Design for Optimal Prediction in Simple Linear Regression

Abstract

Allocation of experimental data points is considered in order to provide efficient prediction of the dependent variable in simple linear regression. The region of experimental points is taken such that it need not coincide with the region for prediction where the regression is linear. The allocation which minimizes the maximum variance for a predicted value of the dependent variable is obtained. The allocation of experimental data points which minimizes the average variance of predicted values, occurring according to a density function in the region of prediction, is derived. The relative efficiency of balanced allocation (one-half of the data points at each end of the experimental region) to minimax or minimum average variance allocation is about 90 percent for prediction near the ends of the experimental region with small samples.