 37 6.598632
## 78 7.497019
## 4 6.090230
## 8 6.279418
## 23 7.432409
## 41 6.453435
## 13 8.384554
## 90 8.694026
## 36 5.817677
## 52 7.439834
## 77 6.925138
## 29 7.471692
## 46 7.765895
## 73 7.638546
## 79 8.507252
## 5 6.518608
## 94 8.315137
##
## , , 4 comps
##
## Satisfaction
## 2 7.168247
## 54 6.394575
## 92 4.686966
## 75 7.436417
## 47 7.725483
## 64 5.272089
## 20 8.132704
## 45 7.071988
## 32 5.548055
## 43 8.687220
## 80 6.049990
## 1 7.525909
## 86 5.931474
## 21 5.591762
## 53 7.318407
## 51 5.859175
## 57 8.283476
## 97 6.394802
## 22 9.653369
## 69 5.739602
## 72 6.477184
## 38 8.027169
## 81 7.284622
## 26 6.499890
## 40 6.722255
## 84 4.458711
## 76 7.608002
## 18 6.985956
## 15 7.456837
## 83 5.986755
## 16 7.479592
## 58 7.872203
## 39 7.233745
## 9 6.496328
## 87 5.048852
## 95 7.359865
## 33 6.313506
## 7 4.598395
## 65 6.105166
## 71 8.372838
## 62 6.970167
## 70 6.313824
## 10 7.044645
## 25 6.289070
## 3 8.514335
## 85 6.609768
## 34 6.835547
## 100 6.308942
## 12 6.271891
## 82 6.697842
## 55 6.362153
## 11 6.714584
## 31 6.683622
## 56 7.288166
## 88 7.018633
## 89 7.080722
## 35 6.162440
## 6 5.322190
## 14 7.399269
## 50 7.859959
## 44 7.721515
## 17 6.570985
## 28 5.663835
## 37 6.843853
## 78 7.488654
## 4 5.712964
## 8 6.135072
## 23 7.632069
## 41 6.373932
## 13 8.841620
## 90 8.415944
## 36 6.181087
## 52 7.105832
## 77 6.643491
## 29 7.162693
## 46 7.298746
## 73 7.712214
## 79 8.839323
## 5 6.526956
## 94 8.621863
##
## , , 5 comps
##
## Satisfaction
## 2 7.036025
## 54 6.321301
## 92 5.117625
## 75 7.373615
## 47 7.950146
## 64 5.198723
## 20 8.282644
## 45 6.853082
## 32 5.601101
## 43 8.799490
## 80 6.041606
## 1 7.502636
## 86 5.957395
## 21 5.474159
## 53 7.374303
## 51 5.856497
## 57 8.602446
## 97 6.298426
## 22 9.887287
## 69 5.859129
## 72 6.104920
## 38 8.490043
## 81 7.238428
## 26 6.359317
## 40 6.683172
## 84 4.608698
## 76 7.313407
## 18 7.085847
## 15 7.527661
## 83 6.045223
## 16 7.488610
## 58 7.477146
## 39 7.037931
## 9 6.547003
## 87 4.972410
## 95 7.439545
## 33 6.124110
## 7 4.925765
## 65 5.839574
## 71 8.337850
## 62 6.973101
## 70 6.202768
## 10 7.049839
## 25 6.347365
## 3 8.280630
## 85 6.737127
## 34 6.592322
## 100 6.008850
## 12 6.351770
## 82 6.953053
## 55 6.505816
## 11 6.927357
## 31 6.394766
## 56 7.518861
## 88 6.873783
## 89 7.179147
## 35 6.452673
## 6 5.104346
## 14 7.840184
## 50 7.786364
## 44 7.709218
## 17 6.530672
## 28 5.824122
## 37 6.879396
## 78 7.577066
## 4 5.480745
## 8 5.827027
## 23 7.604703
## 41 6.629965
## 13 9.182318
## 90 8.327094
## 36 6.111582
## 52 7.088054
## 77 