<\/p>\n
\u0130statistikte regresyon , yorday\u0131c\u0131 de\u011fi\u015fkenler ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi analiz etmek i\u00e7in kullan\u0131labilecek bir tekniktir.<\/span><\/p>\n Regresyon analizini ger\u00e7ekle\u015ftirmek i\u00e7in yaz\u0131l\u0131m (R, SAS, SPSS vb.) kulland\u0131\u011f\u0131n\u0131zda, \u00e7\u0131kt\u0131 olarak regresyon sonu\u00e7lar\u0131n\u0131 \u00f6zetleyen bir regresyon tablosu al\u0131rs\u0131n\u0131z. Regresyon analizi sonu\u00e7lar\u0131n\u0131 anlayabilmeniz i\u00e7in bu tabloyu nas\u0131l okuyaca\u011f\u0131n\u0131z\u0131 bilmeniz \u00f6nemlidir.<\/span><\/p>\n Bu e\u011fitimde bir regresyon analizi \u00f6rne\u011fi g\u00f6sterilmekte ve bir regresyon tablosunun sonucunun nas\u0131l okunaca\u011f\u0131 ve yorumlanaca\u011f\u0131na ili\u015fkin ayr\u0131nt\u0131l\u0131 bir a\u00e7\u0131klama sa\u011flanmaktad\u0131r.<\/span><\/p>\n 12 farkl\u0131 \u00f6\u011frencinin toplam ders saatini, toplam al\u0131nan haz\u0131rl\u0131k s\u0131nav say\u0131s\u0131n\u0131 ve final s\u0131nav notunu g\u00f6steren a\u015fa\u011f\u0131daki veri setine sahip oldu\u011fumuzu varsayal\u0131m:<\/span><\/p>\n \u00c7al\u0131\u015f\u0131lan saat ve al\u0131nan haz\u0131rl\u0131k s\u0131navlar\u0131 ile \u00f6\u011frencinin ald\u0131\u011f\u0131 final s\u0131nav\u0131 notu aras\u0131ndaki ili\u015fkiyi analiz etmek i\u00e7in, \u00e7al\u0131\u015f\u0131lan saatleri<\/em> ve al\u0131nan<\/em> haz\u0131rl\u0131k<\/em> s\u0131navlar\u0131n\u0131 yorday\u0131c\u0131 de\u011fi\u015fkenler olarak ve s\u0131navdaki final notunu<\/em> yan\u0131t de\u011fi\u015fkeni olarak kullanarak \u00e7oklu do\u011frusal regresyon uyguluyoruz.<\/span><\/p>\n A\u015fa\u011f\u0131daki sonucu al\u0131yoruz:<\/span><\/p>\n \u0130lk b\u00f6l\u00fcm, regresyon modeli uyumunu, yani regresyon modelinin veri setine ne kadar iyi “uyabildi\u011fini” \u00f6l\u00e7en birka\u00e7 farkl\u0131 say\u0131y\u0131 g\u00f6sterir.<\/span><\/p>\n Bu b\u00f6l\u00fcmdeki say\u0131lar\u0131n her birini nas\u0131l yorumlayaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n Bu korelasyon katsay\u0131s\u0131d\u0131r<\/a> . Tahmin edici de\u011fi\u015fkenler ile yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki do\u011frusal ili\u015fkinin g\u00fcc\u00fcn\u00fc \u00f6l\u00e7er. 1’in R kat\u0131, m\u00fckemmel bir do\u011frusal ili\u015fkiyi belirtirken, 0’\u0131n R kat\u0131, do\u011frusal bir ili\u015fkinin olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir. \u00c7oklu R, R karenin karek\u00f6k\u00fcd\u00fcr (a\u015fa\u011f\u0131ya bak\u0131n\u0131z).<\/span><\/p>\n Bu \u00f6rnekte, \u00e7oklu R 0,72855’tir<\/strong> ; bu, yorday\u0131c\u0131lar\u0131n \u00e7al\u0131\u015fma saatleri<\/em> ve haz\u0131rl\u0131k s\u0131navlar\u0131<\/em> ile yan\u0131t de\u011fi\u015fkeninin final s\u0131nav notu<\/em> aras\u0131nda olduk\u00e7a g\u00fc\u00e7l\u00fc bir do\u011frusal ili\u015fkiye i\u015faret eder.<\/span><\/p>\n Bu genellikle r2<\/sup> olarak yaz\u0131l\u0131r ve belirleme<\/span> katsay\u0131s\u0131<\/em> olarak da bilinir. Bu, yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan a\u00e7\u0131klanabilen yan\u0131t de\u011fi\u015fkenindeki varyans\u0131n oran\u0131d\u0131r.