Linear Models with Python

by Julian Faraway


This is a book about linear models in Statistics. A linear model describes a quantitative response in terms of a linear combination of predictors. You can use a linear model to make predictions or explain the relationship between the response and the predictors. Linear models are very flexible and widely used in applications in physical science, engineering, social science and business. Linear models are part of the core of Statistics and understanding them well is crucial to a broader competence in the practice of statistics.

This is not an introductory textbook. You will need some basic prior knowledge of statistics as might be obtained in one or two courses at the university level. You will need to be familiar with essential ideas such as hypothesis testing, confidence intervals, likelihood and parameter estimation. You will also need to be competent in the mathematical methods of calculus and linear algebra. This is not a particularly theoretical book as I have preferred intuition over rigorous proof. Nevertheless, successful statistics requires an appreciation of the principles and it is my hope that the reader will absorb these through the many examples I present.

This book is written in three languages: English, Mathematics and Python. I aim to combine these three seamlessly to allow coherent exposition of the practice of linear modeling. This requires the reader to become somewhat fluent in Python. This is not a book about learning Python but like any foreign language, one becomes proficient by practicing it rather than by memorizing the dictionary. The reader is advised to look elsewhere for a basic introduction to Python but should not hesitate to dive into this book and pick it up as you go. I shall try to help. See the appendix to get started.

This book has an ancestor entitled Linear Models with R. Clearly the book you hold now is about Python and not R but it is not an exact translation. Although I was able to accomplish almost all of the R book in this Python book, I found reason for variation:

If your sole objective is to do Statistics, R is more attractive. Yet there are several reasons why you might prefer Python. You may already know Python and use it for other tasks. Indeed it would be unusual for someone to solely do Statistics. The data in this text is already clean and ready to use. In practice, this is rarely the case and flexible software for obtaining and manipulating data is essential. You may already be using Python for this purpose.

Python also has a place at the heart of Machine Learning (ML) but this is a book about Statistics rather than ML. But the aims of these two disciplines overlap considerably to the extent that any data analyst should become familiar with the ideas and methods of both. The datasets in this text are small by ML standards. I hope that a reader coming to this book from an ML background would learn new statistical perspectives on learning from data.

This book would not have been possible without several key open source Python packages. I thank the authors and maintainers of these packages for their outstanding work.