6.472933
## 29 7.261655
## 46 7.016441
## 73 7.443073
## 79 8.619189
## 5 6.844775
## 94 8.555555
##
## , , 6 comps
##
## Satisfaction
## 2 6.984729
## 54 6.147735
## 92 5.123713
## 75 7.422482
## 47 7.909329
## 64 5.212455
## 20 8.388261
## 45 6.803488
## 32 5.643159
## 43 8.848003
## 80 6.015773
## 1 7.506409
## 86 5.953674
## 21 5.453059
## 53 7.444866
## 51 5.808545
## 57 8.643261
## 97 6.274501
## 22 9.724930
## 69 5.840728
## 72 5.916698
## 38 8.559551
## 81 7.275300
## 26 6.371203
## 40 6.603651
## 84 4.615272
## 76 7.424702
## 18 7.040260
## 15 7.492899
## 83 6.048408
## 16 7.405735
## 58 7.389655
## 39 7.238125
## 9 6.537819
## 87 4.775063
## 95 7.498101
## 33 6.240303
## 7 4.885624
## 65 5.847132
## 71 8.551233
## 62 6.969038
## 70 6.126359
## 10 7.008159
## 25 6.284615
## 3 8.270818
## 85 6.677129
## 34 6.818251
## 100 6.266461
## 12 6.261986
## 82 6.964152
## 55 6.612882
## 11 6.908532
## 31 6.333790
## 56 7.620365
## 88 6.904669
## 89 7.356860
## 35 6.342537
## 6 5.155424
## 14 7.834411
## 50 7.604768
## 44 7.452264
## 17 6.367907
## 28 5.908681
## 37 6.960060
## 78 7.809640
## 4 5.614201
## 8 5.786440
## 23 7.484548
## 41 6.716636
## 13 9.227076
## 90 8.152294
## 36 6.123210
## 52 7.004398
## 77 6.610102
## 29 7.180855
## 46 7.045473
## 73 7.451143
## 79 8.637940
## 5 6.860349
## 94 8.519740
##
## , , 7 comps
##
## Satisfaction
## 2 6.878319
## 54 6.099783
## 92 5.074236
## 75 7.492862
## 47 8.105767
## 64 5.264461
## 20 8.393725
## 45 6.743218
## 32 5.634090
## 43 8.829489
## 80 5.945183
## 1 7.631254
## 86 5.984510
## 21 5.397366
## 53 7.431130
## 51 5.872911
## 57 8.575344
## 97 6.345966
## 22 9.684124
## 69 5.926050
## 72 5.848483
## 38 8.539626
## 81 7.276759
## 26 6.544493
## 40 6.687543
## 84 4.612645
## 76 7.380074
## 18 7.048166
## 15 7.389142
## 83 6.008559
## 16 7.360862
## 58 7.409101
## 39 7.237290
## 9 6.455803
## 87 4.699604
## 95 7.451424
## 33 6.156326
## 7 4.935951
## 65 5.841625
## 71 8.601592
## 62 6.940652
## 70 6.239240
## 10 6.941210
## 25 6.302855
## 3 8.330210
## 85 6.680973
## 34 6.843224
## 100 6.202403
## 12 6.241590
## 82 6.958836
## 55 6.687978
## 11 6.864201
## 31 6.296633
## 56 7.611847
## 88 6.913849
## 89 7.344129
## 35 6.224143
## 6 5.146987
## 14 7.759599
## 50 7.596813
## 44 7.494036
## 17 6.359632
## 28 5.919071
## 37 6.956185
## 78 7.738892
## 4 5.622297
## 8 5.880452
## 23 7.547588
## 41 6.791336
## 13 9.224008
## 90 8.195601
## 36 6.108288
## 52 6.952729
## 77 6.646458
## 29 7.275647
## 46 6.985634
## 73 7.362864
## 79 8.662402
## 5 6.928276
## 94 8.526374
##
## , , 8 comps
##
## Satisfaction
## 2 7.077114
## 