**Pure and Applied Undergraduate Texts**

Volume: 28;
2018;
820 pp;
Hardcover

MSC: Primary 62;

**Print ISBN: 978-1-4704-2848-8
Product Code: AMSTEXT/28**

List Price: $139.00

AMS Member Price: $111.20

MAA Member Price: $125.10

**Electronic ISBN: 978-1-4704-4354-2
Product Code: AMSTEXT/28.E**

List Price: $139.00

AMS Member Price: $111.20

MAA Member Price: $125.10

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#### Supplemental Materials

# Foundations and Applications of Statistics: An Introduction Using \(\mathsf {R}\), Second Edition

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*Randall Pruim*

Foundations and Applications of Statistics simultaneously
emphasizes both the foundational and the computational aspects of modern
statistics. Engaging and accessible, this book is useful to undergraduate
students with a wide range of backgrounds and career goals.

The exposition immediately begins with statistics, presenting
concepts and results from probability along the way. Hypothesis
testing is introduced very early, and the motivation for several
probability distributions comes from p-value computations. Pruim
develops the students' practical statistical reasoning through
explicit examples and through numerical and graphical summaries of
data that allow intuitive inferences before introducing the formal
machinery. The topics have been selected to reflect the current
practice in statistics, where computation is an indispensible tool.
In this vein, the statistical computing environment
\(\mathsf{R}\) is used throughout the text and is integral to
the exposition. Attention is paid to developing students' mathematical
and computational skills as well as their statistical reasoning.
Linear models, such as regression and ANOVA, are treated with explicit
reference to the underlying linear algebra, which is motivated
geometrically.

Foundations and Applications of Statistics discusses both
the mathematical theory underlying statistics and practical
applications that make it a powerful tool across disciplines. The
book contains ample material for a two-semester course in
undergraduate probability and statistics. A one-semester course based
on the book will cover hypothesis testing and confidence intervals for
the most common situations.

In the second edition, the \(\mathsf{R}\) code has been updated
throughout to take advantage of new \(\mathsf{R}\) packages and to
illustrate better coding style. New sections have been added covering
bootstrap methods, multinomial and multivariate normal distributions,
the delta method, numerical methods for Bayesian inference, and
nonlinear least squares. Also, the use of matrix algebra has been
expanded, but remains optional, providing instructors with more
options regarding the amount of linear algebra required.

#### Readership

Undergraduate and graduate students interested in teaching and learning mathematical statistics.

#### Reviews & Endorsements

It is recommended to undergraduate students with a wide-range of backgrounds and career goals.

-- Rózsa Horváth-Bokor, Zentralblatt MATH

This is an excellent text for the target audience, and at over 800 pages, as a bonus, students using it will increase their muscle mass by carrying it around, as well as their knowledge of statistics by working through it.

-- Peter Rabinovitch, MAA Reviews

#### Table of Contents

# Table of Contents

## Foundations and Applications of Statistics: An Introduction Using $\mathsf{R}$, Second Edition

- Cover Cover11
- Title page i2
- Contents iii4
- Preface to the Second Edition vii8
- Preface to the First Edition xi12
- What Is Statistics? xvii18
- Chapter 1. Data 122
- Chapter 2. Probability and Random Variables 3354
- 2.1. Introduction to Probability 3455
- 2.2. Additional Probability Rules and Counting Methods 3960
- 2.3. Discrete Distributions 5778
- 2.4. Hypothesis Tests and p-Values 6687
- 2.5. Mean and Variance of a Discrete Random Variable 7495
- 2.6. Joint Distributions 82103
- 2.7. Other Discrete Distributions 92113
- 2.8. Summary 107128
- Exercises 113134

- Chapter 3. Continuous Distributions 131152
- 3.1. pdfs and cdfs 131152
- 3.2. Mean and Variance 145166
- 3.3. Higher Moments 147168
- 3.4. Other Continuous Distributions 155176
- 3.5. Kernel Density Estimation 167188
- 3.6. Quantile-Quantile Plots 173194
- 3.7. Exponential Families 180201
- 3.8. Joint Distributions 183204
- 3.9. Multivariate Normal Distributions 195216
- 3.10. Summary 210231
- Exercises 214235

- Chapter 4. Parameter Estimation and Testing 225246
- 4.1. Statistical Models 225246
- 4.2. Fitting Models by the Method of Moments 227248
- 4.3. Estimators and Sampling Distributions 234255
- 4.4. Limit Theorems 245266
- 4.5. Inference for the Mean (Variance Known) 253274
- 4.6. Estimating Variance 262283
- 4.7. Inference for the Mean (Variance Unknown) 268289
- 4.8. Confidence Intervals for a Proportion 279300
- 4.9. Paired Tests 283304
- 4.10. Developing New Hypothesis Tests 288309
- 4.11. The Bootstrap 301322
- 4.12. The Delta Method 317338
- 4.13. Summary 327348
- Exercises 331352

- Chapter 5. Likelihood 347368
- 5.1. Maximum Likelihood Estimators 347368
- 5.2. Numerical Maximum Likelihood Methods 356377
- 5.3. Likelihood Ratio Tests in One-Parameter Models 369390
- 5.4. Confidence Intervals in One-Parameter Models 379400
- 5.5. Inference in Models with Multiple Parameters 386407
- 5.6. Goodness of Fit Testing 390411
- 5.7. Inference for Two-Way Tables 405426
- 5.8. Rating and Ranking Based on Pairwise Comparisons 415436
- 5.9. Bayesian Inference 424445
- 5.10. Summary 441462
- Exercises 445466

- Chapter 6. Introduction to Linear Models 455476
- 6.1. The Linear Model Framework 456477
- 6.2. Parameter Estimation for Linear Models 462483
- 6.3. Simple Linear Regression 465486
- 6.4. Inference for Simple Linear Regression 480501
- 6.5. Regression Diagnostics 494515
- 6.6. Transformations in Linear Regression 505526
- 6.7. Categorical Predictors 513534
- 6.8. Categorical Response (Logistic Regression) 522543
- 6.9. Simulating Linear Models to Check Robustness 534555
- 6.10. Summary 538559
- Exercises 542563

- Chapter 7. More Linear Models 553574
- 7.1. The Multiple Quantitative Predictors 553574
- 7.2. Assessing the Quality of a Model 575596
- 7.3. One-Way ANOVA 599620
- 7.4. Two-Way ANOVA 634655
- 7.5. Model Selection 648669
- 7.6. More Examples 656677
- 7.7. Permutation Tests 668689
- 7.8. Non-linear Least Squares 672693
- 7.9. Summary 680701
- Exercises 684705

- Appendix A. A Brief Introduction to R 697718
- Appendix B. Some Mathematical Preliminaries 749770
- Appendix C. Geometry and Linear Algebra Review 759780
- Hints, Answers, and Solutions to Selected Exercises 783804
- Bibliography 799820
- Index to R Functions, Packages, and Data Sets 807828
- Index 813834
- Back Cover Back Cover1842