Using Monte Carlo Techniques to Demonstrate the Meaning and Implications of Multicollinearity

Abstract

This article presents an in-class Monte Carlo demonstration, designed to demonstrate to students the implications of multicollinearity in a multiple regression study. In the demonstration, students already familiar with multiple regression concepts are presented with a scenario in which the “true” relationship between the response and predictor variables is known. Two alternative data generation mechanisms are applied to this scenario, one in which the predictor variables are mutually independent, and another where two predictor variables are correlated. A number of independent realizations of data samples are generated under each scenario, and the regression coefficients for an appropriately specified model are estimated with respect to each sample. Scatter-plots of the estimated regression coefficients under the two scenarios provide a clear visual demonstration of the effects of multicollinearity. The two scenarios are also used to examine the effects of model specification error.

• Multiple regression
• Simulation