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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 Proofs involving ordinary least squares ： ウィキペディア英語版 Proofs involving ordinary least squares The purpose of this page is to provide supplementary materials for the Ordinary least squares article, reducing the load of the main article with mathematics and improving its accessibility, while at the same time retaining the completeness of exposition. == Least squares estimator for ''β'' == Using matrix notation, the sum of squared residuals is given by : $S(b)\; =\; (y-Xb)\text{'}(y-Xb)\; \backslash ,$ Where $\text{'}$ denotes the matrix transpose. Since this is a quadratic expression and ''S''(''b'') ≥ 0, the global minimum will be found by differentiating it with respect to ''b'': : $0\; =\; \backslash frac(\backslash hat\backslash beta)\; =\; \backslash frac\backslash bigg(y\text{'}y\; -\; b\text{'}X\text{'}y\; -\; y\text{'}Xb\; +\; b\text{'}X\text{'}Xb\backslash bigg)\backslash bigg|\_\; =\; -2X\text{'}y\; +\; 2X\text{'}X\backslash hat\backslash beta$ By assumption matrix ''X'' has full column rank, and therefore ''X'X'' is invertible and the least squares estimator for ''β'' is given by : $\backslash hat\backslash beta\; =\; (X\text{'}X)^X\text{'}y\; \backslash ,$ 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「Proofs involving ordinary least squares」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.