Fraction of variance unexplained

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 f {\displaystyle f} yielding for each y i {\displaystyle y_{i}} an estimate y ^ i = f ( x i ) {\displaystyle {\widehat {y}}_{i}=f(x_{i})} where x i {\displaystyle x_{i}} is the vector of the ith observations on all the explanatory variables. We define the fraction of variance unexplained (FVU) as: FVU = VAR err VAR tot = SS err / N SS tot / N = SS err SS tot ( = 1 − SS reg SS tot , only true in some cases such as linear regression ) = 1 − R 2 {\displaystyle {\begin{aligned}{\text{FVU}}&={{\text{VAR}}_{\text{err}} \over {\text{VAR}}_{\text{tot}}}={{\text{SS}}_{\text{err}}/N \over {\text{SS}}_{\text{tot}}/N}={{\text{SS}}_{\text{err}} \over {\text{SS}}_{\text{tot}}}\left(=1-{{\text{SS}}_{\text{reg}} \over {\text{SS}}_{\text{tot}}},{\text{ only true in some cases such as linear regression}}\right)\\[6pt]&=1-R^{2}\end{aligned}}} where R2 is the coefficient of determination and VARerr and VARtot are the variance of the residuals and the sample variance of the dependent variable.

Source: Wikipedia — Fraction of variance unexplained (CC BY-SA 4.0)

Fraction of variance unexplained

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 f {\displaystyle f} yielding for each y i {\displaystyle y_{i}} an estimate y ^ i = f ( x i ) {\displaystyle {\widehat {y}}_{i}=f(x_{i})} where x i {\displaystyle x_{i}} is the vector of the ith observations on all the explanatory variables. We define the fraction of variance unexplained (FVU) as: FVU = VAR err VAR tot = SS err / N SS tot / N = SS err SS tot ( = 1 − SS reg SS tot , only true in some cases such as linear regression ) = 1 − R 2 {\displaystyle {\begin{aligned}{\text{FVU}}&={{\text{VAR}}_{\text{err}} \over {\text{VAR}}_{\text{tot}}}={{\text{SS}}_{\text{err}}/N \over {\text{SS}}_{\text{tot}}/N}={{\text{SS}}_{\text{err}} \over {\text{SS}}_{\text{tot}}}\left(=1-{{\text{SS}}_{\text{reg}} \over {\text{SS}}_{\text{tot}}},{\text{ only true in some cases such as linear regression}}\right)\\[6pt]&=1-R^{2}\end{aligned}}} where R2 is the coefficient of determination and VARerr and VARtot are the variance of the residuals and the sample variance of the dependent variable.

Source: Wikipedia "Fraction of variance unexplained" · CC BY-SA 4.0

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