Multiple Regression with Varying Levels of Correlation among Predictors: Monte Carlo Sampling from Normal and Non-Normal Populations

Abstract

This study investigated the effects of the violation of the assumption of normality in the conditional distributions of the dependent variable coupled with the condition of multicollinearity upon the outcome of testing the hypothesis H ₀:β' = 0 in the two-predictor regression equation. A monte carlo approach was utilized in which three different distributions were sampled for two sample sizes over thirty-four population correlation matrices. Based upon the results of this study, the violation of this assumption in the conditional distributions of the criterion has no systematic effect upon the testing of the hypothesis H ₀:β _i ' = 0 (i = 1, 2)(α =.05) in the three variable regression equation.

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