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The purpose of this paper is to present the theory and develop an algorithm associated with the exploration of a dual response surface system. The approach is to find conditions on a set of independent or "design" variables which maximize (or minimize) a "primary response" function subject to the condition that a "constraint response" function takes on some specified or desirable value. A method is outlined whereby a user can generate simple two dimensional plots to determine the conditions of constrained maximum primary response regardless of the number of independent variables in the system. He thus is able to reduce to simple plotting the complex task of exploring the dual response system. The procedure that is used to generate the plots depends on the nature of the individual univariate response functions. In certain situations it becomes necessary to apply the additional constraint that the located operating conditions are a certain "distance" from the origin of the independent variables (or the center of the experimental design). The methods derived and discussed in the paper are applicable only to quadratic response functions. [ABSTRACT FROM AUTHOR]

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]

This paper presents the algorithm "DETMAX" whose purpose is to construct experimental designs that are "D-optimal," These are designs for which the determinant of X'X is maximum, where X is the "matrix of independent variables" in the usual linear model y = Xβ + ε. Although the algorithm does not guarantee D-optimality, it has performed well in many cases where D-optimal designs are known. Five examples are given, illustrating the use of DETMAX to construct designs "from scratch" and to augment existing data. A FORTRAN listing is available on request. [ABSTRACT FROM AUTHOR]

Extensions of Yates' algorithm (1937) for the analysis of variance of 2[sup n] experiments have been described by many authors but for some reason the general method docs not appear to be particularly well known. The purpose of this paper is to bring together the various extensions, and to present a unified account of the method. This method is particularly useful as the main pang of a general computer program for analysis of complete factorial experiments. [ABSTRACT FROM AUTHOR]