A Comparison of Least Squares and Latent Root Regression Estimators

Abstract

Miilticollinesrity among the columns of regressor variables is known to cause severe distortion of the least squares estimates of the parameters in a multiple linear regression model. An alternate method of estimating the parameters which was proposed by the authors in a previous paper is Latent Root Regression Analysis. In this article several comparisons between the two methods of estimation are presented. The improvement of Latent Root Regression over ordinary least squares is shown to depend on the orientation of the parameter vector with respect to a vector defining the multicollinearity. Despite this dependence on orientation, the authors conclude that witch multicollinear data Latent Root, Regression Analysis is preferable to ordinary least squares for parameter estimation and variable selectJion.

KEY WORDS:

• Latent Root Regression
• Least Squares
• Multicollinearity
• Multiple Linear Regression