The technique of general weighted least squares is shown to be a useful tool in the formulation and evaluation of certain models appropriate to data in the form of multidimensional contingency tables. This is demonstrated for the Ries-Smith [1963] data by fitting a series of linear regression models which are directed at determining that model which explains almost all of the statistically significant variation among the cell frequencies in terms of a minimum number of parameters. The spirit of this approach is analogous to that used in stepwise regression for continuous data. The test criteria are Wald statistics or minimum-Neyman-chi-square as described by Bhapkar and Koch [1968].