options(repos = c(CRAN = "https://cloud.r-project.org"))

16.03.2026_4.ders

Bu ders “Yol Analizi” üzerine çalıştık. Biz de kitaptaki veri setinde öğrendiklerimizin bir denemesini yapacaktık fakat ben kitaptaki veri setini bulamadım. Chatten bir veri seti yazdırıp oradan ilerledim.

📔Okuma Notlarım

Öncelikle bu kısımda okumamız istenilen iki kitaba ilişkin aldığım notları aktarmaktayım.

📕Statistical Methods for Psychology-David C.Howell-Chapter 15-Multiple Regression Bölümü Notlarım

Bir veriyi analiz ederken elde edilen sonuç her zaman göründüğü gibi olmayabilir. Bu sebeple sonuçları incelerken pek çok ihtimali ve değişkenin birbirleriyle etkileşimini göz önünde bulundurmak zorundayız. Çoklu regresyonla alakalı bölümde derste işlediklerimizin detaylı bir anlatımı mevcuttu.

📘Modern Psychometrics with R-Patrick Mair Notlarım

Yol Analizi ve Yapısal Eşitlik Modellemesi

Kitaptaki örnek veri seti ve kodları buraya yazarak çalıştım.

Yol Modeli Olarak Çok Değişkenli Regresyon

Multivariate Regression ile Multiple Regression aynı şey değil.

Çok değişkenli regresyonda;

  1. MANOVA

  2. Yol modellemesi

  3. Karma etkili modeller

Regresyon modeli kuralım.

install.packages("MPsychoR")
## Installing package into 'C:/Users/ibrahim/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'MPsychoR' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\ibrahim\AppData\Local\Temp\Rtmpa4732L\downloaded_packages
library("MPsychoR")
data("Bergh")
fitmvreg<-lm(cbind(EP,DP)~A1+A2+O1+O2,data=Bergh)

MANOVA yapalım.

library("car")
## Zorunlu paket yükleniyor: carData
Manova(fitmvreg)
## 
## Type II MANOVA Tests: Pillai test statistic
##    Df test stat approx F num Df den Df    Pr(>F)    
## A1  1  0.001205    0.516      2    855    0.5971    
## A2  1  0.103297   49.247      2    855 < 2.2e-16 ***
## O1  1  0.023774   10.411      2    855 3.411e-05 ***
## O2  1  0.026217   11.510      2    855 1.168e-05 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
  1. Yol modellemesi
library("lavaan")
## This is lavaan 0.6-21
## lavaan is FREE software! Please report any bugs.
mvreg.model<-'
EP~b11*A1+b12*A2+b13*O1+ b14*O2
DP~b21*A1+b22*A2+b23*O1+ b24*O2'
fitmvreg2<-sem(mvreg.model,data=Bergh)
library("semPlot")
semPaths(fitmvreg2,what="est",edge.label.cex=1,
layout="tree",residuals=FALSE,edge.color=1,
esize=1,rotation=3,sizeMan=8,asize=2.5,
fade=FALSE,optimizeLatRes=TRUE)

Multivariate regression as path model (unstandardized parameters). Agreeableness/openness predictors: A1, A2, O1, O2. Prejudice responses: DP, EP

🧩 Moderatör Modeller (Düzenleyicilik Etkisi)

Katılımcı iklimin, iş yoğunlaşması ve bilişsel değerlendirme (kavramsal temsil) arasındaki ilişki üzerindeki düzenleyici etkisi:

library("MPsychoR")
data("Paskvan")
wintense.c<-scale(Paskvan$wintense,scale=FALSE) ##center
fit.YX<-lm(cogapp~wintense.c,data=Paskvan) ##YonX
round(summary(fit.YX)$coefficients,4)
##             Estimate Std. Error  t value Pr(>|t|)
## (Intercept)   3.7265     0.0227 164.4470        0
## wintense.c    0.5458     0.0237  22.9954        0
pclimate.c<-scale(Paskvan$pclimate,scale=FALSE) ##center
fit.YZ<-lm(cogapp~pclimate.c,data=Paskvan) ##YonZ
round(summary(fit.YZ)$coefficients,4)
##             Estimate Std. Error  t value Pr(>|t|)
## (Intercept)   3.7265     0.0272 136.8341        0
## pclimate.c   -0.3324     0.0304 -10.9408        0