<\/span><\/p>\n R-kare de\u011feri 0 ila 1 aras\u0131nda de\u011fi\u015febilir. 0 de\u011feri, yan\u0131t de\u011fi\u015fkeninin yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan hi\u00e7bir \u015fekilde a\u00e7\u0131klanamayaca\u011f\u0131n\u0131 g\u00f6sterir. 1 de\u011feri, yan\u0131t de\u011fi\u015fkeninin yorday\u0131c\u0131 de\u011fi\u015fken taraf\u0131ndan hatas\u0131z olarak m\u00fckemmel bir \u015fekilde a\u00e7\u0131klanabilece\u011fini g\u00f6sterir.<\/span><\/p>\n Bu \u00f6rnekte R-kare 0,5307’dir<\/strong> ; bu, final s\u0131nav\u0131 puanlar\u0131ndaki varyans\u0131n %53,07’sinin \u00e7al\u0131\u015f\u0131lan saat say\u0131s\u0131 ve ge\u00e7mi\u015f deneme s\u0131navlar\u0131n\u0131n say\u0131s\u0131yla a\u00e7\u0131klanabilece\u011fini g\u00f6sterir.<\/span><\/p>\n \u0130lgili:<\/strong><\/span> \u0130yi bir R-kare de\u011feri nedir?<\/p>\n Bu, modeldeki \u00f6ng\u00f6r\u00fcc\u00fclerin say\u0131s\u0131na g\u00f6re ayarlanan R-karenin de\u011fi\u015ftirilmi\u015f bir versiyonudur. Her zaman R kareden k\u00fc\u00e7\u00fckt\u00fcr. D\u00fczeltilmi\u015f R-kare, farkl\u0131 regresyon modellerinin uyumunun birbiriyle kar\u015f\u0131la\u015ft\u0131r\u0131lmas\u0131nda faydal\u0131 olabilir.<\/span><\/p>\n Bu \u00f6rnekte d\u00fczeltilmi\u015f R-kare 0,4265’tir.<\/strong><\/span><\/p>\n Regresyonun standart hatas\u0131, g\u00f6zlemlenen de\u011ferler ile regresyon \u00e7izgisi aras\u0131ndaki ortalama mesafedir. Bu \u00f6rnekte g\u00f6zlemlenen de\u011ferler regresyon do\u011frusundan ortalama 7,3267 birim sapmaktad\u0131r.<\/strong><\/span><\/p>\n \u0130lgili:<\/strong><\/span> Regresyonun Standart Hatas\u0131n\u0131 Anlamak<\/p>\n Bu sadece veri setimizdeki g\u00f6zlemlerin<\/a> say\u0131s\u0131d\u0131r. Bu \u00f6rnekte toplam g\u00f6zlem say\u0131s\u0131 12’dir<\/strong> .<\/span><\/p>\n A\u015fa\u011f\u0131daki b\u00f6l\u00fcmde regresyon modelinin serbestlik dereceleri, kareler toplam\u0131, ortalama kareler, F istatisti\u011fi ve genel \u00f6nemi g\u00f6sterilmektedir.<\/span><\/p>\n Bu b\u00f6l\u00fcmdeki say\u0131lar\u0131n her birini nas\u0131l yorumlayaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n Bu say\u0131 \u015funa e\u015fittir: regresyon katsay\u0131lar\u0131n\u0131n say\u0131s\u0131 \u2013 1.<\/span> Bu \u00f6rnekte, bir orijinal terimimiz ve iki yorday\u0131c\u0131 de\u011fi\u015fkenimiz var, yani toplamda \u00fc\u00e7 regresyon katsay\u0131m\u0131z var, bu da regresyonun serbestlik derecelerinin 3 \u2013 1 oldu\u011fu<\/strong> anlam\u0131na geliyor. = 2<\/strong> .<\/span><\/p>\n Bu say\u0131 \u015funa e\u015fittir: g\u00f6zlem say\u0131s\u0131 \u2013 1.<\/span> Bu \u00f6rnekte 12 g\u00f6zlemimiz var, dolay\u0131s\u0131yla toplam serbestlik derecesi say\u0131s\u0131 12 \u2013 1 = 11<\/strong> .<\/span><\/p>\n Bu say\u0131 \u015funa e\u015fittir: toplam df \u2013 regresyon df. Bu \u00f6rnekte art\u0131k serbestlik derecesi 11 \u2013 2 = 9’dur<\/strong> .<\/span><\/p>\n Regresyon ortalama kareleri SS regresyonu\/sd regresyonu ile hesaplan\u0131r. Bu \u00f6rnekte regresyon MS = 546,53308 \/ 2 = 273,2665<\/strong> .