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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.

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

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