STAT2

Modeling with Regression and ANOVA

Second Edition

Publication Date: September 05, 2019

E-book ISBN: 9781319350413

To help all students make a smooth transition to this course, Chapter 0 reminds students of basic statistical terminology and also uses the familiar two-sample t-test as a way to illustrate the approach of specifying, estimating, and testing a statistical model. Using STAT2, students will: Go beyond their Stat 101 experience by learning to develop and apply models with both quantitative and categorical response variables, and with multiple explanatory variables. STAT2 Chapters are grouped into units that consider models based on the type of response and type of predictors.

Discover that the practice of statistical modeling involves applying an interactive process. STAT2 employs a four-step process in all statistical modeling: Choose a form for the model, fit the model to the data, assess how well the model describes the data, and use the model to address the question of interest. Learn how to apply their developing judgment about statistical modeling. STAT2 introduces the idea of constructing statistical models at the very beginning, in a setting that students encountered in their Stat 101 course. This modeling focus continues throughout the course as students encounter new and increasingly more complicated scenarios. Analyze and draw conclusions from real data, which is crucial for preparing students to use statistical modeling in their professional lives. STAT2 incorporates real and rich data throughout the text. Using real data to address genuine research questions helps motivate students to study statistics. The richness stems not only from interesting contexts in a variety of disciplines, but also from the multivariable nature of most datasets.

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STAT2

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About this Book

Cover Page

Title Page

Brief Contents

Contents

To the Teacher

Media and Supplements

Acknowledgments

To the Student

Dedication

Chapter 0: What Is a Statistical Model?
0.1 Model Basics
0.2 A Four-Step Process
Chapter Summary
Exercises

Unit A: Linear Regression

Chapter 1: Simple Linear Regression
1.1 The Simple Linear Regression Model
1.2 Conditions for a Simple Linear Model
1.3 Assessing Conditions
1.4 Transformations/Reexpressions
1.5 Outliers and Influential Points
Chapter Summary
Exercises

Chapter 2: Inference for Simple Linear Regression
2.1 Inference for Regression Slope
2.2 Partitioning Variability—ANOVA
2.3 Regression and Correlation
2.4 Intervals for Predictions
2.5 Case Study: Butterfly Wing
sChapter Summary
Exercises

Chapter 3: Multiple Regression
3.1 Multiple Linear Regression Model
3.2 Assessing a Multiple Regression Model
3.3 Comparing Two Regression Lines
3.4 New Predictors from Old
3.5 Correlated Predictors
3.6 Testing Subsets of Predictors
3.7 Case Study: Predicting in Retail Clothing
Chapter Summary
Exercises

Chapter 4: Additional Topics in Regression
Topic 4.1 Added Variable Plots
Topic 4.2 Techniques for Choosing Predictors
Topic 4.3 Cross-validation
Topic 4.4 Identifying Unusual Points in Regression
Topic 4.5 Coding Categorical Predictors
Topic 4.6 Randomization Test for a Relationship
Topic 4.7 Bootstrap for RegressionExercises

Unit B: Analysis of Variance

Chapter 5: One-way ANOVA and Randomized Experiments
5.1 Overview of ANOVA
5.2 The One-way Randomized Experiment and Its Observational Sibling
5.3 Fitting the Model
5.4 Formal Inference: Assessing and Using the Model
5.5 How Big Is the Effect?: Confidence Intervals and Effect Sizes
5.6 Using Plots to Help Choose a Scale for the Response
5.7 Multiple Comparisons and Fisher’s Least Significant Difference
5.8 Case Study: Words with Friends
Chapter Summary
Exercises

Chapter 6: Blocking and Two-way ANOVA
6.1 Choose: RCB Design and Its Observational Relatives
6.2 Exploring Data from Block Designs
6.3 Fitting the Model for a Block Design
6.4 Assessing the Model for a Block Design
6.5 Using the Model for a Block Design
Chapter Summary
Exercises

