Coefficient of Determination
As before,
Where,
We can show that TSS = RSS + ESS
We can also show that
F
is an F distribution with k degrees of freedom in the numerator and n - (k + 1) degrees of freedom in the denominator.
Let us look at two extreme cases
The model is perfect.
This implies that ESS = 0 and F = ∞
The model does not exist.
This implies that RSS = 0 and F = 0
Intuitively, it should then be clear that if F is too small, the model should be rejected.