The Analysis of Nonlinearity Via Linear Regression with Polynomial and Product Variables: An Examination

Recent works by Cohen (1968), Kelly, Beggs, McNeil, Eichelberger, and Lyon (1969), Kerlinger and Pedhazur (1973), McNeil (1970), Walberg (1971), and Bottenberg and Ward (Note 1) have attested to the flexibility of the General Linear Model. These publications have shown the capabilities of a single approach to the solution of correlation, regression, and Fisherian analysis of variance problems. It is noteworthy that all six of these publications claim, more or less, to be using the General Linear Model, but in no case has the particular linear model and its assumptions been clearly specified and consistently applied. The General Linear Model is a name given to the family of models possessing a common characteristic, namely, linearity in the parameters of the equation specifying the model. The members of this family are distinguishable in terms of their various assumptions, and it is the contention of this author that the distinctions among these different linear models are of more than just passing interest. The above publications, plus those of Digman (1966) and of McNeil and Spaner (1971), have shown the capabilities of the General Linear Model in handling the analysis of nonlinear data.1 This approach, with a history dating back to Court (1930),