Some time ago, I had a post
that discussed the fact that the usual coefficient of determination (R2
) for a linear regression model is a sample statistic, and as such it has its own sampling distribution. Some of the characteristics of that sampling distribution were discussed in that earlier post.
You probably know already that we can manipulate the formula for calculating R2, to show that it can be expressed as a simple function of the usual F-statistic that we use to test if all of the slope coefficients in the regression model are zero. This being the case, there are some interesting things that we can say about the behaviour of R2, as a random variable, when the null hypothesis associated with that F-test is in fact true.
Let's explore this a little.