13.1 Basics

Regression is the most common way in which we fit a line to explain variation.

• also used for causal effects: closing back doors (controlling)
• use the values of one variable ($X$) to predict the values of another ($Y$)
• one way: fit a line that describes the relationship
• interpretation of coefficient: slope
• plugging prediction in, we get prediction: $\hat{Y}$
• difference between $Y$ and $\hat{Y}$ is the residual
• we can make the line curvy by adding polynomials (i.e. $\beta_1 X + \beta_2 X^2$)