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: $$Y_i=\alpha_0+\alpha_1 x_i +\alpha_2 x_i^2$$
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.
• @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? May 10, 2015 at 17:04
• Oh it does. So what is meant by linear in this case is the $\alpha$'s right? Thank you very much! May 10, 2015 at 17:06