There is always a reference to F distribution in regression and frankly I never cared a damn as I had never really paid attention. Working with markets makes you think hard about statistics.

The reason F stats comes in to picture is this :

Let X be a random var and you want to test the hypo X= b,

You can use X-b/ sigma ~ Normal

or

Square the LHS and divide by degrees of freedom. Substitute sigma by sample sigma which is again a Chi Square with different dof.
So Chi square (1) / Chi square (2) is an F distribution and thats the reason F is used everywhere..

From Johnston, my bible , you can clearly see it below :

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