54 6.002251
## 92 4.971706
## 75 7.602246
## 47 8.179271
## 64 5.406985
## 20 8.430610
## 45 6.915288
## 32 5.759941
## 43 8.937556
## 80 5.962872
## 1 7.612197
## 86 6.097179
## 21 5.501966
## 53 7.350351
## 51 5.852596
## 57 8.488712
## 97 6.351507
## 22 9.671592
## 69 5.774191
## 72 5.606317
## 38 8.641310
## 81 7.590137
## 26 6.702851
## 40 6.534560
## 84 4.707113
## 76 7.419173
## 18 7.033694
## 15 7.368306
## 83 6.014594
## 16 7.255755
## 58 7.241090
## 39 7.302534
## 9 6.616716
## 87 4.532210
## 95 7.336785
## 33 6.345921
## 7 5.180480
## 65 5.703873
## 71 8.468947
## 62 7.457666
## 70 6.173108
## 10 7.080256
## 25 6.052403
## 3 8.167289
## 85 6.804751
## 34 6.960933
## 100 6.279282
## 12 6.378454
## 82 6.889904
## 55 6.705363
## 11 6.747157
## 31 6.160928
## 56 7.706393
## 88 7.034717
## 89 7.151165
## 35 6.261285
## 6 5.004460
## 14 7.462840
## 50 7.664368
## 44 7.620044
## 17 6.477307
## 28 5.864177
## 37 6.829241
## 78 7.688023
## 4 5.356920
## 8 5.895116
## 23 7.432975
## 41 6.965010
## 13 9.026356
## 90 8.301447
## 36 6.002719
## 52 7.009047
## 77 6.433696
## 29 7.133087
## 46 6.808202
## 73 7.347947
## 79 8.790973
## 5 6.733612
## 94 8.692885
##
## , , 9 comps
##
## Satisfaction
## 2 6.871729
## 54 6.044675
## 92 4.772621
## 75 7.669707
## 47 7.772395
## 64 5.447896
## 20 8.951308
## 45 6.641352
## 32 5.948870
## 43 8.434590
## 80 6.422276
## 1 7.826449
## 86 5.960631
## 21 5.427668
## 53 7.959119
## 51 5.517295
## 57 8.550490
## 97 6.401967
## 22 9.395849
## 69 5.707700
## 72 5.633378
## 38 8.537700
## 81 7.566207
## 26 6.566912
## 40 6.355415
## 84 5.188961
## 76 7.828986
## 18 6.907761
## 15 7.290123
## 83 6.067688
## 16 7.384285
## 58 7.438156
## 39 7.225713
## 9 6.868774
## 87 4.675830
## 95 7.334232
## 33 5.826716
## 7 5.159847
## 65 5.549568
## 71 8.776645
## 62 7.298907
## 70 6.495701
## 10 6.708427
## 25 5.997024
## 3 8.354825
## 85 7.045423
## 34 6.749351
## 100 6.460715
## 12 6.015657
## 82 6.908337
## 55 6.873005
## 11 6.940733
## 31 5.974251
## 56 7.606010
## 88 7.012434
## 89 7.067557
## 35 6.845329
## 6 4.994464
## 14 7.402825
## 50 7.716887
## 44 7.972643
## 17 6.395025
## 28 5.941754
## 37 6.761743
## 78 7.625362
## 4 5.093930
## 8 6.100935
## 23 7.152527
## 41 6.968362
## 13 8.841237
## 90 8.361702
## 36 5.365677
## 52 6.988357
## 77 6.625873
## 29 6.845531
## 46 6.528069
## 73 7.163594
## 79 9.053450
## 5 6.773951
## 94 9.164931
##
## , , 10 comps
##
## Satisfaction
## 2 6.674090
## 54 6.029309
## 92 4.552095
## 75 7.719648
## 47 7.202063
## 64 5.384185
## 20 8.800080
## 45 6.537360
## 32 5.896522
## 43 8.263097
## 80 6.425040
## 1 