A Comparison of Single Sample and Cross‐validation Methods for Estimating the Mean Squared Error of Prediction in Multiple Linear Regression

Two procedures for estimating the mean squared error of prediction of an empirically determined linear prediction equation are examined. The method usually employed makes use of a second validation sample; another method makes use of the calibration sample alone. The mean squared error of estimation is derived for each of the two estimation procedures and a comparison made. A test is provided also for the hypothesis that use of a prespecified subset of predictors results in no increase in the expected mean squared error of prediction.