“QuantPsyc” paketi moderate.lm fonksiyonu kullanılmakta:

install.packages("QuantPsyc")
## Installing package into 'C:/Users/ibrahim/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'QuantPsyc' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\ibrahim\AppData\Local\Temp\Rtmpa4732L\downloaded_packages
library("QuantPsyc")
## Zorunlu paket yükleniyor: boot
## 
## Attaching package: 'boot'
## The following object is masked from 'package:car':
## 
##     logit
## Zorunlu paket yükleniyor: dplyr
## 
## Attaching package: 'dplyr'
## The following object is masked from 'package:car':
## 
##     recode
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
## Zorunlu paket yükleniyor: purrr
## 
## Attaching package: 'purrr'
## The following object is masked from 'package:car':
## 
##     some
## Zorunlu paket yükleniyor: MASS
## 
## Attaching package: 'MASS'
## The following object is masked from 'package:dplyr':
## 
##     select
## 
## Attaching package: 'QuantPsyc'
## The following object is masked from 'package:base':
## 
##     norm
fit.mod<-moderate.lm(x=wintense,z=pclimate,y=cogapp,
data=Paskvan)
round(summary(fit.mod)$coefficients,4)
##             Estimate Std. Error  t value Pr(>|t|)
## (Intercept)   3.7097     0.0227 163.0954   0.0000
## mcx           0.5003     0.0241  20.7653   0.0000
## mcz          -0.1790     0.0257  -6.9765   0.0000
## mcx:mcz      -0.0663     0.0236  -2.8094   0.0051

sim.slopes fonksiyonu

fit.ss<-sim.slopes(fit.mod,Paskvan$pclimate)
round(fit.ss,4)
##             INT  Slope     SE    LCL    UCL
## at zHigh 3.5492 0.4407 0.0313 0.3793 0.5022
## at zMean 3.7097 0.5003 0.0241 0.4530 0.5475
## at zLow  3.8703 0.5598 0.0328 0.4953 0.6242

🧩Mediatör Modeller (Aracılık Etkisi)

Kısmi aracılık ya da tam aracılık

Burada geçen dönemki derslerde de görmüştük. Bozucu değişken (dondurma-boğulma vakası örneği), bastırıcı değişken (x kontrol edildiğinde x in y üzerindeki etkisinin daha belirgin olduğu değişkenler)

mediation paketi kullanılmaktadır. Sobel Testine alternatiftir. Bootstraping yöntemi kullanılıyor.

install.packages("mediation")
## Installing package into 'C:/Users/ibrahim/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'mediation' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\ibrahim\AppData\Local\Temp\Rtmpa4732L\downloaded_packages
library("mediation")
## Zorunlu paket yükleniyor: Matrix
## Zorunlu paket yükleniyor: mvtnorm
## Zorunlu paket yükleniyor: sandwich
## mediation: Causal Mediation Analysis
## Version: 4.5.1
fit.MX <- lm(cogapp ~ wintense, data = Paskvan)
fit.YXM <- lm(emotion ~ wintense + cogapp, data = Paskvan)

Not: İki aracı değişkenin yer aldığı durumlarda: paralel aracılık, seri aracılık

set.seed(123)
fitmed <- mediation::mediate(fit.MX, fit.YXM,
treat = "wintense", mediator = "cogapp",
sims = 999, boot = TRUE, boot.ci.type = "bca")
## Running nonparametric bootstrap
summary(fitmed)
## 
## Causal Mediation Analysis 
## 
## Nonparametric Bootstrap Confidence Intervals with the BCa Method
## 
##                Estimate 95% CI Lower 95% CI Upper   p-value    
## ACME            0.33370      0.26244      0.42043 < 2.2e-16 ***
## ADE             0.24926      0.13986      0.37070 < 2.2e-16 ***
## Total Effect    0.58297      0.50044      0.67547 < 2.2e-16 ***
## Prop. Mediated  0.57242      0.43215      0.75245 < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Sample Size Used: 803 
## 
## 
## Simulations: 999

  • ACME(average causal mediation effect); dolaylı etki abyi temsil eder, toplam etkiyi gösteriyor.

  • ADE (average direct effect); c üssüyü temsil eder, doğrudan etkiyi gösteriyor.

  • Total effect; ab + c üssüyü yani ACME+ADE’yi göstermektedir.

  • Prop. mediated; indirect effect bölü total effect, kestirimlerin oranını göstermektedir.

library("lavaan")
med.model <- '
emotion ~ c*wintense + b*cogapp
cogapp ~ a*wintense
ind := a*b
tot := ind+c
prop := ind/tot'
set.seed(123)
fitmedsem <- lavaan::sem(med.model, Paskvan, se = "bootstrap",
bootstrap = 999)
parameterEstimates(fitmedsem, zstat = FALSE, pvalue = FALSE,
boot.ci.type = "bca.simple")[c(7,1,8,9),]
##       lhs op      rhs label   est    se ci.lower ci.upper
## 7     ind :=      a*b   ind 0.334 0.039    0.263    0.416
## 1 emotion  ~ wintense     c 0.249 0.054    0.140    0.357
## 8     tot :=    ind+c   tot 0.583 0.042    0.500    0.667
## 9    prop :=  ind/tot  prop 0.572 0.075    0.439    0.735