7.718024
## 86 5.921879
## 21 5.134506
## 53 8.142558
## 51 5.644990
## 57 8.518451
## 97 6.383902
## 22 9.575420
## 69 5.926492
## 72 5.645143
## 38 8.625861
## 81 7.906162
## 26 6.639815
## 40 6.164346
## 84 4.704327
## 76 7.671213
## 18 6.912847
## 15 7.292981
## 83 6.079980
## 16 6.941989
## 58 7.283649
## 39 7.198613
## 9 6.976674
## 87 4.729825
## 95 7.458713
## 33 5.892642
## 7 5.325194
## 65 5.422130
## 71 8.890115
## 62 7.561377
## 70 6.356740
## 10 6.714932
## 25 6.115740
## 3 8.810415
## 85 7.174656
## 34 6.904078
## 100 6.369044
## 12 6.142272
## 82 7.266993
## 55 6.875838
## 11 7.138148
## 31 6.104316
## 56 7.636391
## 88 7.237316
## 89 7.027798
## 35 7.153594
## 6 4.973550
## 14 7.491105
## 50 7.842791
## 44 7.794307
## 17 6.294013
## 28 5.721766
## 37 6.800474
## 78 7.413739
## 4 5.338244
## 8 6.115899
## 23 7.413216
## 41 7.252551
## 13 8.353666
## 90 8.421279
## 36 5.006773
## 52 6.680478
## 77 6.592289
## 29 7.099197
## 46 6.778117
## 73 7.150216
## 79 8.973769
## 5 6.879441
## 94 8.911542
##
## , , 11 comps
##
## Satisfaction
## 2 6.517026
## 54 6.066074
## 92 4.332538
## 75 7.760147
## 47 7.060017
## 64 5.582926
## 20 8.750778
## 45 6.527656
## 32 5.883794
## 43 8.336849
## 80 6.695363
## 1 7.919795
## 86 5.768826
## 21 5.140573
## 53 8.123507
## 51 5.874647
## 57 8.498052
## 97 6.340480
## 22 9.607492
## 69 5.707220
## 72 5.735409
## 38 8.665855
## 81 7.666003
## 26 6.699594
## 40 6.326838
## 84 4.952991
## 76 7.349307
## 18 7.056184
## 15 7.180456
## 83 6.012111
## 16 6.863949
## 58 7.325640
## 39 7.066232
## 9 7.104783
## 87 4.637056
## 95 7.617726
## 33 6.081162
## 7 5.350590
## 65 5.544823
## 71 8.823527
## 62 7.423397
## 70 6.258326
## 10 6.648793
## 25 6.009413
## 3 8.846626
## 85 7.333490
## 34 6.779039
## 100 6.397073
## 12 6.001802
## 82 7.231784
## 55 6.785404
## 11 7.060099
## 31 6.127212
## 56 7.895344
## 88 7.451201
## 89 7.033127
## 35 7.126205
## 6 4.950782
## 14 7.556388
## 50 7.824372
## 44 7.791606
## 17 5.997930
## 28 5.707087
## 37 6.753770
## 78 7.383379
## 4 5.476785
## 8 5.988417
## 23 7.340717
## 41 7.357503
## 13 8.342971
## 90 8.352451
## 36 5.137297
## 52 6.609820
## 77 6.252234
## 29 7.157391
## 46 6.731636
## 73 7.309658
## 79 9.152056
## 5 6.899244
## 94 9.064176Cross-Validation
Modelde gorulmeyen veriler uzerindeki peerformansini mumkun oldugunca objektif ve dogru bir sekilde degerlendirmek icin kullanılan istatistiksel bir yeniden ornekleme yontemidir.
Olusturdumuz PCR modeline Cross-Validation yontemi kullanarak yeni bir model olusturalim;
modelpcr_cv<-pcr(Satisfaction~.,data=trainset,scale=TRUE,validation="CV")
