GivenSuppose we are given a regression function ''ƒ'' yielding for each ''y<sub>i</sub>'', 1 ≤ ''i'' ≤ ''N'', an estimate <math>\widehat{y}_i = f(x_i)</math>,wewhere <math>x_i</math> is the vector of the ''i''<sup>th</sup> observations on all the explanatory variables. We have: