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

CC BY-SA 4.0
2020-08-14T08:02:13.580Z
2020-08-14T08:02:13.580Z
kurtosis
<p>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.</p>

CC BY-SA 4.0
2020-08-14T07:30:23.700Z
Your regression is quadratic, like (A) $Y = (\alpha + \beta_1 X_1 + \beta_2 X_2)^2 + \epsilon$ or (B)  $Y = \alpha + \beta_1 X_1 + \gamma_1 X_1^2 + \beta_2 X_2  + \gamma_2 X_2^2 + \epsilon$?
kurtosis
CC BY-SA 4.0
2020-08-14T07:58:36.210Z
@kurtosis it is like (B).
Esther Blaese
CC BY-SA 4.0
2020-08-14T08:05:15.647Z
Ah. Then it is a linear model. Model A is quadratic in the terms while model B is linear in the terms.
kurtosis
<econometrics>
Can an F-test be used in a regression that is quadratic, or can it only be used in a linear regression model?
Esther Blaese
# Can an F-test be used in a regression that is quadratic, or can it only be used in a linear regression model?

(Asked by: username_0 on 2020-08-14)

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.

**Tags:** econometrics
> **Comments:**
> **username_1**: Your regression is quadratic, like (A) $Y = (\alpha + \beta_1 X_1 + \beta_2 X_2)^2 + \epsilon$ or (B)  $Y = \alpha + \beta_1 X_1 + \gamma_1 X_1^2 + \beta_2 X_2  + \gamma_2 X_2^2 + \epsilon$?  
> **username_0**: @kurtosis it is like (B).  
> **username_1**: Ah. Then it is a linear model. Model A is quadratic in the terms while model B is linear in the terms.  

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## 1 answers

### Answer by username_1 on 2020-08-14. Score: 2 | Accepted answer

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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