summary(modelpcr_cv)## Data: X dimension: 80 11
## Y dimension: 80 1
## Fit method: svdpc
## Number of components considered: 11
##
## VALIDATION: RMSEP
## Cross-validated using 10 random segments.
## (Intercept) 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps
## CV 1.249 0.8251 0.8316 0.8538 0.7561 0.7305 0.7212
## adjCV 1.249 0.8199 0.8294 0.8511 0.7519 0.7161 0.7176
## 7 comps 8 comps 9 comps 10 comps 11 comps
## CV 0.7326 0.7216 0.6887 0.6453 0.6263
## adjCV 0.7288 0.7188 0.6791 0.6404 0.6212
##
## TRAINING: % variance explained
## 1 comps 2 comps 3 comps 4 comps 5 comps 6 comps 7 comps
## X 33.40 56.08 71.92 80.47 85.90 91.25 94.50
## Satisfaction 58.98 59.08 59.11 68.54 71.07 71.75 72.01
## 8 comps 9 comps 10 comps 11 comps
## X 96.54 98.05 99.24 100.00
## Satisfaction 73.44 77.64 80.27 81.45Yukaridaki kod ciktisinda random_state ler icin accuracy skorlaini goruyoruz. Farkli train-test bolumleri sonucunda farkli accuarty degerleri elde edildigini ama bunlarin birbirine oldukca yakin oldugunu gozlemliyoruz. Accuracy degeri bizwe dogru tahmin etme oranini verir. Buyuk olmasini isteriz.
Her bir bilesen icin, MSEP hata metrigine ait degerler grafikteki gibidir.
MODEL KARSİLASTİRMASİ
Burada biz modelpcr ile modelpcr_cv modelini karsilastirarak nihai modele ulasacagiz.
Kolay yorumlayabilmek adina metrikleri kisaca tanimlayacak olursak ; RMSE= Gercek degerler ile tahmin edilen degerler arasindaki farkin ortalama buyuklugunu olcer. Rsquared = Gercek deger ile modelin tahminleri arasindaki uyumun bir olcusudur. MAE= Gercek gegerler ile tahmin edilen degerler arasindaki hatalarin mutlak degerlerinin ortalamasidir.
library(caret)
ozet_<-defaultSummary(data.frame(obs=trainset$Satisfaction,pred=as.vector(modelpcr_cv$fitted.values)))
ozet_## RMSE Rsquared MAE
## 0.6721901 0.7030421 0.5373387ozet_1<-defaultSummary(data.frame(obs=trainset$Satisfaction,pred=as.vector(modelpcr$fitted.values)))
ozet_1## RMSE Rsquared MAE
## 0.6721901 0.7030421 0.5373387Degerleri inceledigimizde iki modelin de degerlerinin ayni oldugunu gozlemliyoruz. Burada ben modelpcr_cv modelini kullanacagim. Daha iyi bir medel oldugu icin.
Burun bilesenler icin gozlem degerlerini hesaplayalim (tahmin edilen degerler);
predict(modelpcr_cv,test_x)## , , 1 comps
##
## Satisfaction
## 19 7.113184
## 24 7.862512
## 27 7.732496
## 30 6.211028
## 42 6.913414
## 48 8.421477
## 49 7.545170
## 59 6.722577
## 60 7.429298
## 61 7.867130
## 63 6.438612
## 66 7.573730
## 67 7.499744
## 68 6.880030
## 74 7.601646
## 91 6.956398
## 93 7.491082
## 96 7.107793
## 98 5.415395
## 99 7.320597
##
## , , 2 comps
##
## Satisfaction
## 19 7.143612
## 24 7.812834
## 27 7.666396
## 30 6.243233
## 42 6.916137
## 48 8.458070
## 49 7.550191
## 59 6.690149
## 60 7.356242
## 61 7.787114
## 63 6.444094
## 66 7.627984
## 67 7.483911
## 68 6.895005
## 74 7.592413
## 91 6.936809
## 93 7.472121
## 96 7.110596
## 98 5.373603
## 99 7.374836
##
## , , 3 comps
##
## Satisfaction
## 19 7.156690
## 24 7.849796
## 27 7.661060
## 30 6.266125
## 42 6.937565
## 48 8.450323
## 49 7.562508
## 59 6.677577
## 60 7.362284
## 61 7.772868
## 63 6.460224
## 66 7.649067
## 67 7.455360
## 68 6.903352
## 74 7.561970
## 91 6.906692
## 93 7.481722
## 96 7.107852
## 98 5.396947
## 99 7.359354
##
## , , 4 comps
##
## Satisfaction
## 19 6.362832
## 24 7.353931
## 27 7.488897
## 30 6.473324
## 42 7.199392
## 48 7.556705
## 49 8.152949
## 59 7.582314
