# What assumptions must be satisfied to use R^2 to compute the F statistic?

Suppose I know R^2 for my symbolic regression. Can I use the formula $$F = \frac{R^2}{1-R^2}\cdot \frac{n-p}{p-1}$$ to do an F test?

My symbolic regression is of the form Y = a + bf(A,B,C,D,E,G) + cg(A,B,C,D,E,G) + dh(A,B,C,D,E,G) + error term, where the functions f(), g(), and h() are nonlinear products like A*(C^2)DE*(G^3).

Do I need to perform statistical tests to ensure that certain assumptions are satisfied, and if so what are those tests? What might be the consequence of not doing those tests?

Thank you for your kind help!

• Could you explain what hypothesis you want to test? E.g. do you want to compare your model to a constant model, test for inclusion of certain terms, ... ? Commented Jul 13, 2020 at 7:20
• At this stage, I would like to compare the model returned by genetic programming/symbolic regression to the constant model. Eventually I would like to test whether the model produced when using that variable as a building block has a better fit than the model produced when the algorithm wasn't allowed to use that variable as a building block. Commented Jul 13, 2020 at 7:30
• Above I meant to write "when using a Certain variable" instead of "when using that variable." Commented Jul 13, 2020 at 7:37
• @Richard Hardy May I please ask you to take a look at this question? Thank you! Commented Jul 13, 2020 at 18:01
• Sorry, I do not think I can answer it on the spot, and I am in a bit of a time crunch otherwise. Commented Jul 18, 2020 at 13:53