|
In statistics, the fraction of variance unexplained (FVU) in the context of a regression task is the fraction of variance of the regressand (dependent variable) ''Y'' which cannot be explained, i.e., which is not correctly predicted, by the explanatory variables ''X''. ==Formal definition== Suppose we are given a regression function ''ƒ'' yielding for each ''yi'', 1 ≤ ''i'' ≤ ''N'', an estimate where is the vector of the ''i''th observations on all the explanatory variables. We define the fraction of variance unexplained (FVU) as: : where ''R''2 is the coefficient of determination and ''VAR''err and ''VAR''tot are the variance of the estimated residuals and the sample variance of the dependent variable. ''SS''''err'' (the sum of squared predictions errors, equivalently the residual sum of squares), ''SS''''tot'' (the total sum of squares), and ''SS''''reg'' (the sum of squares of the regression, equivalently the explained sum of squares) are given by : Alternatively, the fraction of variance unexplained can be defined as follows: : where MSE(''f'') is the mean squared error of the regression function ''ƒ''. 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「fraction of variance unexplained」の詳細全文を読む スポンサード リンク
|