F-Distribution

The F-Distribution is a probability distribution that models the sampling distribution of F under the empty model (the null hypothesis that there is no effect of the explanatory variable); this theoretical distribution takes into account both model degrees of freedom and error degrees of freedom.

Another way of saying this, is that the F-Distribution is a sampling distribution that represents the distribution of all the possible F values we would expect to observe if the empty model (𝛽1 = 0) were the true model of the Data Generating Process (DGP). We can compare the value of our sample F statistic to the F-Distribution to help us figure out whether our sample was likely to have come from a DGP where the empty model is true. 

The shape and spread of the F-Distribution slightly varies depending on the model degrees of freedom and error degrees of freedom.

Below is an example of the F-Distribution generated via randomized sampling in R.

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