Monte Carlo methods were used to investigate the effects of removing extreme data points identified by five indices of influence. Multivariate normal data were simulated and observations were removed from samples if they exceeded the criteria suggested in the literature for each influence statistic. Factors included in the design of the Monte Carlo study were the number of regressor variables, population multiple correlation, degree of multicolinearity, and sample size. Conditions were simulated in which all sample observations were drawn from a single population and conditions in which a single observation in each sample was drawn from a different population (presenting either an extreme residual or an extreme value in the space of the regressor variables). Results were evaluated in terms of statistical bias in the regression parameter estimates and the sample R squared value. Results in general suggest that caution is needed in the screening of samples for outliers and influential observations. (Contains 4 figures, 12 tables, and 6 references.) (Author/SLD)