Robust regression procedures are designed to reduce the influence of outliers and influential points by reducing the weights given to large residuals. This can be done by the use of M-estimators, the class of estimators that minimizes some function of the residuals other than the sum of squares. M-estimators can be implemented as iteratively reweighted least squares, in which each observation's weight depends on the corresponding residual. Each of these estimators requires the analyst to specify a certain tuning constant. The method of cross-validatory choice is used to select an optimal value of the tuning constant c for use with the weight of function. The procedure selects that value of c which minimizes the median of the absolute predicted residuals (PRM). A resistant fit to initiate the iterative procedure is obtained by using Andrews' method of regression by medians. Two examples are presented.