Regression and Other Stories

Most textbooks on regression focus on theory and the simplest of examples. Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors’ experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

Review

‘Gelman, Hill and Vehtari provide an introductory regression book that hits an amazing trifecta: it motivates regression using real data examples, provides the necessary (but not superfluous) theory, and gives readers tools to implement these methods in their own work. The scope is ambitious – including introductions to causal inference and measurement – and the result is a book that I not only look forward to teaching from, but also keeping around as a reference for my own work.’ Elizabeth Tipton, Northwestern University

‘Regression and Other Stories is simply the best introduction to applied statistics out there. Filled with compelling real-world examples, intuitive explanations, and practical advice, the authors offer a delightfully modern perspective on the subject. It’s an essential resource for students and practitioners across the statistical and social sciences.’ Sharad Goel, Department of Management Science and Engineering, Stanford University

‘With modern software it is very easy to fit complex regression models, and even easier to get their interpretation completely wrong. This wonderful book, summarising the authors’ years of experience, stays away from mathematical proofs, and instead focuses on the insights to be gained by careful plotting and modelling of data. In particular the chapters on causal modelling, and the challenges of working with selected samples, provide some desperately needed lessons.’ David Spiegelhalter, University of Cambridge

‘Gelman and Hill, have done it again, this time with Aki Vehtari. They have written a textbook that should be on every applied quantitative researcher’s bookshelf. Most importantly they explain how to do and interpret regression with real world, complicated examples. Practicing academics in addition to students will benefit from giving this book a close read.’ Christopher Winship, Harvard University, Massachusetts

‘Comprehensive and charming, this regression manual belongs on every regressor’s shelf.’ Joshua Angrist, Massachusetts Institute of Technology

Book Descriptions

A practical approach to using regression and computation to solve real-world problems of estimation, prediction, and causal inference.

Table of Contents

Part 1: Fundamentals

Chapter 1: Overview

Chapter 2: Data and measurement

Chapter 3: Some basic methods in mathematics and probability

Chapter 4: Statistical inference

Chapter 5: Simulation

Part 2: Linear Regression

Chapter 6: Background on regression modeling

Chapter 7: Linear regression with a single predictor

Chapter 8: Fitting regression models

Chapter 9: Prediction and Bayesian inference

Chapter 10: Linear regression with multiple predictors

Chapter 11: Assumptions, diagnosics, and model evaulation

Chapter 12: Transformations and regression

Part 3: Generalized linear models

Chapter 13: Logistic regression

Chapter 14: Working with logistic regression

Chapter 15: Other generalized linear models

Part 4: Before and after fitting a regression

Chapter 16: Design and sample size decisions

Chapter 17: Poststratification and missing-data imputation

Part 5: Casual inference

Chapter 18: Casual inference and randomized experiments

Chapter 19: Casual inference using regression on the treatment variable

Chapter 20: Observational studies with all confounders assumed to be measured

Chapter 21: Additional topics in causal inference

Part 6: What comes next?

I Chapter 22: Advanced regression and multilevel models

About the Authors

The authors are experienced researchers who have published articles in hundreds of different scientific journals in fields including statistics, computer science, policy, public health, political science, economics, sociology, and engineering. They have also published articles in the Washington Post, New York Times, Slate, and other public venues. Their previous books include Bayesian Data Analysis, Teaching Statistics: A Bag of Tricks, and Data Analysis and Regression Using Multilevel/Hierarchical Models. Andrew Gelman is Higgins Professor of Statistics and Professor of Political Science at Columbia University.

Jennifer Hill is Professor of Applied Statistics at New York University.

Aki Vehtari is Associate Professor in Computational Probabilistic Modeling at Aalto University, Finland.