INVESTIGATING THE IMPACT OF MULTICOLLINEARITY ON LINEAR REGRESSION ESTIMATES

The study was to investigate the impact of multicollinearity on linear regression estimates. The study was guided by the following specific objectives, (i) to examine the asymptotic properties of estimators and (ii) to compare lasso, ridge, elastic net with Ordinary Least Squares (OLS). The study employed Monte-Carlo simulation to generate set of highly collinear and induced multicollinearity variables with sample sizes of 25, 50, 100, 150, 200, 250, 1000 as a source of data in this research work and the data was analyzed with lasso, ridge, elastic net and ordinary least squares using statistical package. The study findings revealed that absolute bias of ordinary least squares was consistent at all sample sizes as revealed by past researched on multicollinearity as well while lasso type estimators fluctuated alternately. Also revealed that, mean square error of ridge regression outperformed other estimators with minimum variance at small sample size and OLS was the best at large sample size. The study recommended that OLS was asymptotically consistent at a specified sample sizes on this research work and ridge regression was efficient at small and moderate sample size.