Regressions by Leaps and Bounds

This paper describes several algorithms for computing the residual sums of squares for all possible regressions with what appears to be a minimum of arithmetic (less than six floating-point operations per regression) and shows how two of these algorithms can be combined to form a simple leap and bound technique for finding the best subsets without examining all possible subsets. The result is a reduction of several orders of magnitude in the number of operations required to find the best subsets.