The F-test: An example

For the sake of this example, let's assume that N=200.

Unrestricted regression




Restricted regression

Null hypothesis

We want to test if the independent variables in this regression are jointly insignificant in determining our dependent variable, we do this by forming the F statistic:

Let's assume that this value is 100, we have to weigh this against our critical value.

Critical Value

This takes the following form, where P is the number of restrictions on our null hypothesis (in our case, this is 2):










If the following holds true, we say that we can reject the null hypothesis. If it does not hold true, then we do not have enough evidence to reject the null hypothesis: