vittorecostao1

2022-07-01

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?

${Y}_{i}={\alpha}_{0}+{\alpha}_{1}{x}_{i}+{\alpha}_{2}{x}_{i}^{2}$

How is this a linear regression when it has quadratic terms in it?

kejohananws

Beginner2022-07-02Added 19 answers

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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