A Note on the Problem of Determining the Most Effective Predictor Variables in Multiple Regression
A PROBLEM that often troubles educators is de termining which variables most effectively predict a certain criterion such as grades. Oftentimes a number of predictor variables are considered and the primary aim is to select as few of these as pos sible for prediction purposes without losing too much predictive power. Several possible approach es to resolving such a problem do not always lead to the same solution. A convenient solution is sometimes found through logical analysis, while other times variables are selected that are most practically feasible. When the problem is consid ered statistically, it is a matter of determining the least number of predictor variables that account for most of the variance in the criterion variable. Fre quently this becomes a question of determining which combination of perhaps two or three predic tor variables appears to be the most useful combi nation of the original six or seven predictors con sidered. Although procedures for handling such a problem statistically are described in many statistics text books, several important points in relation to the application of these procedures seem to be in need of clarification. Specifically, application of such procedures can lead to conflicting results unless caution is exercised in defining the problem. The oretically the problem could be stated in a number of ways, but for illustration purposes this paper will concentrate upon only two of these. First, a solution might be sought by eliminating predictor variables from the total multiple corre lation coefficient for all variables included in the problem, with the aim being not to reduce the size of this R significantly (or the amount of variance accounted for). Those variables that remained af ter this elimination process would be used for pre diction purposes. A second solution to the same multiple regression problem could be found by start ing with a single variable and adding other variables that contribute significant amounts of variance until the best combination is identified. An example will illustrate the divergent outcomes that can be obtained due to the different definitions employed. In solving for these solutions, letus use a set of hypothetical multiple correlation coefficients for eight predictor variables as shown in Table 1.