where formula_2 is the sum of squared prediction errors. these errors are estimated based on cross validation. in the cross validation procedure, the set of support points is mapped to formula_3 subsets. then the approximation model is built by removing subset formula_4 from the support points and approximating the subset model output formula_5 using the remaining point set. this means that the model quality is estimated only at those points which are not used to build the approximation model. since the prediction error is used instead of the fit, this approach applies to regression and even interpolation models.