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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 squared deviations ： ウィキペディア英語版 squared deviations In probability theory and statistics, the definition of variance is either the expected value (when considering a theoretical distribution), or average value (for actual experimental data), of squared deviations from the mean. Computations for analysis of variance involve the partitioning of a sum of squared deviations. An understanding of the complex computations involved is greatly enhanced by a detailed study of the statistical value: : $\backslash operatorname(\; X\; ^\; 2\; ).$ It is well known that for a random variable $X$ with mean $\backslash mu$ and variance $\backslash sigma^2$: : $\backslash sigma^2\; =\; \backslash operatorname(\; X\; ^\; 2\; )\; -\; \backslash mu^2$〔Mood & Graybill: ''An introduction to the Theory of Statistics'' (McGraw Hill)〕 Therefore : $\backslash operatorname(\; X\; ^\; 2\; )\; =\; \backslash sigma^2\; +\; \backslash mu^2.$ From the above, the following are easily derived: : $\backslash operatorname\backslash left(\; \backslash sum\backslash left(\; X\; ^\; 2\backslash right)\; \backslash right)\; =\; n\backslash sigma^2\; +\; n\backslash mu^2$ : $\backslash operatorname\backslash left(\; \backslash left(\backslash sum\; X\; \backslash right)^\; 2\; \backslash right)\; =\; n\backslash sigma^2\; +\; n^2\backslash mu^2$ If $\backslash hat$ is a vector of n predictions, and $Y$ is the vector of the true values, then the SSE of the predictor is: $SSE=\backslash frac\backslash sum\_^n(\backslash hat\; -\; Y\_i)^2$ == Sample variance == (詳細はsample variance (before deciding whether to divide by ''n'' or ''n'' − 1) is most easily calculated as : $S\; =\; \backslash sum\; x\; ^\; 2\; -\; \backslash frac$ From the two derived expectations above the expected value of this sum is : $\backslash operatorname(S)\; =\; n\backslash sigma^2\; +\; n\backslash mu^2\; -\; \backslash frac$ which implies : $\backslash operatorname(S)\; =\; (n\; -\; 1)\backslash sigma^2.$ This effectively proves the use of the divisor ''n'' − 1 in the calculation of an unbiased sample estimate of ''σ''2. 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「squared deviations」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.