A Second Course in Statistics: Regression Analysis

by William Mendenhall, Terry Sincich

Overview

For a second course in a two-semester sequence in Introductory Statistics that includes regression analysis.

Gives students the background and confidence to apply regression analysis techniques

A Second Course in Statistics: Regression Analysis, 8th Edition is a highly readable text that explains concepts in a logical, intuitive manner with worked-out examples. Applications to engineering, sociology, psychology, science, and business are demonstrated throughout; real data and scenarios extracted from news articles, journals, and actual consulting problems are used to apply the concepts, allowing students to gain experience utilizing the techniques outlined in the text.

Seven case studies throughout the text invite students to focus on specific problems, and are suitable for class discussion. The 8th Edition incorporates several substantial changes, additions, and enhancements to the case studies, data sets, and software tutorials.

013516379X / 9780135163795 A SECOND COURSE IN STATISTICS: REGRESSION ANALYSIS, 8/e

Product Details

ISBN-13:	9780135163795
Publisher:	Pearson Education
Publication date:	01/01/2019
Edition description:	8th ed.
Pages:	848
Product dimensions:	8.30(w) x 10.25(h) x 1.70(d)

About the Author

About our Authors

Dr. William Mendenhall (deceased) was the founding chairman of the statistics department at the University of Florida and served the department from 1963 until 1977. Dr. Mendenhall received his Ph.D. in statistics from North Carolina State University and was a professor of mathematics at Bucknell University before teaching at UF. Best known as a prolific textbook author in statistics, his text Introduction to Probability and Statistics has been used throughout the United States and the rest of the world as a canonical introduction to the subject. Dr. Mendenhall retired as professor emeritus in 1978 and continued his textbook writing up until his death in 2009.

Dr. Terry Sincich obtained his Ph.D. in Statistics from the University of Florida in 1980. He is an Associate Professor in the Information Systems & Decision Sciences Department at the University of South Florida in Tampa. Dr. Sincich is responsible for teaching basic statistics to all undergraduates, as well as advanced statistics to all doctoral candidates, in the Muma College of Business. He has published articles in such journals as the Journal of the American Statistical Association, International Journal of Forecasting, Academy of Management Journal, and Auditing: A Journal of Practice & Theory. Dr. Sincich is a co-author of the texts Statistics, Statistics for Business & Economics, Statistics for Engineering & the Sciences, and A Second Course in Statistics: Regression Analysis.

Read an Excerpt

OVERVIEW

This text is designed for two types of statistics courses. The early chapters, combined with a selection of the case study chapters, are designed for use in the second half of a two-semester (or two-quarter) introductory statistics sequence for undergraduates with statistics or non-statistics majors. Or, the text can be used for a course in applied regression analysis for masters or Ph.D. students in other fields.

At first glance, these two uses for the text may seem inconsistent. How could a text be appropriate for both undergraduate and graduate students? The answer lies in the content. In contrast to a course in statistical theory, the level of mathematical knowledge required for an applied regression analysis course is minimal. Consequently, the difficulty encountered in learning the mechanics is much the same for both undergraduate and graduate students. The challenge is in the application-diagnosing practical problems, deciding on the appropriate linear model for a given situation, and knowing which inferential technique will answer the researcher's practical question. This takes experience, and it explains why a student with a non-statistics major can take an undergraduate course in applied regression analysis and still benefit from covering the same ground in a graduate course.

Introductory Statistics Course

It is difficult to identify the amount of material that should be included in the second semester of a two-semester sequence in introductory statistics. Optionally, a few lectures should be devoted to Chapter 1 (A Review of Basic Concepts) to make certain that all students possess a common background knowledge of the basic concepts covered in a first-semester (first-quarter) course. Chapter 2 (Introduction to Regression Analysis), Chapter 3 (Simple Linear Regression), Chapter 4 (Multiple Regression Models), Chapter 5 (Model Building), Chapter 6 (Variable Screening Methods), Chapter 7 (Some Regression Pitfalls), and Chapter 8 (Residual Analysis) provide the core for an applied regression analysis course. These chapters could be supplemented by the addition of Chapter 10 (Introduction to Time Series Modeling and Forecasting), Chapter 11 (Principles of Experimental Design), or Chapter 12 (The Analysis of Variance for Designed Experiments).

