Regression
Regression describes how a response variable changes with one or more explanatory variables.
Simple linear regression
\[Y_i=\beta_0+\beta_1x_i+\varepsilon_i.\]Here \(\beta_0\) is the intercept, \(\beta_1\) is the expected change in the response for a one-unit increase in \(x\), and \(\varepsilon_i\) represents unexplained variation.
Multiple regression
\[Y=\beta_0+\beta_1x_1+\cdots+\beta_px_p+\varepsilon.\]Interpretation
An observed regression association is not automatically causal. Study design, confounding and model assumptions determine what conclusions are justified.
Key idea. Regression quantifies statistical relationships, while biological interpretation requires attention to how the data were generated.