🧩Hem aracı hem de düzenleyici etkinin birlikte olduğu modeller

quantile(Paskvan$pclimate)
##   0%  25%  50%  75% 100% 
##  1.0  2.0  3.0  3.5  5.0
## 0% 25% 50% 75% 100%
## 1.0 2.0 3.0 3.5 5.0
medmod.model <- '
## set of regressions
cogapp ~ a1*wintense + a2*pclimate + a3*wintense:pclimate
emotion ~ c*wintense + b*cogapp
## conditional indirect effects
cie.q1 := (a1 + a3*2)*b
## first quartile
cie.q2 := (a1 + a3*3)*b
cie.q3 := (a1 + a3*3.5)*b
## median
## third quartile
'
set.seed(123)
fitmedmod <- lavaan::sem(medmod.model, data = Paskvan,
se = "bootstrap", bootstrap = 999)
library(semPlot)
semPaths(fitmedmod, layout = "spring", asize = 2.5,
sizeMan = 10, residuals = FALSE, nCharNodes = 7,
edge.label.cex = 1)

İş yoğunlaşması (X), duygusal tükenme (Y), bilişsel değerlendirme (M) ve katılımcı iklim (Z) için moderatörlü arabuluculuk yolu modeli. Düğüm adları kısaltılmıştır (wntns:p, X ve Z arasındaki etkileşimi gösterir)

install.packages("lavaan")  
## Warning: package 'lavaan' is in use and will not be installed
library(lavaan)
parameterEstimates(fitmedmod,zstat= FALSE,pvalue = FALSE,
boot.ci.type= "bca.simple")[c(3,4, 14:16),]
##        lhs op               rhs  label    est    se ci.lower ci.upper
## 3   cogapp  ~ wintense:pclimate     a3 -0.066 0.031   -0.123   -0.008
## 4  emotion  ~          wintense      c  0.249 0.054    0.140    0.357
## 14  cie.q1 :=       (a1+a3*2)*b cie.q1  0.338 0.034    0.276    0.409
## 15  cie.q2 :=       (a1+a3*3)*b cie.q2  0.297 0.036    0.231    0.375
## 16  cie.q3 :=     (a1+a3*3.5)*b cie.q3  0.277 0.040    0.204    0.364

⏳Örnek Bir Analiz

  1. Eksik veri var mı? any_na(....)

  2. Gözlemlerin bağımsızlığı durbinWatssontest(.....)

  3. Doğrusallığın incelenmesi plot(model,1)

  4. Uç değer var mı? boxplot(..)

Mahalanobis uzaklığı, Cooks D, z değerlerine bak. q-q, artıkların dağılımına bak.

eşvaryanslılık

plot(model,3)

library(MVN) -< çok değişkenli normalliği test eder. p büyük 0.05 çok değişkenli normalliği sağlıyor demektir.

  1. Çoklu bağlantı var mı?

lib(olsrr)

VIF 10dan küçük olmalı.

set.seed(123)

############################################
# 1. ÖRNEKLEM BÜYÜKLÜĞÜ
############################################
n <- 300

############################################
# 2. DEĞİŞKENLERİN OLUŞTURULMASI
############################################

# Bağımsız değişken
X <- rnorm(n, mean = 50, sd = 10)

# Düzenleyici değişken
W <- rnorm(n, mean = 0, sd = 1)

# Aracı değişken (X etkiliyor)
M <- 0.6*X + rnorm(n, 0, 5)

# Etkileşim terimi (moderation için)
XW <- X * W

# Bağımlı değişken (hem mediation hem moderation içerir)
Y <- 0.5*M + 0.3*X + 0.4*XW + rnorm(n, 0, 5)

############################################
# 3. VERİ SETİ
############################################
data <- data.frame(X, W, M, Y, XW)