<\/span><\/p>\n Art\u0131k ortalama kareler, art\u0131k SS\/art\u0131k df ile hesaplan\u0131r. Bu \u00f6rnekte, art\u0131k MS = 483,1335 \/ 9 = 53,68151<\/strong> .<\/span><\/p>\n F istatisti\u011fi MS regresyonu\/MS kal\u0131nt\u0131s\u0131 olarak hesaplan\u0131r. Bu istatistik, regresyon modelinin ba\u011f\u0131ms\u0131z de\u011fi\u015fken i\u00e7ermeyen bir modele g\u00f6re verilere daha iyi uyum sa\u011flay\u0131p sa\u011flamad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n Temel olarak regresyon modelinin bir b\u00fct\u00fcn olarak yararl\u0131 olup olmad\u0131\u011f\u0131n\u0131 test eder. Genel olarak, modeldeki yorday\u0131c\u0131 de\u011fi\u015fkenlerden hi\u00e7biri istatistiksel olarak anlaml\u0131 de\u011filse, genel F istatisti\u011fi de istatistiksel olarak anlaml\u0131 de\u011fildir.<\/span><\/p>\n Bu \u00f6rnekte F istatisti\u011fi 273,2665 \/ 53,68151 = 5,09’dur<\/strong> .<\/span><\/p>\n Tablodaki son de\u011fer F istatisti\u011fiyle ili\u015fkili p de\u011feridir. Genel regresyon modelinin anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 g\u00f6rmek i\u00e7in p de\u011ferini bir anlaml\u0131l\u0131k d\u00fczeyiyle kar\u015f\u0131la\u015ft\u0131rabilirsiniz; ortak se\u00e7enekler 0,01, 0,05 ve 0,10’dur.<\/span><\/p>\n P de\u011feri anlaml\u0131l\u0131k seviyesinin alt\u0131ndaysa, regresyon modelinin verilere yorday\u0131c\u0131 de\u011fi\u015fken i\u00e7ermeyen modelden daha iyi uydu\u011fu sonucuna varmak i\u00e7in yeterli kan\u0131t vard\u0131r. Bu sonu\u00e7 olumludur \u00e7\u00fcnk\u00fc bu, modelin yorday\u0131c\u0131 de\u011fi\u015fkenlerinin asl\u0131nda modelin uyumunu iyile\u015ftirdi\u011fi anlam\u0131na gelir.<\/span><\/p>\n Bu \u00f6rnekte p de\u011feri 0,033’t\u00fcr<\/strong> ve bu da 0,05 ortak anlaml\u0131l\u0131k d\u00fczeyinin alt\u0131ndad\u0131r. Bu, bir b\u00fct\u00fcn olarak regresyon modelinin istatistiksel olarak anlaml\u0131 oldu\u011funu, yani modelin, yorday\u0131c\u0131 de\u011fi\u015fkenlerin olmad\u0131\u011f\u0131 modele g\u00f6re verilere daha iyi uyum sa\u011flad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n Son b\u00f6l\u00fcmde regresyon modelindeki her terim i\u00e7in katsay\u0131 tahminleri, tahminlerin standart hatas\u0131, t-istatisti\u011fi, p-de\u011ferleri ve g\u00fcven aral\u0131klar\u0131 sunulmaktad\u0131r.<\/span><\/p>\n Bu b\u00f6l\u00fcmdeki say\u0131lar\u0131n her birini nas\u0131l yorumlayaca\u011f\u0131n\u0131z a\u015fa\u011f\u0131da a\u00e7\u0131klanm\u0131\u015ft\u0131r:<\/span><\/p>\n Katsay\u0131lar bize tahmini regresyon denklemini yazmak i\u00e7in gereken say\u0131lar\u0131 verir:<\/span><\/p>\n y \u015fapka<\/sub> = b 0<\/sub> + b 1<\/sub> x 1<\/sub> + b 2<\/sub> x 2<\/sub> .