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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Frisch–Waugh–Lovell theorem ： ウィキペディア英語版 Frisch–Waugh–Lovell theorem In econometrics, the Frisch–Waugh–Lovell (FWL) theorem is named after the econometricians Ragnar Frisch, Frederick V. Waugh, and Michael C. Lovell. The Frisch–Waugh–Lovell theorem states that if the regression we are concerned with is: :$Y\; =\; X\_1\; \backslash beta\_1\; +\; X\_2\; \backslash beta\_2\; +\; u\; \backslash !$ where $X\_1$ and $X\_2$ are $n\; \backslash times\; k\_1$ and $n\; \backslash times\; k\_2$ respectively and where $\backslash beta\_1$ and $\backslash beta\_2$ are conformable, then the estimate of $\backslash beta\_2$ will be the same as the estimate of it from a modified regression of the form: :$M\_\; Y\; =\; M\_\; X\_2\; \backslash beta\_2\; +\; M\_\; u\; \backslash !,$ where $M\_$ projects onto the orthogonal complement of the image of the projection matrix $X\_1(X\_1\text{'}X\_1)^X\_1\text{'}$. Equivalently, ''M''''X''1 projects onto the orthogonal complement of the column space of ''X''1. Specifically, :$M\_\; =\; I\; -\; X\_1(X\_1\text{'}X\_1)^X\_1\text{'}.\; \backslash !$ This result implies that all these secondary regressions are unnecessary: using projection matrices to make the explanatory variables orthogonal to each other will lead to the same results as running the regression with all non-orthogonal explanators included. ==References== * * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Frisch–Waugh–Lovell theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.