Chapter 7: ANOVA with Interaction and Factorial Designs
7.1 Interaction
7.2 Design: The Two-way Factorial Experiment
7.3 Exploring Two-way Data
7.4 Fitting a Two-way Balanced ANOVA Model
7.5 Assessing Fit: Do We Need a Transformation?
7.6 Using a Two-way ANOVA Model
Chapter Summary
Exercises

Chapter 8: Additional Topics in Analysis of Variance
Topic 8.1 Levene’s Test for Homogeneity of Variances
Topic 8.2 Multiple Tests
Topic 8.3 Comparisons and Contrasts
Topic 8.4 Nonparametric Statistics
Topic 8.5 Randomization F-Test
Topic 8.6 Repeated Measures Designs and Datasets
Topic 8.7 ANOVA and Regression with Indicators
Topic 8.8 Analysis of CovarianceExercises
Chapter 8: Online Sections: More on Repeated Measures
Topic 8.9 Repeated Measures: Mixed Designs
Topic 8.10 Repeated Measures: Advanced Material
Topic 8.11 Randomization Testing for Repeated Measures
Exercises

Unit C: Logistic Regression

Chapter 9: Logistic Regression
9.1 Choosing a Logistic Regression Model
9.2 Logistic Regression and Odds Ratios

STAT2 introduces students to statistical modeling beyond what they have learned in a Stat 101 college course or an AP Statistics course. Building on basic concepts and methods learned in that course, STAT2 empowers students to analyze richer datasets that include more variables and address a broader range of research questions. Other than a working understanding of exponential and logarithmic functions, there are no prerequisites beyond successful completion of their first statistics course. To help all students make a smooth transition to this course, Chapter 0 reminds students of basic statistical terminology and also uses the familiar two-sample t-test as a way to illustrate the approach of specifying, estimating, and testing a statistical model. Using STAT2, students will: Go beyond their Stat 101 experience by learning to develop and apply models with both quantitative and categorical response variables, and with multiple explanatory variables. STAT2 Chapters are grouped into units that consider models based on the type of response and type of predictors. Discover that the practice of statistical modeling involves applying an interactive process. STAT2 employs a four-step process in all statistical modeling: Choose a form for the model, fit the model to the data, assess how well the model describes the data, and use the model to address the question of interest. Learn how to apply their developing judgment about statistical modeling. STAT2 introduces the idea of constructing statistical models at the very beginning, in a setting that students encountered in their Stat 101 course. This modeling focus continues throughout the course as students encounter new and increasingly more complicated scenarios. Analyze and draw conclusions from real data, which is crucial for preparing students to use statistical modeling in their professional lives. STAT2 incorporates real and rich data throughout the text. Using real data to address genuine research questions helps motivate students to study statistics. The richness stems not only from interesting contexts in a variety of disciplines, but also from the multivariable nature of most datasets.

Ann Cannon

Ann Cannon is the Watson M. Davis Professor of Mathematics and Statistics at Cornell College in Mount Vernon, Iowa, where she has taught statistics for 30 years. She earned her MA and PhD in statistics from Iowa State University, and her BA in mathematics from Grinnell College. Ann is a Fellow of the American Statistical Association (ASA) and won the Mu Sigma Rho (national statistics honor society) William D. Warde Statistics Education Award. Ann has been very involved with the Statistics and Data Science Education Section of the ASA, serving on the executive committee as member-at-large, secretary/treasurer, and chair. She has also served on the ASA/MAA Joint Committee on Undergraduate Statistics, and as the Secretary/Treasurer and Chair of the Iowa Chapter of the ASA. Ann is currently associate editor for the Journal of Statistics and Data Science Education. Ann has been involved with the AP® Statistics Reading for 20 years, serving as Reader, Table Leader, Question Leader, and Assistant Chief Reader. Ann is coauthor of STAT2: Modeling with Regression and ANOVA (now in its second edition), a textbook designed for the college statistics course following the introductory statistics course. In her spare time, Ann enjoys playing the French horn (particularly in pit orchestras for musical theater), reading, and traveling.

