# Can an F-test be used in a regression that is quadratic, or can it only be used in a linear regression model?

My regression I'm testing is quadratic but everything I've read about using F-tests state that it is used in a linear regression model.

• Your regression is quadratic, like (A) $Y = (\alpha + \beta_1 X_1 + \beta_2 X_2)^2 + \epsilon$ or (B) $Y = \alpha + \beta_1 X_1 + \gamma_1 X_1^2 + \beta_2 X_2 + \gamma_2 X_2^2 + \epsilon$? Aug 14 '20 at 7:30
• @kurtosis it is like (B). Aug 14 '20 at 7:58
• Ah. Then it is a linear model. Model A is quadratic in the terms while model B is linear in the terms. Aug 14 '20 at 8:05

Since your model is like $$Y = \alpha + \beta_1 X_1 + \gamma_1 X_1^2 + \beta_2 X_2 + \gamma_2 X_2^2 + \epsilon,$$ it is still a linear model -- because it is linear in the terms. ("Linear" refers to the terms like $$X_1$$ and $$X_1^2$$ being linearly combined.)
You can use an $$F$$-test for your model.