Using gret l for Principles of Econometrics, 4th Edition

Relationship Between t — and F-tests

You can certainly use an F-test to test the significance of individual variables in a regression. Consider once again the model for Big Andy

salesi = ві + fi2price + advert + e^advert2 + e (6.3)

and suppose we want to test whether price affects sales. Using the omit command produces the F-test

1 ols sales const price advert sq_advert

2 omit price

The output window is shown in Figure 6.7. The F(1, 71) statistic is equal to 53.3549 and has a p-value that is much smaller than 0.05; the coefficient is significant at the 5% level. Notice also that in the unrestricted model (Model 6 in the output) that the usual t-ratio is -7.304, also significant at 5%. The t-ratio has a t71 distribution if the coefficient is zero. Squaring (—7.304)2 = 53.3549, suggesting that there is a relationship between these two statistics. In fact, t2n is equivalent to F(1,n). This hold for any degrees of freedom parameter, n.