Applied Regression for Graduates

In our opinion, the quality of an applied graduate course is not measured by the number of topics covered or the amount of material memorized by the students. The measure is how well they can apply the techniques covered in the course to the solution of real problems encountered in their field of study. Consequently, we advocate moving on to new topics only after the students have demonstrate ability (through testing) to apply the techniques under discussion. In-class consulting sessions, where a case study is presented and the students have the opportunity to diagnose the problem and recommend an appropriate method of analysis, are very helpful in teaching applied regression analysis. This approach is particularly useful in helping students master the difficult topic of model selection and model building (Chapters 4-8) and relating questions about the model to real-world questions. The case study chapters (Chapters 13-17) illustrate the type of material that might be useful for this purpose.

A course in applied regression analysis for graduate students would start in the same manner as the undergraduate course, but would move more rapidly over the review material and would more than likely be supplemented by Appendix A (The Mechanics of a Multiple Regression Analysis), one of the statistical software Windows tutorials in Appendices D, E, or F (SAS, SPSS, or MINITAB), Chapter 9 (Special Topics in Regression), and other chapters selected by the instructor. in the undergraduate course, we recommend the use of case studies and in-class consulting sessions to help students develop an ability to formulate appropriate statistical models and to interpret the results of their analyses.

FEATURES

1. Readability. We have purposely tried to make this a teaching (rather than a reference) text. Concepts are explained in a logical intuitive manner using worked examples.
2. Emphasis on model building. The formulation of an appropriate statistical model is fundamental to any regression analysis. This topic is treated Chapters 4-8 and is emphasized throughout the text.
3. Emphasis on developing regression skills. In addition to teaching the basic concepts and methodology of regression analysis, this text stresses its use, as tool, in solving applied problems. Consequently, a major objective of the text is to develop a skill in applying regression analysis to appropriate real-life situations.
4. Numerous real data-based examples and exercises. The text contains many worked examples that illustrate important aspects of model construction, data analysis, and the interpretation of results. Nearly every exercise is based on data and a problem extracted from a news article, magazine, or journal. Exercises are located at the ends of key sections and at the ends of chapters.
5. Case study chapters. The text contains five case study chapters, each of which addresses a real-life research problem. The student can see how regression analysis was used to answer the practical questions posed by the problem, proceeding with the formulation of appropriate statistical models to the analysis and interpretation of sample data.
6. Data sets. The text contains four complete data sets that are associated with the case studies (Chapters 13-17). These can be used by instructors and students to practice model-building and data analyses.
7. Extensive use of statistical software. Tutorials on how to use any of three popular statistical software packages, SAS, SPSS, and MINITAB, are provided in Appendices D, E, and F, respectively. The printouts of the respective software packages are presented and discussed throughout the text.

NEW TO THE SIXTH EDITION

Although the scope and coverage remain the same, the sixth edition contains several substantial changes, additions, and enhancements:

1. More computer printouts. A SAS, SPSS, or MINITAB printout now accompanies every statistical technique presented, allowing the instructor to emphasize interpretations of the statistical results rather than the calculations required to obtain the results.
2. Statistical software tutorials. The Appendix now includes basic instructions on how to use the Windows versions of SAS, SPSS, and MINITAB. Step-by-step instructions and screen shots for each method presented in the text are shown.
3. Describing qualitative data. Anew section (Sec. 1.3) on graphical and numerical methods of describing qualitative data has been added to Chapter 1.
4. Paired comparisons for means. New material on comparing two population means using a paired difference experiment is now included in Chapter 1 (Sec. 1.10).
5. Reorganization of multiple regression models. The multiple regression models presented in Chapter 4 have been reorganized according to order and complexity. First-order models are presented first, followed by interaction and second-order models.
6. Model validation. The section on external model validation (previously presented as a special topic in Chapter 9) has been moved to the model building chapter (Chapter 5). Several new examples are presented.
7. Variable screening methods. Stepwise regression and the all-possible-regressions-selection procedure are now included in a separate chapter (Chapter 6).
8. Spline regression. Spline regression methods are now discussed in the section on robust regression (Sec. 9.8) in Chapter 9: Special Topics.
9. Case study 13: Residential property sale price data updated. The data set for the case study on predicting sale prices of residential properties has been updated to reflect current economic trends.

Numerous less obvious changes in details have been made throughout the text in response to suggestions by current users of the earlier editions.

SUPPLEMENTS

The text is also accompanied by the following supplementary material:

1. Student's solutions manual. (by Mark Dummeldinger). A student's exercise solutions manual presents the full solutions to the odd exercises contained in the text.
2. Instructor's solutions manual. (by Mark Dummeldinger). The instructor's exercise solutions manual presents the full solutions to the other half (the even) exercises contained in the text. For adopters, the manual is complimentary from the publisher.
3. Data CD. The text is accompanied by a CD that contains files for all data sets marked with a CD icon in the text. These include data sets for text examples, exercises, and case studies. The data files are saved in ASCII format for easy importing into statistical software (SAS, SPSS, and MINITAB).