############################################
# 4. GÖZDEN GEÇİRME
############################################
head(data)
##          X          W        M        Y        XW
## 1 44.39524 -0.7152422 32.00721 11.55027 -31.75335
## 2 47.69823 -0.7526890 28.48220 10.23323 -35.90193
## 3 65.58708 -0.9385387 39.18560 16.14449 -61.55602
## 4 50.70508 -1.0525133 22.84271 13.48103 -53.36777
## 5 51.29288 -0.4371595 34.72765 29.20551 -22.42317
## 6 67.15065  0.3311792 39.23672 45.53628  22.23890
summary(data)
##        X               W                   M               Y         
##  Min.   :26.91   Min.   :-2.809775   Min.   :12.32   Min.   :-36.39  
##  1st Qu.:44.24   1st Qu.:-0.603559   1st Qu.:25.39   1st Qu.: 16.10  
##  Median :49.56   Median : 0.045284   Median :29.74   Median : 29.35  
##  Mean   :50.34   Mean   : 0.009109   Mean   :30.29   Mean   : 30.34  
##  3rd Qu.:56.32   3rd Qu.: 0.688690   3rd Qu.:35.24   3rd Qu.: 44.68  
##  Max.   :82.41   Max.   : 2.571458   Max.   :54.47   Max.   : 95.99  
##        XW           
##  Min.   :-173.3177  
##  1st Qu.: -31.8641  
##  Median :   2.6620  
##  Mean   :  -0.1071  
##  3rd Qu.:  30.1530  
##  Max.   : 134.1258
# 1. GEREKLİ PAKETLER
install.packages(c("lmtest", "car", "olsrr", "MVN"))
## Warning: package 'car' is in use and will not be installed
## Installing packages into 'C:/Users/ibrahim/AppData/Local/R/win-library/4.5'
## (as 'lib' is unspecified)
## package 'lmtest' successfully unpacked and MD5 sums checked
## Warning: cannot remove prior installation of package 'lmtest'
## Warning in file.copy(savedcopy, lib, recursive = TRUE): problem copying
## C:\Users\ibrahim\AppData\Local\R\win-library\4.5\00LOCK\lmtest\libs\x64\lmtest.dll
## to C:\Users\ibrahim\AppData\Local\R\win-library\4.5\lmtest\libs\x64\lmtest.dll:
## Permission denied
## Warning: restored 'lmtest'
## package 'olsrr' successfully unpacked and MD5 sums checked
## package 'MVN' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\ibrahim\AppData\Local\Temp\Rtmpa4732L\downloaded_packages
library(lmtest)
## Zorunlu paket yükleniyor: zoo
## 
## Attaching package: 'zoo'
## The following objects are masked from 'package:base':
## 
##     as.Date, as.Date.numeric
library(car)
library(olsrr)
## 
## Attaching package: 'olsrr'
## The following object is masked from 'package:MASS':
## 
##     cement
## The following object is masked from 'package:datasets':
## 
##     rivers
library(MVN)

# 2. MODEL TANIMI
model <- lm(Y ~ X + W + M, data = data)

# 3. EKSİK VERİ KONTROLÜ
cat("=== Eksik Veri Kontrolü ===\n")
## === Eksik Veri Kontrolü ===
print(anyNA(data))
## [1] FALSE
print(colSums(is.na(data)))
##  X  W  M  Y XW 
##  0  0  0  0  0
# 4. BAĞIMSIZLIK (Durbin-Watson)
cat("\n=== Durbin-Watson Testi ===\n")
## 
## === Durbin-Watson Testi ===
print(dwtest(model))
## 
##  Durbin-Watson test
## 
## data:  model
## DW = 2.1319, p-value = 0.8753
## alternative hypothesis: true autocorrelation is greater than 0
# 5. DOĞRUSALLIK
cat("\n=== Doğrusallık (Residuals vs Fitted) ===\n")
## 
## === Doğrusallık (Residuals vs Fitted) ===
plot(model, 1)

# 6. UÇ DEĞERLER (Z skorları)
cat("\n=== Standartlaştırılmış Artıklar ===\n")
## 
## === Standartlaştırılmış Artıklar ===
z <- rstandard(model)
print(which(abs(z) > 3))
##  11  43 298 
##  11  43 298
# 7. COOK'S DISTANCE
cat("\n=== Cook's Distance ===\n")
## 
## === Cook's Distance ===
cook <- cooks.distance(model)
print(which(cook > 1))
## named integer(0)
# 8. MAHALANOBIS DISTANCE

cat("\n=== Mahalanobis Distance ===\n")
## 
## === Mahalanobis Distance ===
vars <- model.matrix(model)[,-1]  # bağımsız değişkenler
mah <- mahalanobis(vars, colMeans(vars), cov(vars))

cutoff <- qchisq(0.001, df = ncol(vars))
print(which(mah > cutoff))
##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
##   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19  20 
##  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
##  21  22  23  24  25  26  27  28  29  30  31  32  33  34  35  36  37  38  39  40 
##  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60 
##  41  42  43  44  45  46  47  48  49  50  51  52  53  54  55  56  57  58  59  60 
##  61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80 
##  61  62  63  64  65  66  67  68  69  70  71  72  73  74  75  76  77  78  79  80 
##  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100 
##  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  97  98  99 100 
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 
## 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 
## 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 
## 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 
## 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 
## 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 
## 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 
## 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 
## 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 
## 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 281 
## 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 281 
## 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 
## 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300
# 9. NORMALLİK
cat("\n=== Normallik (Q-Q Plot) ===\n")
## 
## === Normallik (Q-Q Plot) ===
plot(model, 2)

cat("\n=== Histogram ===\n")
## 
## === Histogram ===
hist(residuals(model))