## 60 7.105322
## 61 7.390001
## 63 7.030081
## 66 7.228290
## 67 6.554350
## 68 6.567889
## 74 8.231153
## 91 7.166545
## 93 7.784815
## 96 7.229923
## 98 5.982967
## 99 7.714662
##
## , , 5 comps
##
## Satisfaction
## 19 6.349957
## 24 7.529839
## 27 7.279172
## 30 6.257321
## 42 7.464188
## 48 7.223124
## 49 8.371376
## 59 7.596507
## 60 7.207531
## 61 7.449132
## 63 7.003452
## 66 6.966470
## 67 6.600980
## 68 6.291570
## 74 8.206190
## 91 7.228499
## 93 7.931823
## 96 7.749064
## 98 5.990461
## 99 7.819898
##
## , , 6 comps
##
## Satisfaction
## 19 6.337021
## 24 7.586213
## 27 7.295969
## 30 6.326214
## 42 7.578412
## 48 7.292270
## 49 8.410495
## 59 7.543597
## 60 7.326004
## 61 7.441489
## 63 6.990975
## 66 6.921829
## 67 6.464558
## 68 6.124627
## 74 8.350881
## 91 7.362005
## 93 7.967078
## 96 7.656938
## 98 5.926995
## 99 7.824209
##
## , , 7 comps
##
## Satisfaction
## 19 6.320622
## 24 7.737731
## 27 7.325074
## 30 6.425876
## 42 7.533101
## 48 7.351482
## 49 8.412816
## 59 7.628490
## 60 7.497911
## 61 7.482761
## 63 7.130578
## 66 6.859565
## 67 6.516540
## 68 6.152821
## 74 8.298821
## 91 7.367045
## 93 7.864512
## 96 7.759428
## 98 5.929915
## 99 7.832001
##
## , , 8 comps
##
## Satisfaction
## 19 6.460978
## 24 7.338230
## 27 7.141818
## 30 6.165415
## 42 7.586968
## 48 7.420091
## 49 8.329255
## 59 7.319435
## 60 7.689454
## 61 7.398180
## 63 7.092462
## 66 6.930845
## 67 6.580755
## 68 6.137275
## 74 8.211655
## 91 7.021028
## 93 7.498836
## 96 7.670867
## 98 5.590125
## 99 7.877711
##
## , , 9 comps
##
## Satisfaction
## 19 6.516152
## 24 8.288041
## 27 6.820006
## 30 5.943559
## 42 7.249559
## 48 7.338771
## 49 9.052996
## 59 7.151253
## 60 7.428718
## 61 7.014249
## 63 6.808670
## 66 7.214862
## 67 6.523346
## 68 5.988541
## 74 8.560279
## 91 7.110056
## 93 7.332879
## 96 7.300299
## 98 5.091411
## 99 7.801265
##
## , , 10 comps
##
## Satisfaction
## 19 6.875447
## 24 8.102153
## 27 6.997456
## 30 6.077623
## 42 7.506527
## 48 7.614192
## 49 9.081032
## 59 6.848855
## 60 7.298391
## 61 7.228557
## 63 6.497711
## 66 7.315270
## 67 6.390544
## 68 6.055032
## 74 9.093438
## 91 7.315528
## 93 7.426233
## 96 7.299522
## 98 4.917956
## 99 7.967114
##
## , , 11 comps
##
## Satisfaction
## 19 7.099400
## 24 8.432045
## 27 6.938620
## 30 5.990686
## 42 7.512206
## 48 7.704770
## 49 9.404799
## 59 6.269121
## 60 7.330837
## 61 7.148929
## 63 6.672320
## 66 7.169810
## 67 6.174731
## 68 5.885022
## 74 9.166616
## 91 7.409267
## 93 7.504902
## 96 7.371944
## 98 4.979938
## 99 7.982921Testsetden sadece ilk 5 gozlemin ilk 2 bilesene gore olusturulmus modelden elde edilen tahminleri;
predict(modelpcr_cv,test_x[1:5,],ncomp = 1:2) #testsetden sadeceilk 5 gozlemin ilk 2 bilesene gore olusturulmus modelden elde edilen tahminleri## , , 1 comps
##
## Satisfaction
## 19 7.113184
## 24 7.862512
## 27 7.732496
## 30 6.211028
## 42 6.913414
##
## , , 2 comps
##
## Satisfaction
## 19 7.143612
## 24 7.812834
## 27 7.666396
## 30 6.243233
## 42 6.916137Bu predictionlar topluca bir hata metriği ile degerlendirilirse;
library(caret)
testperf<-defaultSummary(data.frame(obs = test_y, pred=as.vector(predict(modelpcr_cv,test_x, ncomp = 1:2))))
testperf## RMSE Rsquared MAE
## 0.7665706 0.3745319 0.6452308Modelde tahminlerimin hatalarinin mutlak deger ortalamasi(MAE) 0.6452308 Hatalarin karesinin ortalamasi (RMSE) 0.7665706 Oranlar modelpcr ye gore daha iyidir.
