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

Randall Pruim Calvin College, Grand Rapids, MI
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Hardcover ISBN: 978-1-4704-2848-8
Product Code: AMSTEXT/28
List Price: $139.00 MAA Member Price:$125.10
AMS Member Price: $111.20 Electronic ISBN: 978-1-4704-4354-2 Product Code: AMSTEXT/28.E List Price:$139.00
MAA Member Price: $125.10 AMS Member Price:$111.20
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $208.50 MAA Member Price:$187.65
AMS Member Price: $166.80 Click above image for expanded view Foundations and Applications of Statistics: An Introduction Using$\mathsf{R}$, Second Edition Randall Pruim Calvin College, Grand Rapids, MI Available Formats:  Hardcover ISBN: 978-1-4704-2848-8 Product Code: AMSTEXT/28  List Price:$139.00 MAA Member Price: $125.10 AMS Member Price:$111.20
 Electronic ISBN: 978-1-4704-4354-2 Product Code: AMSTEXT/28.E
 List Price: $139.00 MAA Member Price:$125.10 AMS Member Price: $111.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$208.50 MAA Member Price: $187.65 AMS Member Price:$166.80
• Book Details

Pure and Applied Undergraduate Texts
Volume: 282018; 820 pp
MSC: Primary 62;

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.

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

• Cover
• Title page
• Contents
• Preface to the Second Edition
• Companion Website
• Acknowledgments
• Preface to the First Edition
• What Is Statistics?
• Chapter 1. Data
• 1.1. Data Frames
• 1.2. Graphical and Numerical Summaries Data
• 1.3. Summary
• Exercises
• Chapter 2. Probability and Random Variables
• 2.1. Introduction to Probability
• 2.2. Additional Probability Rules and Counting Methods
• 2.3. Discrete Distributions
• 2.4. Hypothesis Tests and p-Values
• 2.5. Mean and Variance of a Discrete Random Variable
• 2.6. Joint Distributions
• 2.7. Other Discrete Distributions
• 2.8. Summary
• Exercises
• Chapter 3. Continuous Distributions
• 3.1. pdfs and cdfs
• 3.2. Mean and Variance
• 3.3. Higher Moments
• 3.4. Other Continuous Distributions
• 3.5. Kernel Density Estimation
• 3.6. Quantile-Quantile Plots
• 3.7. Exponential Families
• 3.8. Joint Distributions
• 3.9. Multivariate Normal Distributions
• 3.10. Summary
• Exercises
• Chapter 4. Parameter Estimation and Testing
• 4.1. Statistical Models
• 4.2. Fitting Models by the Method of Moments
• 4.3. Estimators and Sampling Distributions
• 4.4. Limit Theorems
• 4.5. Inference for the Mean (Variance Known)
• 4.6. Estimating Variance
• 4.7. Inference for the Mean (Variance Unknown)
• 4.8. Confidence Intervals for a Proportion
• 4.9. Paired Tests
• 4.10. Developing New Hypothesis Tests
• 4.11. The Bootstrap
• 4.12. The Delta Method
• 4.13. Summary
• Exercises
• Chapter 5. Likelihood
• 5.1. Maximum Likelihood Estimators
• 5.2. Numerical Maximum Likelihood Methods
• 5.3. Likelihood Ratio Tests in One-Parameter Models
• 5.4. Confidence Intervals in One-Parameter Models
• 5.5. Inference in Models with Multiple Parameters
• 5.6. Goodness of Fit Testing
• 5.7. Inference for Two-Way Tables
• 5.8. Rating and Ranking Based on Pairwise Comparisons
• 5.9. Bayesian Inference
• 5.10. Summary
• Exercises
• Chapter 6. Introduction to Linear Models
• 6.1. The Linear Model Framework
• 6.2. Parameter Estimation for Linear Models
• 6.3. Simple Linear Regression
• 6.4. Inference for Simple Linear Regression
• 6.5. Regression Diagnostics
• 6.6. Transformations in Linear Regression
• 6.7. Categorical Predictors
• 6.8. Categorical Response (Logistic Regression)
• 6.9. Simulating Linear Models to Check Robustness
• 6.10. Summary
• Exercises
• Chapter 7. More Linear Models
• 7.1. The Multiple Quantitative Predictors
• 7.2. Assessing the Quality of a Model
• 7.3. One-Way ANOVA
• 7.4. Two-Way ANOVA
• 7.5. Model Selection
• 7.6. More Examples
• 7.7. Permutation Tests
• 7.8. Non-linear Least Squares
• 7.9. Summary
• Exercises
• Appendix A. A Brief Introduction to R
• A.1. Getting Up and Running
• A.2. Getting Data into \R
• A.3. Saving Data
• A.4. Transforming Data with dplyr and tidyr
• A.5. Primary \R Data Structures
• A.6. Functions in \R
• A.7. ggformula Graphics
• Exercises
• Appendix B. Some Mathematical Preliminaries
• B.1. Sets
• B.2. Functions
• B.3. Sums and Products
• Exercises
• Appendix C. Geometry and Linear Algebra Review
• C.1. Vectors, Spans, and Bases
• C.2. Dot Products and Projections
• C.3. Orthonormal Bases
• C.4. Matrices
• Exercises
• Hints, Answers, and Solutions to Selected Exercises
• Bibliography
• Index to R Functions, Packages, and Data Sets
• Index
• Back Cover

• Reviews

• 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
• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 282018; 820 pp
MSC: Primary 62;

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.

