Individual Degrees of Freedom for Testing Homogeneity of Regression Coefficients in a One-Way Analysis of Covariance

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Abstract
If the underlying linear regressions in a one-way analysis of covariance are not parallel then their slopes can be expressed as a polynomial function of the intercepts. Heterogeneity of linear regression may therefore be tested by fitting an orthogonal polynomial to the relation between slope and adjusted intercept and testing successively the coefficients in the orthogonal polynomial. This procedure is equivalent to partitioning the conventional F-test for homogeneity of regressions into single degrees of freedom. An exactly analagous, dual procedure may be used to test the homogeneity of intercepts.