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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 Cook's distance ： ウィキペディア英語版 Cook's distance In statistics, Cook's distance or Cook's ''D'' is a commonly used estimate of the influence of a data point when performing least squares regression analysis. In a practical ordinary least squares analysis, Cook's distance can be used in several ways: to indicate data points that are particularly worth checking for validity; to indicate regions of the design space where it would be good to be able to obtain more data points. It is named after the American statistician R. Dennis Cook, who introduced the concept in 1977. ==Definition== Cook's distance measures the effect of deleting a given observation. Data points with large residuals (outliers) and/or high leverage may distort the outcome and accuracy of a regression. Points with a large Cook's distance are considered to merit closer examination in the analysis. For the algebraic expression, first define :$\backslash mathbf\; \backslash equiv\; \backslash mathbf\; (\; \backslash mathbf^\; \backslash mathbf)^\; \backslash mathbf^$ as the $(n\; \backslash times\; n)$ hat matrix (or projection matrix) of the $n$ observations of each explanatory variables. Then let $\backslash hat^$ be the OLS estimate of $\backslash beta$ that results from omitting the $i$-th observation ($i\; =\; 1,\; 2,\; \backslash dots,\; n$). Then we have :$\backslash hat\; -\; \backslash hat^\; =\; \backslash left(\; \backslash frac^\; \backslash mathbf)^\; \backslash mathbf$ where $e\_i\; \backslash ,$ is the residual (i.e., the difference between the observed value and the value fitted by the proposed model), and $h\_\; \backslash ,$, defined as :$h\_\; \backslash equiv\; \backslash mathbf\_i^\; (\; \backslash mathbf^\; \backslash mathbf)^\; \backslash mathbf\_$ is the leverage, i.e., the $i$-th diagonal element of $\backslash mathbf\; \backslash ,$. With this, we can define Cook's distance as :$D\_i\; =\; \backslash frac\}\backslash right"\; TITLE="\backslash frac)^2\}\backslash right">),$ where $k$ is the number of fitted parameters, and $\backslash mathrm\; \backslash ,$ is the mean square error of the regression model. Algebraically equivalent is the following expression :$D\_i\; =\; \backslash frac^)^\; \backslash mathbf^\; \backslash mathbf\; (\backslash hat\; -\; \backslash hat^)\; \}\; ,$ where $s^$ is the OLS estimate of the variance of the error term, defined as :$s^\; \backslash equiv\; \backslash frac\; \backslash mathbf\; \}$ And a third equivalent expression is :$D\_i\; =\; \backslash frac)^2\; \}\backslash ,$ is the prediction for observation ''j'' from a refitted regression model in which observation ''i'' has been omitted; 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「Cook's distance」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.