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?
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.