# 10. EŞVARYANSLILIK
cat("\n=== Homoscedasticity (Scale-Location) ===\n")
## 
## === Homoscedasticity (Scale-Location) ===
plot(model, 3)

cat("\n=== Breusch-Pagan Testi ===\n")
## 
## === Breusch-Pagan Testi ===
print(bptest(model))
## 
##  studentized Breusch-Pagan test
## 
## data:  model
## BP = 0.76394, df = 3, p-value = 0.8581
# 11. ÇOK DEĞİŞKENLİ NORMALLİK
cat("\n=== Çok Değişkenli Normallik ===\n")
## 
## === Çok Değişkenli Normallik ===
print(MVN::mvn(vars, mvn_test = "mardia"))
## $multivariate_normality
##              Test Statistic p.value     Method      MVN
## 1 Mardia Skewness    11.919   0.291 asymptotic ✓ Normal
## 2 Mardia Kurtosis    -0.504   0.615 asymptotic ✓ Normal
## 
## $univariate_normality
##               Test Variable Statistic p.value    Normality
## 1 Anderson-Darling        X     0.884   0.024 ✗ Not normal
## 2 Anderson-Darling        W     0.279   0.645     ✓ Normal
## 3 Anderson-Darling        M     0.535   0.170     ✓ Normal
## 
## $descriptives
##   Variable   n   Mean Std.Dev Median    Min    Max   25th   75th   Skew
## 1        X 300 50.344   9.458 49.561 26.908 82.410 44.241 56.322  0.341
## 2        W 300  0.009   0.989  0.045 -2.810  2.571 -0.604  0.689 -0.180
## 3        M 300 30.290   7.500 29.738 12.324 54.474 25.385 35.243  0.241
##   Kurtosis
## 1    2.927
## 2    2.982
## 3    2.983
## 
## $data
##            X           W        M
## 1   44.39524 -0.71524219 32.00721
## 2   47.69823 -0.75268897 28.48220
## 3   65.58708 -0.93853870 39.18560
## 4   50.70508 -1.05251328 22.84271
## 5   51.29288 -0.43715953 34.72765
## 6   67.15065  0.33117917 39.23672
## 7   54.60916 -2.01421050 29.48178
## 8   37.34939  0.21198043 15.34950
## 9   43.13147  1.23667505 24.38007
## 10  45.54338  2.03757402 23.08072
## 11  62.24082  1.30117599 35.35934
## 12  53.59814  0.75677476 26.07088
## 13  54.00771 -1.72673040 40.84258
## 14  51.10683 -0.60150671 30.58408
## 15  44.44159 -0.35204646 32.03968
## 16  67.86913  0.70352390 27.71298
## 17  54.97850 -0.10567133 30.72111
## 18  30.33383 -1.25864863 14.82289
## 19  57.01356  1.68443571 28.09350
## 20  45.27209  0.91139129 34.89630
## 21  39.32176  0.23743027 16.51665
## 22  47.82025  1.21810861 30.28410
## 23  39.73996 -1.33877429 28.07615
## 24  42.71109  0.66082030 26.51760
## 25  43.74961 -0.52291238 21.87349
## 26  33.13307  0.68374552 24.58567
## 27  58.37787 -0.06082195 35.87966
## 28  51.53373  0.63296071 25.60275
## 29  38.61863  1.33551762 16.23093
## 30  62.53815  0.00729009 47.95648
## 31  54.26464  1.01755864 29.16627
## 32  47.04929 -1.18843404 18.95171
## 33  58.95126 -0.72160444 38.03705
## 34  58.78133  1.51921771 36.81995
## 35  58.21581  0.37738797 28.16031
## 36  56.88640 -2.05222282 24.41706
## 37  55.53918 -1.36403745 32.74199
## 38  49.38088 -0.20078102 35.32551
## 39  46.94037  0.86577940 31.34484
## 40  46.19529 -0.10188326 25.25249
## 41  43.05293  0.62418747 21.66082
## 42  47.92083  0.95900538 30.10783
## 43  37.34604  1.67105483 23.19439
## 44  71.68956  0.05601673 46.16229
## 45  62.07962 -0.05198191 35.26878
## 46  38.76891 -1.75323736 27.75812
## 47  45.97115  0.09932759 23.42863
## 48  45.33345 -0.57185006 25.54734
## 49  57.79965 -0.97400958 38.38386
## 50  49.16631 -0.17990623 34.44964
## 51  52.53319  1.01494317 21.82739
## 52  49.71453 -1.99274849 30.36467
## 53  49.57130 -0.42727929 32.78667
## 54  63.68602  