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.
is the vector of the ith observations on all the explanatory variables.
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 Alternatively, the fraction of variance unexplained can be defined as follows: where MSE(f) is the mean squared error of the regression function ƒ.
It follows that the MSE of this function equals the variance of Y; that is, SSerr = SStot, and SSreg = 0.
In this case, no variation in Y can be accounted for, and the FVU then has its maximum value of 1.
More generally, the FVU will be 1 if the explanatory variables X tell us nothing about Y in the sense that the predicted values of Y do not covary with Y.
But as prediction gets better and the MSE can be reduced, the FVU goes down.
for all i, the MSE is 0, SSerr = 0, SSreg = SStot, and the FVU is 0.