Table of Contents

1. A Review of Basic Concepts (Optional)

• 1.1 Statistics and Data
• 1.2 Populations, Samples, and Random Sampling
• 1.3 Describing Qualitative Data
• 1.4 Describing Quantitative Data Graphically
• 1.5 Describing Quantitative Data Numerically
• 1.6 The Normal Probability Distribution
• 1.7 Sampling Distributions and the Central Limit Theorem
• 1.8 Estimating a Population Mean
• 1.9 Testing a Hypothesis About a Population Mean
• 1.10 Inferences About the Difference Between Two Population Means
• 1.11 Comparing Two Population Variances

2. Introduction to Regression Analysis

• 2.1 Modeling a Response
• 2.2 Overview of Regression Analysis
• 2.3 Regression Applications
• 2.4 Collecting the Data for Regression

3. Simple Linear Regression

• 3.1 Introduction
• 3.2 The Straight-Line Probabilistic Model
• 3.3 Fitting the Model: The Method of Least Squares
• 3.4 Model Assumptions
• 3.5 An Estimator of σ²
• 3.6 Assessing the Utility of the Model: Making Inferences About the Slope β₁
• 3.7 The Coefficient of Correlation
• 3.8 The Coefficient of Determination
• 3.9 Using the Model for Estimation and Prediction
• 3.10 A Complete Example
• 3.11 Regression Through the Origin (Optional)
• Case Study 1: Legal Advertising–Does It Pay?

4. Multiple Regression Models

• 4.1 General Form of a Multiple Regression Model
• 4.2 Model Assumptions
• 4.3 A First-Order Model with Quantitative Predictors
• 4.4 Fitting the Model: The Method of Least Squares
• 4.5 Estimation of σ², the Variance of ε
• 4.6 Testing Overall Model Utility: The Analysis of Variance F-Test
• 4.7 Inferences About the Individual β Parameters
• 4.8 Multiple Coefficients of Determination: R² and R²_adj
• 4.9 Using the Model for Estimation and Prediction
• 4.10 An Interaction Model with Quantitative Predictors
• 4.11 A Quadratic (Second-Order) Model with a Quantitative Predictor
• 4.12 More Complex Multiple Regression Models (Optional)
• 4.13 A Test for Comparing Nested Models
• 4.14 A Complete Example
• Case Study 2: Modeling the Sale Prices of Residential Properties in Four Neighborhoods

5. Principles of Model-Building

• 5.1 Introduction: Why Model Building is Important
• 5.2 The Two Types of Independent Variables: Quantitative and Qualitative
• 5.3 Models with a Single Quantitative Independent Variable
• 5.4 First-Order Models with Two or More Quantitative Independent Variables
• 5.5 Second-Order Models with Two or More Quantitative Independent Variables
• 5.6 Coding Quantitative Independent Variables (Optional)
• 5.7 Models with One Qualitative Independent Variable
• 5.8 Models with Two Qualitative Independent Variables
• 5.9 Models with Three or More Qualitative Independent Variables
• 5.10 Models with Both Quantitative and Qualitative Independent Variables
• 5.11 External Model Validation

6. Variable Screening Methods

• 6.1 Introduction: Why Use a Variable-Screening Method?
• 6.2 Stepwise Regression
• 6.3 All-Possible-Regressions-Selection Procedure
• 6.4 Caveats
• Case Study 3: Deregulation of the Intrastate Trucking Industry

7. Some Regression Pitfalls

• 7.1 Introduction
• 7.2 Observational Data Versus Designed Experiments
• 7.3 Parameter Estimability and Interpretation
• 7.4 Multicollinearity
• 7.5 Extrapolation: Predicting Outside the Experimental Region
• 7.6 Variable Transformations

8. Residual Analysis

• 8.1 Introduction
• 8.2 Plotting Residuals and Detecting Lack of Fit
• 8.3 Detecting Unequal Variances
• 8.4 Checking the Normality Assumption
• 8.5 Detecting Outliers and Identifying Influential Observations
• 8.6 Detection of Residual Correlation: The Durbin-Watson Test
• Case Study 4: An Analysis of Rain Levels in California
• Case Study 5: Factors Affecting the Sale Price of Condominium Units Sold at Public Auction

