{"id":2119,"date":"2023-07-23T15:01:59","date_gmt":"2023-07-23T15:01:59","guid":{"rendered":"https:\/\/statorials.org\/tr\/mukemmel-coklu-baglanti\/"},"modified":"2023-07-23T15:01:59","modified_gmt":"2023-07-23T15:01:59","slug":"mukemmel-coklu-baglanti","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/mukemmel-coklu-baglanti\/","title":{"rendered":"M\u00fckemmel \u00e7oklu ba\u011flant\u0131 nedir? (tan\u0131m ve \u00f6rnekler)"},"content":{"rendered":"

<\/p>\n

\n

\u0130statistiklerde, \u00e7oklu do\u011frusall\u0131k,<\/a> iki veya daha fazla yorday\u0131c\u0131 de\u011fi\u015fkenin regresyon modelinde benzersiz veya ba\u011f\u0131ms\u0131z bilgi sa\u011flamayacak \u015fekilde birbiriyle y\u00fcksek d\u00fczeyde korelasyona sahip olmas\u0131 durumunda ortaya \u00e7\u0131kar.<\/span><\/p>\n

De\u011fi\u015fkenler aras\u0131ndaki korelasyon derecesi yeterince y\u00fcksekse, bu durum regresyon modelinin yerle\u015ftirilmesinde ve yorumlanmas\u0131nda sorunlara neden olabilir.<\/span><\/p>\n

\u00c7oklu do\u011frusall\u0131\u011f\u0131n en u\u00e7 durumu, m\u00fckemmel \u00e7oklu do\u011frusall\u0131k<\/strong> olarak adland\u0131r\u0131l\u0131r. Bu, iki veya daha fazla \u00f6ng\u00f6r\u00fcc\u00fc de\u011fi\u015fkenin birbiriyle tam bir do\u011frusal ili\u015fkiye sahip olmas\u0131 durumunda ortaya \u00e7\u0131kar.<\/span><\/p>\n

\u00d6rne\u011fin a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span> <\/p>\n

\"\"<\/p>\n

Tahmin de\u011fi\u015fkeni x 2’nin<\/sub> de\u011ferlerinin basit\u00e7e x 1’in<\/sub> 2 ile \u00e7arp\u0131lan de\u011ferleri oldu\u011funa dikkat edin.<\/span> <\/p>\n

\"m\u00fckemmel<\/p>\n

Bu m\u00fckemmel \u00e7oklu ba\u011flant\u0131n\u0131n<\/strong> bir \u00f6rne\u011fidir.<\/span><\/p>\n

M\u00fckemmel \u00e7oklu ba\u011flant\u0131 sorunu<\/strong><\/span><\/h2>\n

Bir veri setinde m\u00fckemmel \u00e7oklu ba\u011flant\u0131 mevcut oldu\u011funda, s\u0131radan en k\u00fc\u00e7\u00fck kareler, regresyon katsay\u0131lar\u0131n\u0131n tahminlerini \u00fcretemez.<\/span><\/p>\n

Asl\u0131nda, ba\u015fka bir yorday\u0131c\u0131 de\u011fi\u015fkeni ( x2<\/sub> ) sabit tutarken, bir yorday\u0131c\u0131 de\u011fi\u015fkenin ( x1<\/sub> ) tepki de\u011fi\u015fkeni (y) \u00fczerindeki marjinal etkisini tahmin etmek m\u00fcmk\u00fcn de\u011fildir \u00e7\u00fcnk\u00fc x2<\/sub> her zaman tam olarak x1<\/sub> hareket etti\u011finde hareket eder.<\/span><\/p>\n

K\u0131sacas\u0131, m\u00fckemmel \u00e7oklu do\u011frusall\u0131k, bir regresyon modelinde her katsay\u0131 i\u00e7in bir de\u011fer tahmin etmeyi imkans\u0131z hale getirir.<\/span><\/p>\n

M\u00fckemmel \u00e7oklu ba\u011flant\u0131yla nas\u0131l ba\u015fa \u00e7\u0131k\u0131l\u0131r?<\/strong><\/span><\/h2>\n

