 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".Suppose we are given a regression function formula_1 yielding for each formula_2 an estimate formula_3 where formula_4 is the vector of the "i"th observations on all the explanatory variables.