<\/span><\/strong><\/p>\n Bu \u00f6rnekte tahmini regresyon denklemi \u015f\u00f6yledir:<\/span><\/p>\n Final s\u0131nav puan\u0131 = 66.99 + 1.299 (\u00e7al\u0131\u015fma saati) + 1.117 (haz\u0131rl\u0131k s\u0131navlar\u0131)<\/span><\/strong><\/p>\n Her bir katsay\u0131, di\u011fer t\u00fcm yorday\u0131c\u0131 de\u011fi\u015fkenlerin sabit kald\u0131\u011f\u0131 varsay\u0131larak, belirli bir yorday\u0131c\u0131 de\u011fi\u015fkendeki her bir birimlik art\u0131\u015f i\u00e7in yan\u0131t de\u011fi\u015fkenindeki ortalama art\u0131\u015f olarak yorumlan\u0131r. \u00d6rne\u011fin, haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n say\u0131s\u0131n\u0131n sabit kald\u0131\u011f\u0131 varsay\u0131ld\u0131\u011f\u0131nda, \u00e7al\u0131\u015f\u0131lan her ek saat i\u00e7in final s\u0131nav puan\u0131nda beklenen ortalama art\u0131\u015f 1.299 puand\u0131r.<\/em><\/span><\/p>\n Kesi\u015fme noktas\u0131, s\u0131f\u0131r saat ders \u00e7al\u0131\u015fan ve haz\u0131rl\u0131k s\u0131nav\u0131na girmeyen bir \u00f6\u011frencinin final s\u0131nav\u0131ndan beklenen ortalama notu olarak yorumlan\u0131r. Bu \u00f6rnekte, bir \u00f6\u011frencinin s\u0131f\u0131r saat \u00e7al\u0131\u015f\u0131p haz\u0131rl\u0131k s\u0131nav\u0131na girmemesi durumunda 66,99 puan almas\u0131 beklenir. Bir regresyon sonucunun kesi\u015fimini yorumlarken dikkatli olun \u00e7\u00fcnk\u00fc bunu yapmak her zaman anlaml\u0131 de\u011fildir.<\/span><\/p>\n \u00d6rne\u011fin, baz\u0131 durumlarda kesi\u015fimin negatif bir say\u0131 oldu\u011fu ortaya \u00e7\u0131kabilir ve bunun \u00e7o\u011funlukla a\u00e7\u0131k bir yorumu yoktur. Bu, modelin yanl\u0131\u015f oldu\u011fu anlam\u0131na gelmez; yaln\u0131zca m\u00fcdahalenin kendisinin herhangi bir anlam ifade edecek \u015fekilde yorumlanmamas\u0131 gerekti\u011fi anlam\u0131na gelir.<\/span><\/p>\n Standart hata, her de\u011fi\u015fken i\u00e7in katsay\u0131 tahmini etraf\u0131ndaki belirsizli\u011fin bir \u00f6l\u00e7\u00fcs\u00fcd\u00fcr.<\/span><\/p>\n T-stat basit\u00e7e katsay\u0131n\u0131n standart hataya b\u00f6l\u00fcnmesiyle elde edilir. \u00d6rne\u011fin \u00e7al\u0131\u015fma saatleri<\/em> i\u00e7in t-istatistiki 1,299 \/ 0,417 = 3,117’dir.<\/span><\/p>\n Sonraki s\u00fctun t-istatistikiyle ili\u015fkili p-de\u011ferini g\u00f6sterir. Bu say\u0131 bize belirli bir yan\u0131t de\u011fi\u015fkeninin modelde anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 s\u00f6yler. Bu \u00f6rnekte ders \u00e7al\u0131\u015fma saatleri<\/em> i\u00e7in p de\u011ferinin 0,012, haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n<\/em> p de\u011ferinin ise 0,304 oldu\u011funu g\u00f6r\u00fcyoruz. Bu durum, \u00e7al\u0131\u015fma saatlerinin<\/em> deneme s\u0131navlar\u0131ndan<\/em> farkl\u0131 olarak final s\u0131nav\u0131 notunun \u00f6nemli bir belirleyicisi oldu\u011funu g\u00f6stermektedir.<\/span><\/p>\n Tablonun son iki s\u00fctunu katsay\u0131 tahminleri i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n alt ve \u00fcst s\u0131n\u0131rlar\u0131n\u0131 sa\u011flamaktad\u0131r.<\/span><\/p>\n \u00d6rne\u011fin \u00e7al\u0131\u015fma saatlerine<\/em> ili\u015fkin katsay\u0131 tahmini 1.299’dur ancak bu tahminin etraf\u0131nda baz\u0131 belirsizlikler bulunmaktad\u0131r. Bunun kesin katsay\u0131 olup olmad\u0131\u011f\u0131ndan asla emin olamay\u0131z. Yani %95’lik bir g\u00fcven aral\u0131\u011f\u0131 bize ger\u00e7ek katsay\u0131 i\u00e7in bir dizi olas\u0131 de\u011fer verir.