9. Special Topics in Regression (Optional)

• 9.1 Introduction
• 9.2 Piecewise Linear Regression
• 9.3 Inverse Prediction
• 9.4 Weighted Least Squares
• 9.5 Modeling Qualitative Dependent Variables
• 9.6 Logistic Regression
• 9.7 Poisson Regression
• 9.8 Ridge and Lasso Regression
• 9.9 Robust Regression
• 9.10 Nonparametric Regression Models

10. Time Series Modeling and Forecasting

• 10.1 What is a Time Series?
• 10.2 Time Series Components
• 10.3 Forecasting Using Smoothing Techniques (Optional)
• 10.4 Forecasting: The Regression Approach
• 10.5 Autocorrelation and Autoregressive Error Models
• 10.6 Other Models for Autocorrelated Errors (Optional)
• 10.7 Constructing Time Series Models
• 10.8 Fitting Time Series Models with Autoregressive Errors
• 10.9 Forecasting with Time Series Autoregressive Models
• 10.10 Seasonal Time Series Models: An Example
• 10.11 Forecasting Using Lagged Values of the Dependent Variable (Optional)
• Case Study 6: Modeling Daily Peak Electricity Demands

11. Principles of Experimental Design

• 11.1 Introduction
• 11.2 Experimental Design Terminology
• 11.3 Controlling the Information in an Experiment
• 11.4 Noise-Reducing Designs
• 11.5 Volume-Increasing Designs
• 11.6 Selecting the Sample Size
• 11.7 The Importance of Randomization

12. The Analysis of Variance for Designed Experiments

• 12.1 Introduction
• 12.2 The Logic Behind an Analysis of Variance
• 12.3 One-Factor Completely Randomized Designs
• 12.4 Randomized Block Designs
• 12.5 Two-Factor Factorial Experiments
• 12.6 More Complex Factorial Designs (Optional)
• 12.7 Follow-Up Analysis: Tukey's Multiple Comparisons of Means
• 12.8 Other Multiple Comparisons Methods (Optional)
• 12.9 Checking ANOVA Assumptions
• Case Study 7: Voice Versus Face Recognition — Does One Follow the Other?

Appendices

• A: Derivation of the Least Squares Estimates of β₀ and β₁ in Simple Linear Regression
• A.1 Introduction
• A.2 Matrices and Matrix Multiplication
• A.3 Identity Matrices and Matrix Inversion
• A.4 Solving Systems of Simultaneous Linear Equations
• A.5 The Least Squares Equations and Their Solution
• A.6 Calculating SSE and s²
• A.7 Standard Errors of Estimators, Test Statistics, and Confidence Intervals for β₀, β₁, ... , β_k
• A.8 A Confidence Interval for a Linear Function of the β Parameters and for E(y)
• A.9 A Prediction Interval for Some Value of y to be Observed in the Future
• B: The Mechanics of a Multiple Regression Analysis
• C: A Procedure for Inverting a Matrix
• D: Statistical Tables
• Table 1: Normal Curve Areas
• Table 2: Critical Values for Student's t
• Table 3: Critical Values for the F Statistic: F_.10
• Table 4: Critical Values for the F Statistic: F_.05
• Table 5: Critical Values for the F Statistic: F_.025
• Table 6: Critical Values for the F Statistic: F_.01
• Table 7: Critical Values for the Durbin-Watson d Statistic (α=.05)
• Table 8: Critical Values for the Durbin-Watson d Statistic (α=.01)
• Table 9: Critical Values for the X²-Statistic
• Table 10: Percentage Points of the Studentized Range, q(p,v), Upper 5%
• Table 11: Percentage Points of the Studentized Range, q(p,v), Upper 1%
• E: File Layouts for Case Study Data Sets Answers to Odd Numbered Exercises Index Online:
  • SAS Tutorial
  • SPSS Tutorial
  • MINITAB Tutorial
  • R Tutorial

Introduction

OVERVIEW

This text is designed for two types of statistics courses. The early chapters, combined with a selection of the case study chapters, are designed for use in the second half of a two-semester (or two-quarter) introductory statistics sequence for undergraduates with statistics or non-statistics majors. Or, the text can be used for a course in applied regression analysis for masters or Ph.D. students in other fields.

At first glance, these two uses for the text may seem inconsistent. How could a text be appropriate for both undergraduate and graduate students? The answer lies in the content. In contrast to a course in statistical theory, the level of mathematical knowledge required for an applied regression analysis course is minimal. Consequently, the difficulty encountered in learning the mechanics is much the same for both undergraduate and graduate students. The challenge is in the application-diagnosing practical problems, deciding on the appropriate linear model for a given situation, and knowing which inferential technique will answer the researcher's practical question. This takes experience, and it explains why a student with a non-statistics major can take an undergraduate course in applied regression analysis and still benefit from covering the same ground in a graduate course.

