Testing hypotheses in nested regression models

Abstract

In addition to testing compound hypotheses, the F test can be used to test hypotheses associated with ``nested'' regression models. Nested hypotheses arise whenever we are interested in comparing two regression equations that are identical except that one contains restrictions that are not imposed on the other. By convention, the regression equation that is free of any restrictions is referred to as the ``full'' model. Conversely, the regression equation that contains one or more restrictions is referred to as the ``restricted'' model. Although we can impose different types of restrictions on the restricted model, the most common restriction is simply that one or more partial regression coefficients are equal to zero. In this case, the restricted model becomes a subset of the full model inasmuch as it contains only some of the independent variables contained in the full model. The utility of this application of the F test is that it enables us to evaluate simultaneously the statistical significance of one set of independent variables, controlling for another set independent variables.