M\u00fckemmel \u00e7oklu do\u011frusall\u0131\u011f\u0131 ele alman\u0131n en basit yolu, ba\u015fka bir de\u011fi\u015fkenle tam do\u011frusal ili\u015fkiye sahip olan de\u011fi\u015fkenlerden birini \u00e7\u0131karmakt\u0131r.<\/span><\/p>\n

\u00d6rne\u011fin, \u00f6nceki veri k\u00fcmemizde tahmin de\u011fi\u015fkeni olarak x 2’yi<\/sub> basit\u00e7e kald\u0131rabilirdik.<\/span> <\/p>\n

\"\"<\/p>\n

Daha sonra x1’i<\/sub> yorday\u0131c\u0131 de\u011fi\u015fken olarak ve y’yi yan\u0131t de\u011fi\u015fkeni olarak kullanarak bir regresyon modeli yerle\u015ftirirdik.<\/span><\/p>\n

M\u00fckemmel \u00e7oklu ba\u011flant\u0131 \u00f6rnekleri<\/strong><\/span><\/h2>\n

A\u015fa\u011f\u0131daki \u00f6rnekler uygulamada m\u00fckemmel \u00e7oklu ba\u011flant\u0131n\u0131n en yayg\u0131n \u00fc\u00e7 senaryosunu g\u00f6stermektedir.<\/span><\/p>\n

1. Bir yorday\u0131c\u0131 de\u011fi\u015fken di\u011ferinin kat\u0131d\u0131r<\/strong><\/span><\/h3>\n

Belirli bir yunus t\u00fcr\u00fcn\u00fcn a\u011f\u0131rl\u0131\u011f\u0131n\u0131 tahmin etmek i\u00e7in “santimetre cinsinden y\u00fckseklik” ve “metre cinsinden y\u00fckseklik” kullanmak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n

Veri setimiz \u015f\u00f6yle g\u00f6r\u00fcnebilir:<\/span> <\/p>\n

\"\"<\/p>\n

“Santimetre cinsinden y\u00fckseklik” de\u011ferinin “metre cinsinden y\u00fckseklik”in 100 ile \u00e7arp\u0131m\u0131na e\u015fit oldu\u011funa dikkat edin. Bu, m\u00fckemmel bir \u00e7oklu ba\u011flant\u0131 durumudur.<\/span><\/p>\n

Bu veri k\u00fcmesini kullanarak R’ye \u00e7oklu do\u011frusal regresyon modeli uydurmaya \u00e7al\u0131\u015f\u0131rsak, “metre” tahmin de\u011fi\u015fkeni i\u00e7in bir katsay\u0131 tahmini \u00fcretemeyece\u011fiz:<\/span><\/p>\n

