ABSTRACT
This chapter discusses the effects of multicollinearities on least squares estimators and test statistics. Least squares parameter estimation and its associated regression methodology are highly susceptible to the effects of multicollinearities. Numerical values of coefficient estimates, variances and covariances of the estimators, test statistics, and predicted responses can all be adversely affected by strong multicollinearities among the predictor variables. All terms suggest that the predictor variables are providing some redundant information that is to be used to predict the response variable. Numerical comparison of the magnitudes of estimated regression coefficients and their variances and covariances must be made with standardized predictor variables in order to remove the distortions due to different scales and locations for the predictors. The effect of multicollinearities on least squares estimates can be as dramatic as the effect on the estimator variances. It discusses the unit length standardization.
