In multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory, if not incorrect, if the prediction vectors are not orthogonal. Proposed is an estimation procedure based on adding small positive quantities to the diagonal of X′X. Introduced is the ridge trace, a method for showing in two dimensions the effects of nonorthogonality. It is then shown how to augment X′X to obtain biased estimates with smaller mean square error.

It appears to be common practice with ridge regression to obtain a decomposition of the total sum of squares, and assign degrees of freedom, according to established least squares theory. This discussion notes the obvious fallacies of such an approach, and introduces a decomposition based on orthogonality, and degrees of freedom based on expected mean squares, for non-stochastic k.

An iterative method is given for selecting the biasing parameter, k, in RIDGE regression. The method produces a distribution of squared errors for the regression coefficients that has a smaller mean and a smaller variance than least squares or the single iteration estimate.

An algorithm is given for selacting the biasing paramatar, k, in RIDGE regrassion. By means of simulaction it is shown that the algorithm has the following properties: (i) it produces an aberaged squared error for the regrassion coafficiants that is les than least squares, (ii) the distribuction of squared arrots for the regression coafficiants has a smallar variance than does that for last squares, and (iii) regradless of he signal-to-noiss retio the probability that RIDGE producas a smaller squared error than least squares is greatar than 0.50.

In this note we investigate the problem of power generalization of ordinary ridge estimator (ORE) and provide some justification in favour of Hoerl and Kennard (1975) that this generalization is not a useful extension.

This paper is an exposition of the use of ridge regression methods. Two examples from the literature are used as a base. Attention is focused on the RIDGE TRACE which is a two-dimensional graphical procedure for portraying the complex relationships in multifactor data. Recommendations are made for obtaining a better regression equation than that given by ordinary least squares estimation. This article is referred to by:Ridge Regression: A Historical Context

A computer oriented method which assists in the construction of response surface type experimental plans is described. It takes into account constraints met in practice that standard procedures do not consider explicitly. The method is a sequential one and each step covers the experimental region uniformly. Applications to well-known situations are given to demonstrate the reasonableness of the procedure. Application to a ‘messy” design situation is given to demonstrate its novelty.