STAT2: Modeling with Regression and ANOVA: Modelling with Regression and ANOVA

About the Book

Now available with Macmillan’s online learning platform Achieve Essentials, 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.

Achieve Essentials for Stat2 connects the problem-solving techniques and real world examples in the book to rich digital resources that foster further understanding and application of statistics. Assets in Achieve Essentials support learning before, during, and after class for students, while providing instructors with class performance analytics in an easy-to-use interface.

Table of Contents:

Data Set files needed to complete exercises and examples in the book can be downloaded from the open-access student companion website. Data Sets are available in Excel, CSV, Minitab, R, JMP, TI, SPSS, PC-Text, and Mac-Text formats.

Chapter 0 What Is a Statistical Model?0.1 Model Basics
0.2 A Four-Step Process 
 
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 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 Wings 
 
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 4 Additional Topics in Regression
4.1 Topic: Added Variable Plots
4.2 Topic: Techniques for Choosing Predictors
4.3 Cross-validation
4.4 Topic: Identifying Unusual Points in Regression
4.5 Topic: Coding Categorical Predictors
4.6 Topic: Randomization Test for a Relationship
4.7 Topic: Bootstrap for Regression
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 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 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 8 Additional Topics in Analysis of Variance
8.1 Topic: Levene’s Test for Homogeneity of Variances
8.2 Topic: Multiple Tests
8.3 Topic: Comparisons and Contrasts
8.4 Topic: Nonparametric Statistics
8.5 Topic: Randomization F-Test
8.6 Topic: Repeated Measures Designs and Data Sets
8.7 Topic: ANOVA and Regression with Indicators
8.8 Topic: Analysis of Covariance
Unit C: Logistic Regression
 
Chapter 9 Logistic Regression
9.1 Choosing a Logistic Regression Model
9.2 Logistic Regression and Odds Ratios
9.3 Assessing the Logistic Regression Model
9.4 Formal Inference: Tests and Intervals 
 
Chapter 10 Multiple Logistic Regression
10.1 Overview
10.2 Choosing, Fitting, and Interpreting Models
10.3 Checking Conditions
10.4 Formal Inference: Tests and Intervals
10.5 Case study: Attractiveness and Fidelity
Chapter 11 Additional Topics in Logistic Regression
11.1 Topic: Fitting the Logistic Regression Model
11.2 Topic: Assessing Logistic Regression Models
11.3 Randomization Tests for Logistic Regression
11.4 Analyzing Two-Way Tables with Logistic Regression
11.5 Simpson’s Paradox 
 
Chapter 12 Time Series Analysis
12.1 Functions of Time
12.2 Measuring Dependence on Past Values: Autocorrelation
12.3 ARIMA models
12.4 Case Study: Residual Oil 
 
 
Answers to Selected Exercises
General Index
Dataset Index