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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 monotone functions of the residual sum of squares 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. Hocking and R. N. Leslie, 1967) a method was described for identifying such subsets without considering all possible subsets. However, 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.

Multinomial samples may be fully or partially classified. In this paper, procedures for optimally determining sample size allocations between fully and partially classified data sets are described and illustrated. Expressions for the large-sample variances of the maximum likeli-hood estimators using both completely and partially classified data are given which reduce the design problems to convex programming problems.