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

• Cover
• Title page
• Contents
• Preface to the Second Edition
• Companion Website
• Acknowledgments
• Preface to the First Edition
• What Is Statistics?
• Chapter 1. Data
• 1.1. Data Frames
• 1.2. Graphical and Numerical Summaries Data
• 1.3. Summary
• Exercises
• Chapter 2. Probability and Random Variables
• 2.1. Introduction to Probability
• 2.2. Additional Probability Rules and Counting Methods
• 2.3. Discrete Distributions
• 2.4. Hypothesis Tests and p-Values
• 2.5. Mean and Variance of a Discrete Random Variable
• 2.6. Joint Distributions
• 2.7. Other Discrete Distributions
• 2.8. Summary
• Exercises
• Chapter 3. Continuous Distributions
• 3.1. pdfs and cdfs
• 3.2. Mean and Variance
• 3.3. Higher Moments
• 3.4. Other Continuous Distributions
• 3.5. Kernel Density Estimation
• 3.6. Quantile-Quantile Plots
• 3.7. Exponential Families
• 3.8. Joint Distributions
• 3.9. Multivariate Normal Distributions
• 3.10. Summary
• Exercises
• Chapter 4. Parameter Estimation and Testing
• 4.1. Statistical Models
• 4.2. Fitting Models by the Method of Moments
• 4.3. Estimators and Sampling Distributions
• 4.4. Limit Theorems
• 4.5. Inference for the Mean (Variance Known)
• 4.6. Estimating Variance
• 4.7. Inference for the Mean (Variance Unknown)
• 4.8. Confidence Intervals for a Proportion
• 4.9. Paired Tests
• 4.10. Developing New Hypothesis Tests
• 4.11. The Bootstrap
• 4.12. The Delta Method
• 4.13. Summary
• Exercises
• Chapter 5. Likelihood
• 5.1. Maximum Likelihood Estimators
• 5.2. Numerical Maximum Likelihood Methods
• 5.3. Likelihood Ratio Tests in One-Parameter Models
• 5.4. Confidence Intervals in One-Parameter Models
• 5.5. Inference in Models with Multiple Parameters
• 5.6. Goodness of Fit Testing
• 5.7. Inference for Two-Way Tables
• 5.8. Rating and Ranking Based on Pairwise Comparisons
• 5.9. Bayesian Inference
• 5.10. Summary
• Exercises
• Chapter 6. Introduction to Linear Models
• 6.1. The Linear Model Framework
• 6.2. Parameter Estimation for Linear Models
• 6.3. Simple Linear Regression
• 6.4. Inference for Simple Linear Regression
• 6.5. Regression Diagnostics
• 6.6. Transformations in Linear Regression
• 6.7. Categorical Predictors
• 6.8. Categorical Response (Logistic Regression)
• 6.9. Simulating Linear Models to Check Robustness
• 6.10. Summary
• Exercises
• Chapter 7. More Linear Models
• 7.1. The Multiple Quantitative Predictors
• 7.2. Assessing the Quality of a Model
• 7.3. One-Way ANOVA
• 7.4. Two-Way ANOVA
• 7.5. Model Selection
• 7.6. More Examples
• 7.7. Permutation Tests
• 7.8. Non-linear Least Squares
• 7.9. Summary
• Exercises
• Appendix A. A Brief Introduction to R
• A.1. Getting Up and Running
• A.2. Getting Data into \R
• A.3. Saving Data
• A.4. Transforming Data with dplyr and tidyr
• A.5. Primary \R Data Structures
• A.6. Functions in \R
• A.7. ggformula Graphics
• Exercises
• Appendix B. Some Mathematical Preliminaries
• B.1. Sets
• B.2. Functions
• B.3. Sums and Products
• Exercises
• Appendix C. Geometry and Linear Algebra Review
• C.1. Vectors, Spans, and Bases
• C.2. Dot Products and Projections
• C.3. Orthonormal Bases
• C.4. Matrices
• Exercises
• Hints, Answers, and Solutions to Selected Exercises
• Bibliography
• Index to R Functions, Packages, and Data Sets
• Index
• Back Cover
• 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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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