A Method for Calculating a Weight Averaged Prediction from Multiple Linear Regression Equations
Authors
Fei Pan
University of Idaho
Christopher J. Williams
University of Idaho
Leonard R. Johnson
University of Idaho
Abstract
This study proposes a method for combining regression equations using a relevance network model, a weight generating function, and a generalized mixed operator. The combination of these methods puts a relative weight on the predictions of each of the individual equations and then calculates a weighted average estimate. The method was validated using computer simulation structured within the Statistical Analysis System (SAS). The simulation tests demonstrated that the method is capable of making a prediction that is not significantly different from the true prediction provided the input values for the combined model fall within the valid range of at least one variable. The mean difference between the predictions using the proposed method and the prediction from the true models was less than 9.5 percent of the true model predictions for the complete set of randomized simulations. Prediction accuracy can be improved by increasing the number of variables in an equation and by broadening the width of the variable valid interval, but not necessarily by increasing the number of equations in an equation set. Individually, the number of variables is more influential than variable valid interval width on prediction accuracy.