<\/span><\/p>\n Bu durumda \u00e7al\u0131\u015fma saatlerine<\/em> ili\u015fkin %95 g\u00fcven aral\u0131\u011f\u0131 (0,356, 2,24) olur. Bu g\u00fcven aral\u0131\u011f\u0131n\u0131n “0” say\u0131s\u0131n\u0131 i\u00e7ermedi\u011fine dikkat edin; bu, \u00e7al\u0131\u015fma saatleri<\/em> katsay\u0131s\u0131n\u0131n ger\u00e7ek de\u011ferinin s\u0131f\u0131rdan farkl\u0131, yani pozitif bir say\u0131 oldu\u011fundan tamamen emin oldu\u011fumuz anlam\u0131na gelir.<\/span><\/p>\n Buna kar\u015f\u0131l\u0131k haz\u0131rl\u0131k s\u0131navlar\u0131<\/em> i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 (-1,201, 3,436)’d\u0131r. Bu g\u00fcven aral\u0131\u011f\u0131n\u0131n “0” say\u0131s\u0131n\u0131 i\u00e7erdi\u011fini<\/em> unutmay\u0131n; bu, haz\u0131rl\u0131k s\u0131navlar\u0131n\u0131n<\/em> katsay\u0131s\u0131n\u0131n ger\u00e7ek de\u011ferinin s\u0131f\u0131r olabilece\u011fi, yani final s\u0131nav\u0131 sonu\u00e7lar\u0131n\u0131 tahmin etmede anlaml\u0131 olmad\u0131\u011f\u0131 anlam\u0131na gelir.<\/span><\/p>\n Do\u011frusal Regresyon \u0130\u00e7in S\u0131f\u0131r Hipotezini Anlamak<\/a> \u0130statistikte regresyon , yorday\u0131c\u0131 de\u011fi\u015fkenler ile bir yan\u0131t de\u011fi\u015fkeni aras\u0131ndaki ili\u015fkiyi analiz etmek i\u00e7in kullan\u0131labilecek bir tekniktir. Regresyon analizini ger\u00e7ekle\u015ftirmek i\u00e7in yaz\u0131l\u0131m (R, SAS, SPSS vb.) kulland\u0131\u011f\u0131n\u0131zda, \u00e7\u0131kt\u0131 olarak regresyon sonu\u00e7lar\u0131n\u0131 \u00f6zetleyen bir regresyon tablosu al\u0131rs\u0131n\u0131z. Regresyon analizi sonu\u00e7lar\u0131n\u0131 anlayabilmeniz i\u00e7in bu tabloyu nas\u0131l okuyaca\u011f\u0131n\u0131z\u0131 bilmeniz \u00f6nemlidir. Bu e\u011fitimde bir regresyon analizi \u00f6rne\u011fi g\u00f6sterilmekte ve […]<\/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-470","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\n Bir regresyon \u00f6rne\u011fi<\/strong><\/span><\/h2>\n
Model uyumunun incelenmesi<\/strong><\/span><\/h2>\n
Birka\u00e7 Rs<\/strong><\/span><\/h3>\n
R-kare<\/span><\/strong><\/h3>\n
D\u00fczeltilmi\u015f R-kare<\/strong><\/span><\/h3>\n
Regresyonun standart hatas\u0131<\/strong><\/span><\/h3>\n
Yorumlar<\/strong><\/span><\/h3>\n
Regresyon modelinin genel anlaml\u0131l\u0131\u011f\u0131n\u0131n test edilmesi<\/strong><\/span><\/h2>\n
Regresyon serbestlik dereceleri<\/strong><\/span><\/h3>\n
Toplam serbestlik derecesi<\/span><\/strong><\/h3>\n
Kalan serbestlik dereceleri<\/strong><\/span><\/h3>\n
Ortalama kareler<\/strong><\/span><\/h3>\n
F istatisti\u011fi<\/strong><\/span><\/h3>\n
F’nin \u00d6nemi (P de\u011feri)<\/span><\/strong><\/h3>\n
Regresyon modelinin genel anlaml\u0131l\u0131\u011f\u0131n\u0131n test edilmesi<\/strong><\/span><\/h2>\n
Katsay\u0131lar<\/strong><\/span><\/h3>\n
Standart hata, t istatistikleri ve p de\u011ferleri<\/strong><\/span><\/h3>\n
Katsay\u0131 tahminleri i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n
Ek kaynaklar<\/strong><\/h3>\n
Regresyonda Genel \u00d6nem i\u00e7in F Testini Anlamak<\/a>
Regresyon sonu\u00e7lar\u0131 nas\u0131l raporlan\u0131r?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"