Precision efficacy analysis for regression: Development and justification of a new sample size method for multiple linear regressio

The study examines the efficiency of the Precision Efficacy Analysis for Regression (PEAR) method for choosing appropriate sample sizes in regression studies used for prediction. The PEAR method, based on the algebraic manipulation of an accepted cross-validity formula, provides sample sizes that limit the cross-validity shrinkage expected to occur when a regression prediction model is used in future samples. Previous research has shown the PEAR method to be more efficient than other common regression sample size methods.;A Monte Carlo simulation study was performed to investigate the PEAR method at population squared multiple correlation effect sizes of.10,.25, and.40, predictor sets of size 3, 7, 11, and 15, and a priori precision efficacy levels of.60,.70, and.80 (which correspond to squared cross-validity estimates expected to be at least 60%, 70%, and 80%, respectively, of the sample squared multiple correlation values). There were 10,000 samples created for each of these conditions. The PEAR method was analyzed for both standard regression and stepwise regression, each with four levels of predictor multicollinearity ranging from orthogonal to extensively multicollinear.;The results show the PEAR method to provide accurate average cross-validity for all cases of the.80 and.70 precision efficacy levels, and in most cases for.60. Analysis of the root mean squared error (RMSE) shows the PEAR method at the.80 level of precision efficacy to be approximately 20% more efficient than the.70 level. That is, RMSE for the cross-validity estimates and also for the regression coefficients was about 20% smaller for the.80 level than it was for the.70 level. Similarly, the.70 level was approximately 14% more efficient than the.60 level. The results also showed this pattern of relative efficiency to hold true no matter what level of multicollinearity was present in the predictor sets. The stepwise regression results do not provide clear patterns, but the precision efficacy level of 80% is generally more efficient than the others. In general, it is recommended that practitioners use the PEAR method with.80 precision efficacy for moderate estimated effect sizes.