 #define data\n<\/span>df <- data. frame<\/span> (weight=c(400, 460, 470, 475, 490, 440, 430, 490, 500, 540),\n                 m=c(1.3, .7, .6, 1.3, 1.2, 1.5, 1.2, 1.6, 1.1, 1.4),\n                 cm=c(130, 70, 60, 130, 120, 150, 120, 160, 110, 140))\n\n#fit multiple linear regression model\n<\/span>model <- lm(weight~m+cm, data=df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = weight ~ m + cm, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-70,501 -25,501 5,183 19,499 68,590 \n\nCoefficients: (1 not defined because of singularities)\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 458,676 53,403 8,589 2.61e-05 ***\nm 9.096 43.473 0.209 0.839    \ncm NA NA NA NA    \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 41.9 on 8 degrees of freedom\nMultiple R-squared: 0.005442, Adjusted R-squared: -0.1189 \nF-statistic: 0.04378 on 1 and 8 DF, p-value: 0.8395<\/strong><\/pre>\n
 2. Bir yorday\u0131c\u0131 de\u011fi\u015fken, ba\u015fka bir de\u011fi\u015fkenin d\u00f6n\u00fc\u015ft\u00fcr\u00fclm\u00fc\u015f versiyonudur<\/strong><\/span><\/h3>\n
 Basketbol oyuncular\u0131n\u0131n reytingini tahmin etmek i\u00e7in “puan” ve “\u00f6l\u00e7eklendirilmi\u015f puan” kullanmak istedi\u011fimizi varsayal\u0131m.<\/span><\/p>\n
 “\u00d6l\u00e7eklendirilmi\u015f noktalar” de\u011fi\u015fkeninin \u015fu \u015fekilde hesapland\u0131\u011f\u0131n\u0131 varsayal\u0131m:<\/span><\/p>\n
 \u00d6l\u00e7eklendirilmi\u015f noktalar = (noktalar \u2013 \u03bc noktalar<\/sub> ) \/ \u03c3 noktalar<\/sub><\/span><\/p>\n
 Veri setimiz \u015f\u00f6yle g\u00f6r\u00fcnebilir:<\/span> <\/p>\n
\"\"<\/p>\n
 Her “\u00f6l\u00e7eklendirilmi\u015f puan” de\u011ferinin yaln\u0131zca “puanlar\u0131n” standartla\u015ft\u0131r\u0131lm\u0131\u015f bir versiyonu oldu\u011funu unutmay\u0131n. Bu m\u00fckemmel bir \u00e7oklu ba\u011flant\u0131 durumudur.<\/span><\/p>\n
 Bu veri k\u00fcmesini kullanarak R’ye \u00e7oklu do\u011frusal regresyon modeli uydurmaya \u00e7al\u0131\u015f\u0131rsak, “\u00f6l\u00e7eklendirilmi\u015f noktalar” yorday\u0131c\u0131 de\u011fi\u015fkeni i\u00e7in bir katsay\u0131 tahmini \u00fcretemeyece\u011fiz:<\/span><\/p>\n
 #define data\n<\/span>df <- data. frame<\/span> (rating=c(88, 83, 90, 94, 96, 78, 79, 91, 90, 82),\n                 pts=c(17, 19, 24, 29, 33, 15, 14, 29, 25, 22))\n\ndf$scaled_pts <- (df$pts - mean(df$pts)) \/ sd(df$pts)\n\n#fit multiple linear regression model\n<\/span>model <- lm(rating~pts+scaled_pts, data=df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = rating ~ pts + scaled_pts, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-4.4932 -1.3941 -0.2935 1.3055 5.8412 \n\nCoefficients: (1 not defined because of singularities)\n            Estimate Std. Error t value Pr(>|t|)    \n(Intercept) 67.4218 3.5896 18.783 6.67e-08 ***\npts 0.8669 0.1527 5.678 0.000466 ***\nscaled_pts NA NA NA NA    \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 2.953 on 8 degrees of freedom\nMultiple R-squared: 0.8012, Adjusted R-squared: 0.7763 \nF-statistic: 32.23 on 1 and 8 DF, p-value: 0.0004663\n<\/strong><\/pre>\n
 3. Kukla de\u011fi\u015fken tuza\u011f\u0131<\/strong><\/span><\/h3>\n
 M\u00fckemmel \u00e7oklu do\u011frusall\u0131\u011f\u0131n meydana gelebilece\u011fi ba\u015fka bir senaryo , kukla de\u011fi\u015fken tuza\u011f\u0131<\/a> olarak bilinir. Bu, bir regresyon modelinde kategorik bir de\u011fi\u015fkeni al\u0131p onu 0, 1, 2 vb. de\u011ferlerini alan bir “kukla de\u011fi\u015fkene” d\u00f6n\u00fc\u015ft\u00fcrmek istedi\u011fimiz zamand\u0131r.<\/span><\/p>\n
 \u00d6rne\u011fin, geliri tahmin etmek i\u00e7in “ya\u015f” ve “medeni durum” yorday\u0131c\u0131 de\u011fi\u015fkenlerini kullanmak istedi\u011fimizi varsayal\u0131m:<\/span> <\/p>\n
