13.12 Polynomials

A polynomial is when you have the same variable in an equation as itself, as well as powers of itself

\(\beta_1 X + \beta_2 X^2 + \beta_3 X^2\)

• fit non-straight lines
• must always be interpreted together (marginal effects), taking the derivative

Choosing the right number of polynomials:

• gets harder to interpret as you add more

• often, higher-order polynomial terms don’t really do anything

• problem of overfitting

• almost never want to go beyond cubic

• approach 1: check out Y ~ X plot

• approach 2: check out residuals ~ X plot

• approach 3: LASSO