George W. Cobb

George Cobb is Robert l. Rooke Professor emeritus at Mount Holyoke College, where he taught from 1974 to 2009 after earning his PhD in statistics from Harvard University. He is a Fellow of the American Statistical Association, served a term as ASA vice-president, and received the ASA Founder’s award. He is also recipient of the of the Lifetime Achievement award of the US Conference on Teaching Statistics. He is author or co-author of several books, including Introduction to Design and Analysis of Experiments and Statistics in Action. His interests include Markov chain Monte Carlo, applications of statistics to the law, and bluegrass banjo.

Bradley A. Hartlaub

Brad Hartlaub is a Professor in the Department of Mathematics and Statistics at Kenyon College. He is a nonparametric statistician who has served as the Chief Reader of the AP Statistics Program and is an active member of the American Statistical Associations Section on Statistical Education. Brad was selected as a Fellow of the American Statistical Association in 2006. He has served the College as a department chair, a division chair, a supervisor of undergraduate research, and an associate provost. He has received research grants to support his work with undergraduate students from the Andrew W. Mellon Foundation, the Council on Undergraduate Research, and the National Science Foundation. Brad received the Trustee Award for Distinguished Teaching in 1996, and the Distinction in Mentoring Award in 2014.

Julie M. Legler

Julie Legler earned a BA and MS in Statistics from the University of Minnesota and later a doctorate in biostatistics from Harvard. She has taught statistics at the undergraduate level for nearly 20 years. In addition, she spent 7 years at the National Institutes of Health, first as a postdoc and then as a mathematical statistician at the National Cancer Institute. She has published in the areas of latent variable modeling, surveillance modeling, and undergraduate research. Currently she is professor of statistics and director of the Statistics Program at St. Olaf College. Recently she was named the Director of Collaborative Undergraduate Research and Inquiry at St. Olaf.

Robin H. Lock

Robin H. Lock is the Jack and Sylvia Burry Professor of Statistics at St. Lawrence University where he has taught since 1983 after receiving his PhD from the University of Massachusetts- Amherst. He is a Fellow of the American Statistical Association, past Chair of the Joint MAA-ASA Committee on Teaching Statistics, a member of the committee that developed GAISE (Guidelines for Assessment and Instruction in Statistics Education), and on the editorial board of CAUSE (the Consortium for the Advancement of Undergraduate Statistics Education). He has won the national Mu Sigma Rho Statistics Education award and numerous awards for presentations on statistics education at national conferences.

Thomas L. Moore

Thomas Moore earned a B.A. from Carleton College, an M.S. from the University of Iowa, and a Ph.D. from Dartmouth. He has been on the faculty at Grinnell College since 1980 and has concentrated his scholarship on statistics education. He chaired the Statistics Education Section of ASA in 1995 and the MAAs SIGMAA for Statistics Education in 2004. He is a Fellow of American Statistical Association and was the2008 Mu Sigma Rho Statistical Education Award winner.

Allan J. Rossman

Allan J. Rossman is Professor and Chair of the Statistics Department at Cal Poly – San Luis Obispo. He served as Chief Reader of the Advanced Placement program in Statistics from 2009-2014. He was Program Chair for the 2007 Joint Statistical Meetings and for the U.S. Conference in Teaching Statistics since 2013. He is a Fellow of the American Statistical Association and has received the Mathematical Association of America’s Haimo Award for Distinguished College or University Teaching of Mathematics and the ASA’s Waller Distinguished Teaching Career Award.

Jeffrey A. Witmer

Jeff Witmer is Professor of Mathematics at Oberlin College. He earned a doctorate in statistics from the University of Minnesota in 1983. His scholarly work has been primarily in the areas of Bayesian decision theory and statistics education. He is a Fellow of the American Statistical Association and served as editor of STATS magazine. Among the books he has written or co-authored are Activity Based Statistics and Statistics for the Life Sciences.