Clustering on The Basis of Regression Equations Under Heteroscedastic Errors

The Chow test is not robust under heteroscedasticity. The presence of heteroscedasticity will affect level of significance as well as power of the test, especially when the sizes of the samples are small. The present paper not only resolves the problem of heteroscedasticity in the error terms, but also extends the existing method of comparing two linear regressions to one where it is possible not only to compare the equality between the sets of coefficients in the two linear regressions, but also, in case they are not equal, to provide detailed information about the inequality of the sets as well as to accomplish all these for not just only two linear regressions but for the two linear regressions of all possible pairs of linear regressions out of any number of given linear regressions, and then to use the results of all these comparisons in order to form clusters among the regressions on the basis of some principle stated therein. The procedure is then illustrated through comparison of the decadal growth rates of the population of India, using NSSO data.