A test for the parameters of multiple linear regression models

Abstract

A test for the parameters of multiple linear regression models is developed for conducting tests simultaneously on all the parameters of multiple linear regression models. The test is robust relative to the assumptions of homogeneity of variances and absence of serial correlation of the classical F-test.

Under certain null and alternative hypotheses, the new test statistic is shown to have limiting central and noncentral chisquare distributions, respectively. A measure of efficiency due to Pitman is used to obtain the asymptotic efficiency of the new test relative to its classical counterpart. A numerical comparison of the two types of tests shows that the present test is slightly more efficient than the classical F-test.

KEY WORDS: test, multiple linear regression, parameters, robust, homogeneity of variances.

Global Journal of Mathematical Sciences Vol.3(2) 2004: 163-171