Search

A number of criteria have been proposed for selecting the best subset or subsets of independent variables in linear regression analysis. Applying these criteria to all possible subsets is, in general, not feasible if the number of variables is large. Many of the criteria are monotonic functions of the residual sum of squares of hence the problem is reduced to identifying subsets for which this quantity is small. In an earlier paper (Selection of the Best Subset in Regression Analysis by R. R. Hoeking and R. N. Leslie, 1967) a method was described for identifying such subsets without considering all possible subsets. Howerver, the amount of computation required if more than fifteen independent variables were considered was excessive. The present paper extends the basic ideas in that paper so that moderately large problems can how be treated with what appears to be a minimum of computation. [ABSTRACT FROM AUTHOR]

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 s x floating-point operations per regression) and shows how two of these algorithms can be combined to form 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. [ABSTRACT FROM AUTHOR]