The effects of the violation of the assumption of normality coupled with the condition of multicollinearity upon the outcome of testing the hypothesis Beta equals zero in the two-predictor regression equation is investigated. A monte carlo approach was utilized in which three differenct distributions were sampled for two sample sizes over thirty-four population correlation matrices. The preliminary results indicate that the violation of the assumption of normality has significant effect upon the outcome of the hypothesis testing procedure. As was expected, however, the population correlation matrices with extremely high collinearity between the independent variables resulted in large standard errors in the sampling distributions of the standardized regression coefficients. Also, these same population correlation matrices revealed a larger probability of committing a type II error. Many researchers rely on beta weights to measure the importance of predictor variables in a regression equation. With the presence of multicollinearity, however, these estimates of population standardized regression weights will be subject to extreme fluctuation and should be interpreted with caution, especially when the sample size involved is relatively small. (Author/RC)