The Regression Handbook: 250+ Models Explained From Classical Regression to Deep Learning

Regression analysis is the backbone of statistical modeling and data science. From its originsin the work of Gauss and Legendre on least squares to modern deep learning architectures,regression methods have evolved to address an extraordinary range of scientific questions.Yet, despite this rich history, students and practitioners often struggle to navigate the vastlandscape of available methods.Why This Book?During my years of teaching statistics and conducting research at Cairo University and SadatAcademy for Management Sciences, I repeatedly encountered the same challenge: there wasno single resource that comprehensively covered the full spectrum of regression techniques—from classical ordinary least squares to cutting-edge methods like causal forests and transformer-based regression. Students would need to consult dozens of textbooks, research papers,and software manuals to gain a complete understanding.This handbook aims to fill that gap by providing a unified, comprehensive treatment ofover 250 regression models in a single volume. The book is organized to serve both as alearning resource for students and a reference guide for practitioners.Scope and OrganizationThe book is organized into 19 Parts spanning 68 Chapters, plus 4 Appendices:• Parts I–II cover foundations—including model validation and diagnostics as an earlyessential—and generalized linear models, including specialized distribution regression(circular, unit, compositional)• Parts III–IV address multicollinearity and penalization methods• Part V presents mixed effects models and sample selection (Tobit, Heckman)• Part VI explores advanced regression: robust, quantile, nonparametric, and GAMs• Parts VII–VIII provide comprehensive coverage of time series and panel data methods• Part IX covers systems of equations: SUR, simultaneous equations, and SEM• Part X addresses high-dimensional regression and inference, Bayesian regression, andvariable selection• Part XI covers distributional and flexible methods: GAMLSS, functional data analysis,and emerging techniques• Part XII presents machine learning and tree-based methods: random forests, gradientboosting, kernel methods, BART, and MARS• Part XIII covers special topics: measurement error, missing data, and causal inference • Parts XIV–XV present survival analysis and spatial regression• Part XVI covers network, tensor, and deep learning regression methods• Part XVII presents modern causal machine learning: causal forests and moderndifference-in-differences• Parts XVIII–XIX present computational methods, applications, and best practices• Appendices A–D provide additional zero-inflated models, robust methods, distribution catalogs, and a comprehensive regression model indexFeatures of This Book• Comprehensive Coverage: Over 250 regression models from OLS to transformers• Mathematical Rigor: Formal definitions, theorems, and derivations• Practical Implementation: R and Python code for every method• Visual Learning: TikZ diagrams, mathematical plots, and illustrative figures• Modern Methods: Includes cutting-edge techniques from 2020–2024 literature• Consistent Notation: Unified mathematical notation throughout• Exercises: End-of-chapter problems for reinforcementPrerequisitesReaders should have foundational knowledge of:• Linear algebra (matrices, vectors, eigenvalues)• Probability and statistics (distributions, estimation, hypothesis testing)• Basic calculus (derivatives, optimization)• Familiarity with R or Python is helpful but not required