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Product Code:  AMSTEXT/28 
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Electronic ISBN:  9781470443542 
Product Code:  AMSTEXT/28.E 
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MAA Member Price:  $125.10 
AMS Member Price:  $111.20 

Book DetailsPure and Applied Undergraduate TextsVolume: 28; 2018; 820 ppMSC: 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 pvalue 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 twosemester course in undergraduate probability and statistics. A onesemester 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.ReadershipUndergraduate and graduate students interested in teaching and learning mathematical statistics.

Table of Contents

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 pValues

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. QuantileQuantile 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 OneParameter Models

5.4. Confidence Intervals in OneParameter Models

5.5. Inference in Models with Multiple Parameters

5.6. Goodness of Fit Testing

5.7. Inference for TwoWay 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. OneWay ANOVA

7.4. TwoWay ANOVA

7.5. Model Selection

7.6. More Examples

7.7. Permutation Tests

7.8. Nonlinear 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


Additional Material

Reviews

It is recommended to undergraduate students with a widerange of backgrounds and career goals.
Rózsa HorváthBokor, 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


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 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
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 pvalue 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 twosemester course in undergraduate probability and statistics. A onesemester 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 pValues

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. QuantileQuantile 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 OneParameter Models

5.4. Confidence Intervals in OneParameter Models

5.5. Inference in Models with Multiple Parameters

5.6. Goodness of Fit Testing

5.7. Inference for TwoWay 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. OneWay ANOVA

7.4. TwoWay ANOVA

7.5. Model Selection

7.6. More Examples

7.7. Permutation Tests

7.8. Nonlinear 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 widerange of backgrounds and career goals.
Rózsa HorváthBokor, 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