Polinom regresyon<\/strong> veya polinom regresyon<\/strong> , ba\u011f\u0131ms\u0131z de\u011fi\u015fken X ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y aras\u0131ndaki ili\u015fkinin bir polinom kullan\u0131larak modellendi\u011fi bir regresyon modelidir.<\/p>\n \u00d6rne\u011fin, ikinci dereceden bir polinom regresyon modelinin denklemi y=\u03b2 0<\/sub> +\u03b2 1<\/sub> x+\u03b2 2<\/sub> x 2<\/sup> +\u03b5’dir.<\/p>\n Polinom regresyonu, grafikleri polinom e\u011frileri olan veri k\u00fcmelerinin uydurulmas\u0131 i\u00e7in kullan\u0131\u015fl\u0131d\u0131r. Dolay\u0131s\u0131yla, bir veri \u00f6rne\u011finin nokta grafi\u011fi parabol \u015feklindeyse, do\u011frusal regresyon modeli yerine ikinci dereceden regresyon modeli olu\u015fturmak daha iyi olacakt\u0131r. Bu \u015fekilde regresyon modeli denklemi veri \u00f6rne\u011fine daha iyi uyacakt\u0131r.<\/p>\n Polinom regresyonun, t\u0131pk\u0131 \u00fcstel regresyon ve logaritmik regresyon gibi, do\u011frusal olmayan bir regresyon t\u00fcr\u00fc oldu\u011funu unutmay\u0131n. <\/p>\n Bir polinom regresyon modelinin denklemi \u015f\u00f6yledir: y=\u03b2 0<\/sub> +\u03b2 1<\/sub> x+\u03b2 2<\/sub> x 2<\/sup> +\u03b2 3<\/sub> x 3<\/sup> \u2026+\u03b2 m<\/sub> x m<\/sup> +\u03b5.<\/p>\n<\/p>\n Alt\u0131n:<\/p>\n ba\u011f\u0131ml\u0131 de\u011fi\u015fkendir.<\/li>\n ba\u011f\u0131ms\u0131z de\u011fi\u015fkendir.<\/li>\n polinom regresyon denkleminin sabitidir.<\/li>\n de\u011fi\u015fkenle ili\u015fkili regresyon katsay\u0131s\u0131d\u0131r<\/p>\n .<\/li>\n Bu hata veya art\u0131kt\u0131r, yani g\u00f6zlemlenen de\u011fer ile model taraf\u0131ndan tahmin edilen de\u011fer aras\u0131ndaki farkt\u0131r.<\/li>\n<\/ul>\n Toplamda bir \u00f6rne\u011fimiz varsa<\/p>\n<\/p>\n g\u00f6zlemler i\u00e7in polinom regresyon modelini matris bi\u00e7iminde \u00f6nerebiliriz:<\/p>\n<\/p>\n Yukar\u0131daki matris ifadesi, her matrise bir harf atanarak yeniden yaz\u0131labilir:<\/p>\n<\/p>\n B\u00f6ylece, en k\u00fc\u00e7\u00fck kareler kriterini<\/a> uygulayarak, bir polinom regresyon modelinin katsay\u0131lar\u0131n\u0131 tahmin etmek i\u00e7in kullan\u0131lan form\u00fcle<\/strong> ula\u015fabiliriz:<\/p>\n<\/p>\n Ancak bu hesaplamalar\u0131 elle yapmak \u00e7ok zahmetli ve zaman al\u0131c\u0131 oldu\u011fundan, polinom regresyon modelini \u00e7ok daha h\u0131zl\u0131 ger\u00e7ekle\u015ftirmenizi sa\u011flayan bilgisayar yaz\u0131l\u0131mlar\u0131n\u0131 (Minitab veya Excel gibi) kullanmak daha uygundur. <\/p>\n Art\u0131k polinom regresyonun tan\u0131m\u0131n\u0131 ve nas\u0131l yap\u0131ld\u0131\u011f\u0131n\u0131 bildi\u011fimize g\u00f6re, kavram\u0131 tam olarak anlamak i\u00e7in ger\u00e7ek hayattan bir \u00f6rne\u011fe bakal\u0131m.<\/p>\n \u00d6ncelikle veri grafi\u011finin polinom e\u011frisi \u015fekline sahip oldu\u011fu durumlarda polinom regresyon modelinin yap\u0131lmas\u0131 gerekti\u011fi unutulmamal\u0131d\u0131r. \u00d6rne\u011fin nokta grafi\u011fi k\u00fcbik e\u011fri \u015feklindeyse \u00fc\u00e7\u00fcnc\u00fc dereceden polinom regresyon modeli olu\u015fturmam\u0131z gerekir.<\/p>\n Yani a\u015fa\u011f\u0131daki g\u00f6rselde g\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi verilerimizin nokta grafi\u011fi ikinci dereceden bir \u015fekle sahip \u00e7\u00fcnk\u00fc ba\u011f\u0131ms\u0131z de\u011fi\u015fkenin de\u011ferini art\u0131rd\u0131k\u00e7a ba\u011f\u0131ml\u0131 de\u011fi\u015fken daha h\u0131zl\u0131 b\u00fcy\u00fcyor. Bu durumda do\u011frusal bir regresyon modeli uyguland\u0131 ve g\u00f6rd\u00fc\u011f\u00fcn\u00fcz gibi noktalara pek iyi uymuyor \u00e7\u00fcnk\u00fc \u00e7izginin t\u00fcm noktalar\u0131n alt\u0131nda oldu\u011fu b\u00f6l\u00fcmler ve \u00e7izginin bunlar\u0131n \u00fcst\u00fcnde oldu\u011fu b\u00f6l\u00fcmler var. <\/p>\n \u00d6te yandan ikinci dereceden polinom regresyon modelini \u00e7al\u0131\u015ft\u0131r\u0131rsak a\u015fa\u011f\u0131daki g\u00f6rselde de g\u00f6rebilece\u011finiz gibi \u00f6rnek verilere \u00e7ok daha iyi uyum sa\u011fl\u0131yor. <\/p>\n Ayr\u0131ca polinom regresyon modeli geli\u015ftirilirken belirleme katsay\u0131s\u0131 %86,80’den %94,05’e \u00e7\u0131kt\u0131\u011f\u0131 i\u00e7in olduk\u00e7a iyile\u015fir. Dolay\u0131s\u0131yla yeni regresyon modeli veri setini \u00e7ok daha iyi a\u00e7\u0131klamaktad\u0131r.