0.11663728 30.95749
## 55  47.74229 -0.89320757 31.04850
## 56  65.16471  0.33390294 34.95795
## 57  34.51247  0.41142992 25.80875
## 58  55.84614 -0.03303616 36.20009
## 59  51.23854 -2.46589819 34.58839
## 60  52.15942  2.57145815 31.89925
## 61  53.79639 -0.20529926 36.59608
## 62  44.97677  0.65119328 33.88863
## 63  46.66793  0.27376649 37.83200
## 64  39.81425  1.02467323 23.74657
## 65  39.28209  0.81765945 12.32400
## 66  53.03529 -0.20979317 31.97880
## 67  54.48210  0.37816777 33.71706
## 68  50.53004 -0.94540883 29.54130
## 69  59.22267  0.85692301 38.37505
## 70  70.50085 -0.46103834 47.35390
## 71  45.08969  2.41677335 24.46390
## 72  26.90831 -1.65104890 14.67451
## 73  60.05739 -0.46398724 38.02364
## 74  42.90799  0.82537986 22.99368
## 75  43.11991  0.51013255 26.32829
## 76  60.25571 -0.58948104 26.34489
## 77  47.15227 -0.99678074 22.69186
## 78  37.79282  0.14447570 16.03692
## 79  51.81303 -0.01430741 26.81970
## 80  48.61109 -1.79028124 25.70013
## 81  50.05764  0.03455107 31.94611
## 82  53.85280  0.19023032 37.22225
## 83  46.29340  0.17472640 24.13912
## 84  56.44377 -1.05501704 28.88206
## 85  47.79513  0.47613328 23.46864
## 86  53.31782  1.37857014 29.91775
## 87  60.96839  0.45623640 35.38589
## 88  54.35181 -1.13558847 35.02918
## 89  46.74068 -0.43564547 26.43779
## 90  61.48808  0.34610362 26.50040
## 91  59.93504 -0.64704563 35.50385
## 92  55.48397 -2.15764634 39.22632
## 93  52.38732  0.88425082 37.39040
## 94  43.72094 -0.82947761 22.28775
## 95  63.60652 -0.57356027 30.42503
## 96  43.99740  1.50390061 38.68874
## 97  71.87333 -0.77414493 42.31189
## 98  65.32611  0.84573154 38.70841
## 99  47.64300 -1.26068288 30.68867
## 100 39.73579 -0.35454240 15.77128
## 101 42.89593 -0.07355602 22.09647
## 102 52.56884 -1.16865142 23.83909
## 103 47.53308 -0.63474826 25.05438
## 104 46.52457 -0.02884155 28.50899
## 105 40.48381  0.67069597 17.46674
## 106 49.54972 -1.65054654 32.67975
## 107 42.15096 -0.34975424 26.73729
## 108 33.32058  0.75640644 15.47127
## 109 46.19773 -0.53880916 28.85027
## 110 59.18997  0.22729192 39.25439
## 111 44.24653  0.49222857 31.85339
## 112 56.07964  0.26783502 32.58354
## 113 33.82117  0.65325768 19.82452
## 114 49.44438 -0.12270866 29.23306
## 115 55.19407 -0.41367651 40.32375
## 116 53.01153 -2.64314895 37.43228
## 117 51.05676 -0.09294102 34.80607
## 118 43.59294  0.43028470 24.71906
## 119 41.50296  0.53539884 26.76798
## 120 39.75871 -0.55527835 25.87168
## 121 51.17647  1.77950291 25.49751
## 122 40.52525  0.28642442 15.67363
## 123 45.09443  0.12631586 30.26581
## 124 47.43908  1.27226678 20.81689
## 125 68.43862 -0.71846622 41.07159
## 126 43.48050 -0.45033862 27.33954
## 127 52.35387  2.39745248 34.23166
## 128 50.77961  0.01112919 31.41490
## 129 40.38143  1.63356842 20.56459
## 130 49.28692 -1.43850664 34.50398
## 131 64.44551 -0.19051680 47.36047
## 132 54.51504  0.37842390 37.11492
## 133 50.41233  0.30003855 20.52914
## 134 45.77503 -1.00563626 34.46290
## 135 29.46753  0.01925927 17.40024
## 136 61.31337 -1.07742065 39.41259
## 137 35.39360  0.71270333 24.34633
## 138 57.39948  1.08477509 33.95625
## 139 69.09104 -2.22498770 41.07831
## 140 35.56107  1.23569346 26.43243
## 141 57.01784 -1.24104450 37.76872
## 142 47.37803  0.45476927 33.37813
## 143 34.27856  0.65990264 32.48177
## 144 34.85332 -0.19988983 24.23407
## 145 33.98464 -0.64511396 21.42769
