In this article, we considered the asymptotic expectations of the prediction error and the fitting error of a regression model, in which the component functions are chosen from a finite set of orthogonal functions. Under the least squares estimation, we showed that the asymptotic bias in estimating the prediction error based on the fitting error includes the true number of components, which is essentially unknown in practical applications. On the other hand, under a suitable shrinkage method, we showed that an asymptotically unbiased estimate of the prediction error is given by the fitting error plus a known term except the noise variance.