Machine‑Learning Approaches to Regression

Regression analysis sits at the heart of empirical research across the social, natural, and data sciences. Part II shows how modern machine‑learning ideas both generalise and enrich classical regression, yielding models that are more flexible, more accurate, and often more robust to the quirks of real‑world data.

We begin by re‑examining ordinary least squares (OLS) through the lens of predictive performance. By treating OLS as a baseline supervised‑learning algorithm, we motivate the need for regularisation techniques—Ridge, Lasso, and Elastic‑Net—that tame high‑dimensional feature spaces, prevent overfitting, and perform automated variable selection. You will learn how to tune their hyper‑parameters with cross‑validation and how to interpret the resulting shrinkage paths.

The middle chapters extend regression beyond linear additivity. We introduce non‑parametric and semi‑parametric methods—splines, generalized additive models, decision‑tree ensembles (random forests and gradient boosting), and kernel methods—that capture complex non‑linearities and interactions without hand‑crafted transformations. Emphasis is placed on out‑of‑sample validation and on diagnostic tools (partial‑dependence plots, SHAP values) that keep these powerful models interpretable.

Next, we explore probabilistic and Bayesian perspectives, where priors act as a principled form of regularisation and yield full posterior uncertainty. Practical tutorials with Stan and PyMC demonstrate how Bayesian regression scales to large datasets via variational inference and Hamiltonian Monte Carlo, and how it integrates seamlessly with hierarchical structures common in panel or multi‑level data.

Throughout Part II we weave in two unifying themes:

The bias–variance trade‑off—how model complexity, sample size, and noise jointly determine predictive risk—and
The machine‑learning workflow for regression—feature engineering, resampling strategies, hyper‑parameter optimisation, and honest benchmarking.

Each chapter pairs concise theory with hands‑on code (R and Python) and reproducible case studies drawn from economics, public health, and marketing analytics. By the close of Part II you will not only command a rich arsenal of regression techniques but also possess the practical know‑how to choose, tune, evaluate, and interpret them in diverse applied settings.

# Machine‑Learning Approaches to Regression Regression analysis sits at the heart of empirical research across the social, natural, and data sciences. Part II shows how modern machine‑learning ideas both generalise and enrich classical regression, yielding models that are more flexible, more accurate, and often more robust to the quirks of real‑world data. We begin by **re‑examining ordinary least squares (OLS)** through the lens of predictive performance. By treating OLS as a baseline supervised‑learning algorithm, we motivate the need for **regularisation techniques**—Ridge, Lasso, and Elastic‑Net—that tame high‑dimensional feature spaces, prevent overfitting, and perform automated variable selection. You will learn how to tune their hyper‑parameters with cross‑validation and how to interpret the resulting shrinkage paths. The middle chapters extend regression beyond linear additivity. We introduce **non‑parametric and semi‑parametric methods**—splines, generalized additive models, decision‑tree ensembles (random forests and gradient boosting), and kernel methods—that capture complex non‑linearities and interactions without hand‑crafted transformations. Emphasis is placed on **out‑of‑sample validation** and on diagnostic tools (partial‑dependence plots, SHAP values) that keep these powerful models interpretable. Next, we explore **probabilistic and Bayesian perspectives**, where priors act as a principled form of regularisation and yield full posterior uncertainty. Practical tutorials with Stan and PyMC demonstrate how Bayesian regression scales to large datasets via variational inference and Hamiltonian Monte Carlo, and how it integrates seamlessly with hierarchical structures common in panel or multi‑level data. Throughout Part II we weave in two unifying themes: 1. **The bias–variance trade‑off**—how model complexity, sample size, and noise jointly determine predictive risk—and 2. **The machine‑learning workflow for regression**—feature engineering, resampling strategies, hyper‑parameter optimisation, and honest benchmarking. Each chapter pairs concise theory with hands‑on code (R and Python) and reproducible case studies drawn from economics, public health, and marketing analytics. By the close of Part II you will not only command a rich arsenal of regression techniques but also possess the practical know‑how to choose, tune, evaluate, and interpret them in diverse applied settings.