<\/p>\n \u00d6te yandan polinom regresyonu yapmam\u0131z gerekti\u011finin bir di\u011fer g\u00f6stergesi de art\u0131klar\u0131n grafi\u011fidir. Do\u011frusal bir regresyonda art\u0131klar\u0131n grafi\u011fi bir parabol veya ba\u015fka t\u00fcrde bir polinom \u015feklindeyse, bir polinom regresyon modeli \u00e7al\u0131\u015f\u0131lan verilere kesinlikle daha iyi uyar. <\/p>\n Temel olarak \u00fc\u00e7 t\u00fcr do\u011frusal olmayan regresyon vard\u0131r:<\/p>\n Bu makalede istatistikte polinom regresyonunun ne oldu\u011fu ve nas\u0131l yap\u0131ld\u0131\u011f\u0131 anlat\u0131lmaktad\u0131r. Ek olarak polinom regresyonunun ger\u00e7ekle\u015ftirildi\u011fi bir \u00f6rne\u011fi g\u00f6rebileceksiniz. Polinom regresyon nedir? Polinom regresyon veya polinom regresyon , ba\u011f\u0131ms\u0131z de\u011fi\u015fken X ile ba\u011f\u0131ml\u0131 de\u011fi\u015fken Y aras\u0131ndaki ili\u015fkinin bir polinom kullan\u0131larak modellendi\u011fi bir regresyon modelidir. \u00d6rne\u011fin, ikinci dereceden bir polinom regresyon modelinin denklemi y=\u03b2 0 +\u03b2 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[14],"tags":[],"class_list":["post-316","post","type-post","status-publish","format-standard","hentry","category-istatistik"],"yoast_head":"\n<\/span> Polinom Regresyon Form\u00fcl\u00fc<\/span><\/h2>\n
![\"y=\\beta_0+\\beta_1](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-9d195b19a3d6f10a8eb73b13cd90420c_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n\n
![\"y\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-38461fc041e953482219abf5d4cce1cb_l3.png\" "\\"Rendered")
<\/p>\n![\"x\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7e5fbfa0bbbd9f3051cd156a0f1b5e31_l3.png\" "\\"Rendered")
<\/p>\n![\"\\beta_0\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c5ba513cc7e504bc674f76afa70a3442_l3.png\" "\\"Rendered")
<\/p>\n![\"\\beta_i\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ff540c55c6ee8f10a1dab8e2422947ab_l3.png\" "\\"Rendered")
<\/p>\n![\"x^i\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-c6fd71de48bfaa9a0e22d2d633ca6796_l3.png\" "\\"Rendered")
<\/p>\n![\"\\bm{\\varepsilon}\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-29b8f7fac5f2df4b101dff63e95516c5_l3.png\" "\\"Rendered")
<\/p>\n![\"n\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-ec4217f4fa5fcd92a9edceba0e708cf7_l3.png\" "\\"Rendered")
<\/p>\n![\"\\begin{pmatrix}y_1\\\\y_2\\\\y_3\\\\\\vdots\\\\y_n\\end{pmatrix}=\\begin{pmatrix}1&x_1&x_1^2&\\dots&x_1^m\\\\1&x_2&x_2^2&\\dots&x_2^m\\\\1&x_3&x_3^2&\\dots&x_3^m\\\\](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-f29ae985155878617f11afa5f37addef_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"Y=X\\beta+\\varepsilon\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-7614ddbb78ced2e2b8b6c7642d9969c3_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n![\"\\widehat{\\beta}=\\left(X^tX\\right)^{-1}X^tY\"](\"https:\/\/statorials.org\/wp-content\/ql-cache\/quicklatex.com-b6ef097cee722e7355fa4eb77b7ea3e5_l3.png\" "\\"Rendered")
<\/p>\n<\/p>\n<\/span> Polinom regresyon modeli \u00f6rne\u011fi<\/span><\/h2>\n
![\"\"](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/rpol-faux.png\")
<\/figure>\n![\"polinom](\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/exemple-de-regression-polynomiale.png\")
<\/figure>\n<\/span> Di\u011fer do\u011frusal olmayan regresyon t\u00fcrleri<\/span><\/h2>\n
\n
\u27a4<\/span> Bak\u0131n\u0131z:<\/strong> \u00dcstel Regresyon<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"