## 146 44.69093  0.16532102 15.76140
## 147 35.38244  0.43881870 34.68804
## 148 56.87917  0.88330282 31.71412
## 149 71.00109 -2.05233698 54.47433
## 150 37.12970 -1.63637927 24.15103
## 151 57.87739  1.43040234 42.41858
## 152 57.69042  1.04662885 34.06570
## 153 53.32203  0.43528895 34.55057
## 154 39.91623  0.71517841 25.01953
## 155 48.80547  0.91717492 28.35268
## 156 47.19605 -2.66092280 27.71566
## 157 55.62990  1.11027710 38.44211
## 158 46.27561 -0.48498760 26.75808
## 159 59.76973  0.23061683 25.67343
## 160 46.25419 -0.29515780 26.77307
## 161 60.52711  0.87196495 39.01522
## 162 39.50823 -0.34847245 26.78722
## 163 37.39845  0.51850377 25.52191
## 164 82.41040 -0.39068498 40.98573
## 165 45.83142 -1.09278721 29.34256
## 166 52.98228  1.21001051 36.62866
## 167 56.36570  0.74090001 40.20231
## 168 45.16219  1.72426224 25.97251
## 169 55.16862  0.06515393 31.49171
## 170 53.68965  1.12500275 39.65298
## 171 47.84619  1.97541905 20.36808
## 172 50.65293 -0.28148212 28.20761
## 173 49.65933 -1.32295111 32.08291
## 174 71.28452 -0.23935157 34.68184
## 175 42.58664 -0.21404124 26.95012
## 176 39.04004  0.15168050 32.81334
## 177 50.37788  1.71230498 30.20643
## 178 53.10481 -0.32614389 30.47061
## 179 54.36523  0.37300466 34.99370
## 180 45.41635 -0.22768406 25.85445
## 181 39.36674  0.02045071 27.68705
## 182 62.63185  0.31405766 42.10129
## 183 46.50350  1.32821470 27.91556
## 184 41.34487  0.12131838 18.92346
## 185 47.63720  0.71284232 21.99122
## 186 48.02824  0.77886003 25.85196
## 187 61.09920  0.91477327 40.64642
## 188 50.84737 -0.57439455 20.71740
## 189 57.54054  1.62688121 25.09270
## 190 45.00708 -0.38095674 23.73535
## 191 52.14445 -0.10578417 33.25865
## 192 46.75314  1.40405027 23.48405
## 193 50.94584  1.29408391 35.00125
## 194 41.04637 -1.08999187 26.29467
## 195 36.89198 -0.87307100 21.28199
## 196 69.97213 -1.35807906 46.07742
## 197 56.00709  0.18184719 35.54608
## 198 37.48729  0.16484087 20.26270
## 199 43.88834  0.36411469 27.48858
## 200 38.14520  0.55215771 26.12469
## 201 71.98810 -0.60189285 44.97428
## 202 63.12413 -0.99369859 34.58443
## 203 47.34855  1.02678506 32.68514
## 204 55.43194  0.75106130 39.02385
## 205 45.85660 -1.50916654 28.89533
## 206 45.23753 -0.09514745 27.86304
## 207 42.11397 -0.89594782 24.89026
## 208 44.05383 -2.07075107 37.23938
## 209 66.50907  0.15012013 41.28702
## 210 49.45972 -0.07921171 28.88436
## 211 51.19245 -0.09736927 18.17588
## 212 52.43687  0.21615254 23.63572
## 213 62.32476  0.88246516 37.00649
## 214 44.83936  0.20559750 27.93509
## 215 40.07493 -0.61643584 25.42932
## 216 66.75697 -0.73479925 44.16172
## 217 45.58837 -0.13180279 26.38226
## 218 42.76934  0.31001699 31.73455
## 219 37.63727 -1.03968035 17.97478
## 220 37.15284 -0.18430887 16.24949
## 221 44.26027  0.96726726 20.41123
## 222 56.17986 -0.10828009 37.41940
## 223 61.09848 -0.69842067 36.24449
## 224 57.07588 -0.27594517 38.19462
## 225 46.36343  1.11464855 26.47952
## 226 50.59750  0.55004396 27.39904
## 227 42.95404  1.23667580 23.93066
## 228 42.82782  0.13909786 16.43361
## 229 58.84650  0.41027510 29.45983
## 230 39.84407 -0.55845691 16.69627
## 231 69.55294  0.60537067 47.00338
## 232 49.09680 -0.50633354 26.47143
## 233 52.14539 -1.42056550 35.23453
## 234 42.61472  0.12799297 33.15129
## 235 44.25611  1.94585122 25.59479
## 236 36.82984  0.80091434 23.51730
## 237 48.17075  