This chapter develops the classical linear model as the cornerstone of regression methodology. It presents ordinary least squares, its geometric and probabilistic interpretations, and the Gauss–Markov theorem. Diagnostics for multicollinearity, heteroskedasticity, and influential observations are paired with remedies such as generalized least squares and robust variance estimation. Extensions to maximum-likelihood estimation unify treatment of continuous and discrete outcomes, while penalized approaches—including ridge, lasso, and elastic net—address high-dimensional feature spaces. Finally, we introduce partial least squares for dimension reduction and demonstrate applications in marketing analytics, experimental psychology, and economic forecasting.