The Effect of Multicollinearity on the Estimators of the Regression Coefficients

Karadağ F. , Sazak H. S.

5. Uluslararası Araştırmacılar, İstatistikçiler ve Genç İstatistikçiler, Aydın, Turkey, 18 - 20 October 2019, pp.1-2

  • Publication Type: Conference Paper / Summary Text
  • City: Aydın
  • Country: Turkey
  • Page Numbers: pp.1-2


Abstract: Multicollinearity is the existence of linear relationships among two or more independent (explanatory) variables. The presence of multicollinearity poses a serious problem for regression analysis studies. This problem leads to unstable estimates of the regression coefficients and causes some serious problem in validation and interpretation of the regression model. In this study, the effect of multicollinearity on the regression coefficient estimators is examined with a simulation study. In the simulation study, in case of multicollinearity, the least squares estimation method and a robust method (using MATLAB Robustfit command which uses the Tukey M-estimators as default) are compared and the answer to the question of whether there is a difference in the variances of the regression coefficients between the estimations based on the least squares method and the estimations using robust methods is investigated. In other words, we are investigating that whether robust methods can be a remedy against multicollinearity. The simulation results show that the robust methods are also badly affected by multicollinearity because multicollinearity does not influence the residuals and the robust methods mostly produce solutions for the outliers in the residuals. At the end of the study, a real-life application is given. We also discuss the causes of multicollinearity and its detection methods and the possible remedies.

Key words: Regression analysis, Multicollinearity, Least squares method, Robust methods.