If a linear regression model is used for prediction, the mean squared error of prediction (MSEP) measures the performance of the model. The MSEP is a function of unknown parameters and good estimates of it are of interest. This article derives a best unbiased estimator and a minimum MSE estimator under the assumption of a normal distribution. It compares the bias and the MSE of these estimators and some others. Similar results are presented for the case in which the model is used to estimate values of the response function.