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. \(\beta_1 X + \beta_2 X^2\))