A simulation study of five biased estimators for straight line regression

Five biased estimators of the slope in straight line regression are considered. For each, the estimate of the “bias parameter”, k, is a function of N, the number of observations, and rcirc]² , the square of the least squares estimate of the standardized slope, β. The estimators include that of Farebrother, the ridge estimator of Hoerl, Kennard, and Baldwin, Vinod's shrunken estimators., and a new modification of one of the latter. Properties of the estimators are studied for 13 combinations of N and 3. Results of simulation experiments provide empirical evidence concerning the values of means and variances of the biased estimators of the slope and estimates of the “bias parameter”, the mean square errors of the estimators, and the frequency of improvement relative to least squares. Adjustments to degrees of freedom in the biased regression analysis of variance table are also considered. An extension of the new modification to the case of p> 1 independent variables is presented in an Appendix.