Econ 570 - Spring 2012

The discussion of F tests was based primarily on handouts with example regressions and calculated F tests.

The F test is for a null hypothesis that one or more coefficients in a regression equal zero. We take these to be the last q coefficients.

Dougherty and I have slightly different notation for the F test.

The F statistics is non-negative. The table in the back of the book gives critical values. We reviewed the point that, for a one degree of freedom test (one coefficient), the F statistic is the square of the t statistic.

You cannot test the joint hypothesis that two regression coefficients both equal zero with two t tests. The t tests each locate critical points on an axis below and, together, they delineate a rectangle. The rejection region for the F test of this hypothesis is the region outside an ellipse.

It is usually the case that the F test rejects the null hypothesis when at least some of the individual t tests reject the single coefficient null hypothesis of zero. Using the individual t tests to reach a conclusion about the joint hypothesis is, however, non-professional.