Calculation of the Residual Sum of Squares for all Possible Regressions

When the number of independent variables for a regression analysis is not too large, calculation of all possible regressions is an alternative to the various stepwise procedures available. However, the amount of information available from all possible regressions is quite large even for a moderate number of variables. And screening out most of the regressions can be done simply on the basis of information contained in the residual sum of squares. This paper presents an efficient procedure for the calculation of the residual sum of squares for each regression and some suggestions for screening procedures.