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I have a hard time understanding the term 'linear regression'. For what I know, linear means polynomial of degree 1. But then, I found that in one of my lectures, the lecturers are saying that this regression is a linear regression: $$Y_i=\alpha_0+\alpha_1 x_i +\alpha_2 x_i^2$$

How is this a linear regression when it has quadratic terms in it? Does it not make it a non-linear regression? However when there is a quadratic curve as the regression, it is called a non-linear regression. Which is right?

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The data $(x_i,y_i)$ are given, so although it looks like you have a quadratic because of the $x_i^2$, in fact this is just a constant. You're solving for $\alpha_0, \alpha_1$ and $\alpha_2$, and the equation is linear in these terms.

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  • $\begingroup$ ooooh I see then. Also, then what is a non linear regression? $\endgroup$
    – Skipe
    May 10, 2015 at 16:59
  • $\begingroup$ @Skipe Non-linear regression could involve mixing the $\alpha$ terms with each other, or using them inside other functions. For instance, $Y_i = \alpha_0 + \alpha_1x_i + \alpha_2(1-\alpha_0)x_i^2$, or $Y_i = \alpha_0 + \alpha_1 \cos(\alpha_2 x + \alpha_3)$. Does that make sense? $\endgroup$
    – Théophile
    May 10, 2015 at 17:04
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    $\begingroup$ Oh it does. So what is meant by linear in this case is the $\alpha$'s right? Thank you very much! $\endgroup$
    – Skipe
    May 10, 2015 at 17:06
  • $\begingroup$ @Skipe That's right! Glad to help. $\endgroup$
    – Théophile
    May 10, 2015 at 17:12

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