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. 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. 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: 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. SSerr (the sum of squared predictions errors, equivalently the residual sum of squares), SStot (the total sum of squares), and SSreg (the sum of squares of the regression, equivalently the explained sum of squares) are given by