When multiple linear regression is used to develop a prediction model, sample size must be large enough to ensure stable coefficients. If the derivation sample size is inadequate, the model may not predict well for future subjects. The precision efficacy analysis for regression (PEAR) method uses a cross- validity approach to select sample sizes such that models will predict as well as possible in future samples. Previous studies have shown the sample sizes suggested by the PEAR method to be superior to other methods in limited cross-validity shrinkage to acceptable a priori levels. A Monte Carlo study was conducted to verify the PEAR method further for the selection of regression sample sizes and to extend the analysis to include an investigation of the effects of multicollinearity on coefficient estimates obtained through multiple linear regression analysis. Appendixes show the derivation of the PEAR method for sample size selection, and give correlation matrices, stem-and-leaf plots, and histograms of cross-validity for the study. (Contains 10 tables, 4 figures, and 116 references.) (SLD)