\"\"<\/p>\n
 \u201cMedeni durum\u201du yorday\u0131c\u0131 de\u011fi\u015fken olarak kullanmak i\u00e7in \u00f6ncelikle onu kukla de\u011fi\u015fkene d\u00f6n\u00fc\u015ft\u00fcrmeliyiz.<\/span><\/p>\n
 Bunu yapmak i\u00e7in “Bekar”\u0131 temel de\u011fer olarak b\u0131rakabiliriz, \u00e7\u00fcnk\u00fc bu en s\u0131k ger\u00e7ekle\u015fir ve “Evli” ve “Bo\u015fanm\u0131\u015f”a 0 veya 1 de\u011ferlerini a\u015fa\u011f\u0131daki gibi atayabiliriz:<\/span> <\/p>\n
\"\"<\/p>\n
 A\u015fa\u011f\u0131daki gibi \u00fc\u00e7 yeni kukla de\u011fi\u015fken yaratmak bir hata olacakt\u0131r:<\/span> <\/p>\n
\"\"<\/p>\n
 Bu durumda “Bekar” de\u011fi\u015fkeni, “Evli” ve “Bo\u015fanm\u0131\u015f” de\u011fi\u015fkenlerinin m\u00fckemmel bir do\u011frusal birle\u015fimidir. Bu m\u00fckemmel \u00e7oklu ba\u011flant\u0131n\u0131n bir \u00f6rne\u011fidir.<\/span><\/p>\n
 Bu veri k\u00fcmesini kullanarak R’ye \u00e7oklu do\u011frusal regresyon modeli uydurmaya \u00e7al\u0131\u015f\u0131rsak, her yorday\u0131c\u0131 de\u011fi\u015fken i\u00e7in bir katsay\u0131 tahmini \u00fcretemeyece\u011fiz:<\/span><\/p>\n
 #define data\n<\/span>df <- data. frame<\/span> (income=c(45, 48, 54, 57, 65, 69, 78, 83, 98, 104, 107),\n                 age=c(23, 25, 24, 29, 38, 36, 40, 59, 56, 64, 53),\n                 single=c(1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 0),\n                 married=c(0, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1),\n                 divorced=c(0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0))\n\n#fit multiple linear regression model\n<\/span>model <- lm(income~age+single+married+divorced, data=df)\n\n#view summary of model\n<\/span>summary(model)\n\nCall:\nlm(formula = income ~ age + single + married + divorced, data = df)\n\nResiduals:\n    Min 1Q Median 3Q Max \n-9.7075 -5.0338 0.0453 3.3904 12.2454 \n\nCoefficients: (1 not defined because of singularities)\n            Estimate Std. Error t value Pr(>|t|)   \n(Intercept) 16.7559 17.7811 0.942 0.37739   \nage 1.4717 0.3544 4.152 0.00428 **\nsingle -2.4797 9.4313 -0.263 0.80018   \nmarried NA NA NA NA   \ndivorced -8.3974 12.7714 -0.658 0.53187   \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\nResidual standard error: 8.391 on 7 degrees of freedom\nMultiple R-squared: 0.9008, Adjusted R-squared: 0.8584 \nF-statistic: 21.2 on 3 and 7 DF, p-value: 0.0006865\n<\/strong><\/pre>\n
 Ek kaynaklar<\/strong><\/span><\/h3>\n
 Regresyonda \u00c7oklu Ba\u011flant\u0131 ve VIF K\u0131lavuzu<\/a>
 R’de VIF nas\u0131l hesaplan\u0131r<\/a>
 Python’da VIF nas\u0131l hesaplan\u0131r<\/a>
 Excel’de VIF nas\u0131l hesaplan\u0131r<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
\u0130statistiklerde, \u00e7oklu do\u011frusall\u0131k, iki veya daha fazla yorday\u0131c\u0131 de\u011fi\u015fkenin regresyon modelinde benzersiz veya ba\u011f\u0131ms\u0131z bilgi sa\u011flamayacak \u015fekilde birbiriyle y\u00fcksek d\u00fczeyde korelasyona sahip olmas\u0131 durumunda ortaya \u00e7\u0131kar. De\u011fi\u015fkenler aras\u0131ndaki korelasyon derecesi yeterince y\u00fcksekse, bu durum regresyon modelinin yerle\u015ftirilmesinde ve yorumlanmas\u0131nda sorunlara neden olabilir. \u00c7oklu do\u011frusall\u0131\u011f\u0131n en u\u00e7 durumu, m\u00fckemmel \u00e7oklu do\u011frusall\u0131k olarak adland\u0131r\u0131l\u0131r. Bu, iki veya […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"class_list":["post-2119","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\nM\u00fckemmel \u00e7oklu ba\u011flant\u0131 nedir? 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