#
Foundations of Statistics for Data Scientists

With R and Python

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## Book Description

**Foundations of Statistics for Data Scientists: With R and Python** is designed as a textbook for a one- or two-term introduction to mathematical statistics for students training to become data scientists. It is an in-depth presentation of the topics in statistical science with which any data scientist should be familiar, including probability distributions, descriptive and inferential statistical methods, and linear modeling. The book assumes knowledge of basic calculus, so the presentation can focus on "why it works" as well as "how to do it." Compared to traditional "mathematical statistics" textbooks, however, the book has less emphasis on probability theory and more emphasis on using software to implement statistical methods and to conduct simulations to illustrate key concepts. All statistical analyses in the book use R software, with an appendix showing the same analyses with Python.

Key Features:

- Shows the elements of statistical science that are important for students who plan to become data scientists.
- Includes Bayesian and regularized fitting of models (e.g., showing an example using the lasso), classification and clustering, and implementing methods with modern software (R and Python).
- Contains nearly 500 exercises.

The book also introduces modern topics that do not normally appear in mathematical statistics texts but are highly relevant for data scientists, such as Bayesian inference, generalized linear models for non-normal responses (e.g., logistic regression and Poisson loglinear models), and regularized model fitting. The nearly 500 exercises are grouped into "Data Analysis and Applications" and "Methods and Concepts." Appendices introduce R and Python and contain solutions for odd-numbered exercises. The book's website (http://stat4ds.rwth-aachen.de/) has expanded R, Python, and Matlab appendices and all data sets from the examples and exercises.

## Table of Contents

1. Introduction to Statistical Science 2. Probability Distributions 3. Sampling Distributions 4. Statistical Inference: Estimation Skip Product Menu 5. Statistical Inference: Significance Testing 6. Linear Models and Least Squares 7. Generalized Linear Models 8. Classification and Clustering 9. Statistical Science: A Historical Overview Appendices

## Author(s)

### Biography

**Alan Agresti,** Distinguished Professor Emeritus at the University of Florida, is the author of seven books, including *Categorical Data Analysis* (Wiley) and *Statistics: The Art and Science of Learning from Data* (Pearson), and has presented short courses in 35 countries. His awards include an honorary doctorate from De Montfort University (UK) and Statistician of the Year from the American Statistical Association (Chicago chapter).

**Maria Kateri**, Professor of Statistics and Data Science at the RWTH Aachen University, authored the monograph *Contingency Table Analysis: Methods and Implementation Using R* (Birkhäuser/Springer) and a textbook on mathematics for economists (in German). She has long-term experience in teaching statistics courses to students of Data Science, Mathematics, Statistics, Computer Science, Business Administration, and Engineering.

## Reviews

"[...] Overall, I found the book to be a creative and refreshing take on the challenge of building foundations of “classical” statistics while helping introduce newer topics that are increasingly central to the statistical sciences. Important ideas of the past 50 years (see Gelman and Ahtari 2021) such as resampling, regularization, and hierarchical modeling are incorporated as optional sections (marked with an asterisk). The authors have captured much of the excitement of the statistical sciences and shared it in a way that I believe that students (and instructors) will share their enthusiasm. I look forward to teaching using this book."

-Nicholas J. Horton in theJournal of the American Statistical Association,July 2022"The main goal of this textbook is to present foundational statistical methods and theory that are relevant in the field of data science. The authors depart from the typical approaches taken by many conventional mathematical statistics textbooks by placing more emphasis on providing the students with intuitive and practical interpretations of those methods with the aid of R programming codes. The book also takes slightly different organizations and presents a few topics that are not commonly found in conventional mathematical statistics textbooks. Notably, the book introduces both the frequentist approach and the Bayesian approach for each chapter on statistical inference in Chapters 4 – 6...I find its particular strength to be its intuitive presentation of statistical theory and methods without getting bogged down in mathematical details that are perhaps less useful to the practitioners."

-Mintaek Lee, Boise State University"The statistical training for budding data scientists is different than the statistical training for budding statisticians, or other scientists. Data scientists require a different mix of theory and practice than statisticians, plus a great deal more exposure to computation than many other types of scientists. The aspects of this manuscript that I find appealing for the courses I teach: 1. The use of real data. 2. The use of R but with the option to use Python. 3. A good mix of theory and practice. 4. The text is well-written with good exercises. 5. The coverage of topics (e.g. Bayesian methods and clustering) that are not usually part of a course in statistics at the level of this book".

-Jason M. Graham, University of Scranton"This book distinguishes itself with its focus on computational aspects of statistics (the appendices on R and Python and the examples throughout the text that use R). The ‘cost’ of this approach seems to be that much less attention is given to probability than in a standard text. There is a definite market for this approach – computational statistics/data science do not really require as much probability background as is usually given, while more focus on the way that things are actually done in practice (with software such as R or Python) is extremely beneficial to students that are looking to apply statistical methods. There is a wealth of problems in the book, and their variety (both computational and theoretical) is much appreciated. Also, the expansive appendices on R and Python wonderful, and will be of great help to students…Two major reasons that I would adopt the book are that its discussions seem to be slightly nontraditional in some cases (see above), yet still getting the salient points across. I also am happy about the examples throughout the text that use R–this is very useful for my students."

-Christopher Gaffney, Drexel University"I will most likely adopt the proposed book for my class. The book seems to provide just about right level of mathematics—not too theoretical or like many other cookbooks which are available for R programming."

-Tumulesh Solanky, University of New Orleans"The book is well-written and the examples are well-suited for building foundations for statistical science for data science as a discipline. The material covers most of the theoretical backgrounds in statistics. Throughout the book, the authors have used R programming to illustrate the concepts. In many cases, simulations were presented to support the theory. Each chapter has abundant practical exercises for the readers to explore the materials further. This textbook can serve as a textbook for a data science curriculum."

-Steve Chung,Cal State University Fresno