Development of a Reduced Set of Composite Equations for Three Predictors

Abstract

5 primary and 3 reserve equations were developed to span the quadrant containing all possible equations for 3 predictors, with the restriction that no weights be negative. Any empirical equation ever likely to be encountered operationally should be represented adequately by at least one of the primary theoretical composite equations with no more than .01 loss in predictive validity. The theoretical equations were positioned to achieve this result. It is not likely that additional equations will be needed; if so, the equations should be selected from the set of reserve equations to provide the most efficient coverage. The theoretical system was applied to 47 prediction equations for different colleges using SAT-V, SAT-M, and High School Rank-in-class as predictors and college performance as a criterion. The primary composite equations were selected as the appropriate composite equations for all of the original prediction equations except one. For that prediction equation, the appropriate composite equation is one of the reserve theoretical composite equations.