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In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared errors of prediction (SSE), is the sum of the squares of residuals (deviations of predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection. In general, total sum of squares = explained sum of squares + residual sum of squares. For a proof of this in the multivariate ordinary least squares (OLS) case, see partitioning in the general OLS model. ==One explanatory variable== In a model with a single explanatory variable, RSS is given by : where ''y''''i'' is the ''i'' th value of the variable to be predicted, ''x''''i'' is the ''i'' th value of the explanatory variable, and is the predicted value of ''y''''i'' (also termed ). In a standard linear simple regression model, , where ''a'' and ''b'' are coefficients, ''y'' and ''x'' are the regressand and the regressor, respectively, and ε is the error term. The sum of squares of residuals is the sum of squares of estimates of ε''i''; that is : where is the estimated value of the constant term and is the estimated value of the slope coefficient ''b''. 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「Residual sum of squares」の詳細全文を読む スポンサード リンク
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