Testing simple hypotheses using the F test

Abstract

To this point, we have relied solely on the t test to assess the statistical significance of either the simple or partial regression coefficient. However, we can now introduce another statistical test: the F test. As we shall see, the F test is a much more useful statistical test. It can be used to test either simple hypotheses or a variety of compound hypotheses. For example, it can be used to test the significance of either a single regression coefficient or a series of regression coefficients. Consequently, the F test can be substituted for the t test to evaluate the significance of a single regression coefficient. There are many forms of this test; however, for the sake of simplicity, we shall confine ourselves to the F test expressed in terms of the coefficient of determination.