1.16525339 20.14711
## 238 54.18982  0.35885572 28.42055
## 239 53.24304 -0.60855718 32.22690
## 240 42.18464 -0.20224086 26.80622
## 241 42.11378 -0.27324811 21.47128
## 242 44.97801 -0.46869978 40.41110
## 243 64.96061  0.70416728 36.68441
## 244 38.62696 -1.19736350 23.49740
## 245 48.20948  0.86636613 32.17465
## 246 69.02362  0.86415249 41.28408
## 247 48.99025 -1.19862236 26.17631
## 248 36.40159  0.63949200 27.06748
## 249 43.35231  2.43022665 34.08911
## 250 54.85460 -0.55721548 32.76429
## 251 46.24397  0.84490424 30.55772
## 252 44.38124 -0.78220185 26.14168
## 253 46.56083  1.11071142 33.01877
## 254 50.90497  0.24982472 24.76214
## 255 65.98509  1.65191539 51.19535
## 256 49.11435 -1.45897073 26.45095
## 257 60.80799 -0.05129789 29.19055
## 258 56.30754 -0.52692518 32.02994
## 259 48.86360 -0.19726487 30.05170
## 260 34.67098 -0.62957874 28.92069
## 261 44.78883 -0.83384358 31.42934
## 262 45.10130  0.57872237 27.77307
## 263 50.47154 -1.08758071 23.33551
## 264 63.00199  1.48403093 33.47100
## 265 72.93079 -1.18620659 42.94205
## 266 65.47581  0.10107915 52.05062
## 267 48.66849  0.53298929 19.89996
## 268 32.43473  0.58673534 25.11611
## 269 46.11220 -0.30174666 25.03115
## 270 50.89207  0.07950200 38.86520
## 271 58.45013  0.96126415 29.37407
## 272 59.62528 -1.45646592 36.49328
## 273 56.84309 -0.78173971 28.60810
## 274 36.04726  0.32040231 26.14594
## 275 58.49643 -0.44478198 42.51676
## 276 45.53443  1.37000399 37.07426
## 277 51.74803  0.67325386 35.03682
## 278 50.74551  0.07216675 39.66364
## 279 54.28167 -1.50775732 38.80112
## 280 50.24675  0.02610023 29.48868
## 281 33.32525 -0.31641587 22.38034
## 282 57.36496 -0.10234651 29.55900
## 283 53.86027 -1.18155923 31.39015
## 284 47.34348  0.49865804 34.51091
## 285 51.18145 -1.03895644 33.41529
## 286 51.34039 -0.22622198 33.09102
## 287 52.21019  0.38142583 26.13546
## 288 66.40846 -0.78351579 36.82251
## 289 47.80950  0.58299141 24.86267
## 290 51.68065 -1.31651040 32.98487
## 291 61.68384 -2.80977468 32.05777
## 292 60.54181  0.46496799 39.13529
## 293 61.45263  0.84053983 31.28950
## 294 44.22532 -0.28584542 35.67784
## 295 70.02483  0.50412625 44.31785
## 296 50.66701 -1.15591653 26.89519
## 297 68.66852 -0.12714861 42.40634
## 298 36.49097 -1.94151838 20.13232
## 299 50.20984  1.18118089 31.98164
## 300 62.49915  1.85991086 38.71715
## 
## $subset
## NULL
## 
## $outlierMethod
## [1] "none"
## 
## attr(,"class")
## [1] "mvn"
# 12. MULTICOLLINEARITY
cat("\n=== VIF Değerleri ===\n")
## 
## === VIF Değerleri ===
print(vif(model))
##        X        W        M 
## 2.111381 1.005529 2.114985
cat("\n=== Tolerance ve VIF (olsrr) ===\n")
## 
## === Tolerance ve VIF (olsrr) ===
print(ols_vif_tol(model))
##   Variables Tolerance      VIF
## 1         X 0.4736236 2.111381
## 2         W 0.9945010 1.005529
## 3         M 0.4728166 2.114985

🤓Öğrenme Günlüğüm

Bir veri ile karşılaştığımda onu hangi sırayla ve nasıl analiz edeceğim konusunda kendimi daha da geliştirmeliyim. Bilgiler var fakat darmadağın, istatistik ve R konusunda zihnimi dağınık bir odaya benzetiyorum. Bu arada çevremde birileri analizle ilgili bir şey sorduğunda “ya o kolay hemen R’dan bakayım” demek bana iyi gelen bir yan tabi. Hemen derste konuştuğumuz şeylere bakarak çevremdekilere yardımcı olabiliyorum. Fakat yine de kendime not olarak otur kızım biraz daha istatistik çalış diyorum…