An Evaluation of Ridge Regression.

The technique of linear regression has been applied as a tool for predicting the cost of an item based on its most important characteristics. Often these characteristics (variables) tend to be highly intercorrelated (the data are said to exhibit multicollinearity) causing least squares estimates of the regression coefficients to be unstable and possibly leading to erroneous predictions. Ridge regression, a possible remedy for the problems caused by multicollinearity proposed by Hoerl and Kennard, is a biased estimation technique which reduces the variance of estimators and provides more precision (as measured by mean square error of the coefficients) than ordinary least squares (OLS) estimators. A comparison was made between these techniques to determine when ridge regression provides better cost equation coefficient estimates than OLS as a function of the degree of multicollinearity in the data, the number of predictor variables in the model, the degree of model fit (R2), and the amount of bias (k) of the estimate. A regression analysis of both sets showed that the degree of multicollinearity and amount of bias interact in explaining the major part of the improvement (degradation) in the mean square coefficient error.