ozet_## RMSE Rsquared MAE
## 0.6721901 0.7030421 0.5373387Bizim ele alacagimiz modelin matrikleri bu sekildedir.
##Model Tunning
PCR da tune edebilecegimiz parametre sayisi birdir. Optimal Temel bilesen sayisi belirlenmeye calisilir.
ctrl<-trainControl(method = "cv",number = 10) #validasyonda kullanılancak onemli adımlar belirlenir
set.seed(1234)
pcr_opt<-train(train_x,train_y,method = "pcr",trControl = ctrl, preProc=c("center","scale"))
pcr_opt## Principal Component Analysis
##
## 80 samples
## 11 predictors
##
## Pre-processing: centered (11), scaled (11)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 72, 72, 71, 72, 72, 72, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 0.8047135 0.6133528 0.6472494
## 2 0.8090508 0.6151730 0.6544344
## 3 0.8151724 0.6073951 0.6579271
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 1.Nihai olarak 3 tane bilesen denenmis ve bunlar arasinda 1 tane bilesen olmasi durumunun en iyi durum oldugu belirtilmistir. Bunuda RMSE degerinde en dusuk olan bilesen durumuna bakarak karar vermektedir.
Bu sonuclar incelendiginde daha iyi RMSE sonuclari elde edilemeyecegi gorulmektedir. Bunu detaylandirirsak;
ctrl<-trainControl(method = "cv",number = 10) #validasyonda kullanılancak onemli adımlar belirlenir
set.seed(1234)
pcr_opt<-train(train_x,train_y,method = "pcr",trControl = ctrl,
tuneLength = 20,
preProc=c("center","scale"))
pcr_opt## Principal Component Analysis
##
## 80 samples
## 11 predictors
##
## Pre-processing: centered (11), scaled (11)
## Resampling: Cross-Validated (10 fold)
## Summary of sample sizes: 72, 72, 71, 72, 72, 72, ...
## Resampling results across tuning parameters:
##
## ncomp RMSE Rsquared MAE
## 1 0.8047135 0.6133528 0.6472494
## 2 0.8090508 0.6151730 0.6544344
## 3 0.8151724 0.6073951 0.6579271
## 4 0.7022679 0.6916837 0.5880000
## 5 0.7006117 0.6966629 0.5900553
## 6 0.6774046 0.7265402 0.5523550
## 7 0.6873380 0.7185125 0.5638133
## 8 0.6775728 0.7320354 0.5487216
## 9 0.6345869 0.7690780 0.5177718
## 10 0.6028245 0.8001219 0.4874342
##
## RMSE was used to select the optimal model using the smallest value.
## The final value used for the model was ncomp = 10.Bu sonucla da nihai olarak 9 temel bilesen ile daha dusuk hata metrikleri elde edilmistir. Thefinalvalueusedforthemodelwasncomp=9.
plot(pcr_opt)
Modelin son hali şu şekildedir;
pcr_opt$finalModel # tune edilmismodelin nihai hali ## Principal component regression, fitted with the singular value decomposition algorithm.
## Call:
## pcr(formula = .outcome ~ ., ncomp = ncomp, data = dat)Tahminleri elde etme Tune edilmis modelden yararlanarak tahminleri elde edersek;
testperf_tune<-defaultSummary(data.frame(obs=test_y, pred=as.vector(predict(pcr_opt,test_x))))
testperf_tune## RMSE Rsquared MAE
## 0.5130632 0.7424527 0.3628280