Introductory Statistics Course

It is difficult to identify the amount of material that should be included in the second semester of a two-semester sequence in introductory statistics. Optionally, a few lectures should be devoted to Chapter 1 (A Review of Basic Concepts) to make certain that all students possess a common background knowledge of the basicconcepts covered in a first-semester (first-quarter) course. Chapter 2 (Introduction to Regression Analysis), Chapter 3 (Simple Linear Regression), Chapter 4 (Multiple Regression Models), Chapter 5 (Model Building), Chapter 6 (Variable Screening Methods), Chapter 7 (Some Regression Pitfalls), and Chapter 8 (Residual Analysis) provide the core for an applied regression analysis course. These chapters could be supplemented by the addition of Chapter 10 (Introduction to Time Series Modeling and Forecasting), Chapter 11 (Principles of Experimental Design), or Chapter 12 (The Analysis of Variance for Designed Experiments).

Applied Regression for Graduates

In our opinion, the quality of an applied graduate course is not measured by the number of topics covered or the amount of material memorized by the students. The measure is how well they can apply the techniques covered in the course to the solution of real problems encountered in their field of study. Consequently, we advocate moving on to new topics only after the students have demonstrate ability (through testing) to apply the techniques under discussion. In-class consulting sessions, where a case study is presented and the students have the opportunity to diagnose the problem and recommend an appropriate method of analysis, are very helpful in teaching applied regression analysis. This approach is particularly useful in helping students master the difficult topic of model selection and model building (Chapters 4-8) and relating questions about the model to real-world questions. The case study chapters (Chapters 13-17) illustrate the type of material that might be useful for this purpose.

A course in applied regression analysis for graduate students would start in the same manner as the undergraduate course, but would move more rapidly over the review material and would more than likely be supplemented by Appendix A (The Mechanics of a Multiple Regression Analysis), one of the statistical software Windows tutorials in Appendices D, E, or F (SAS, SPSS, or MINITAB), Chapter 9 (Special Topics in Regression), and other chapters selected by the instructor. in the undergraduate course, we recommend the use of case studies and in-class consulting sessions to help students develop an ability to formulate appropriate statistical models and to interpret the results of their analyses.

FEATURES

1. Readability. We have purposely tried to make this a teaching (rather than a reference) text. Concepts are explained in a logical intuitive manner using worked examples.
2. Emphasis on model building. The formulation of an appropriate statistical model is fundamental to any regression analysis. This topic is treated Chapters 4-8 and is emphasized throughout the text.
3. Emphasis on developing regression skills. In addition to teaching the basic concepts and methodology of regression analysis, this text stresses its use, as tool, in solving applied problems. Consequently, a major objective of the text is to develop a skill in applying regression analysis to appropriate real-life situations.
4. Numerous real data-based examples and exercises. The text contains many worked examples that illustrate important aspects of model construction, data analysis, and the interpretation of results. Nearly every exercise is based on data and a problem extracted from a news article, magazine, or journal. Exercises are located at the ends of key sections and at the ends of chapters.
5. Case study chapters. The text contains five case study chapters, each of which addresses a real-life research problem. The student can see how regression analysis was used to answer the practical questions posed by the problem, proceeding with the formulation of appropriate statistical models to the analysis and interpretation of sample data.
6. Data sets. The text contains four complete data sets that are associated with the case studies (Chapters 13-17). These can be used by instructors and students to practice model-building and data analyses.
7. Extensive use of statistical software. Tutorials on how to use any of three popular statistical software packages, SAS, SPSS, and MINITAB, are provided in Appendices D, E, and F, respectively. The printouts of the respective software packages are presented and discussed throughout the text.

NEW TO THE SIXTH EDITION

Although the scope and coverage remain the same, the sixth edition contains several substantial changes, additions, and enhancements:

1. More computer printouts. A SAS, SPSS, or MINITAB printout now accompanies every statistical technique presented, allowing the instructor to emphasize interpretations of the statistical results rather than the calculations required to obtain the results.
2. Statistical software tutorials. The Appendix now includes basic instructions on how to use the Windows versions of SAS, SPSS, and MINITAB. Step-by-step instructions and screen shots for each method presented in the text are shown.
3. Describing qualitative data. Anew section (Sec. 1.3) on graphical and numerical methods of describing qualitative data has been added to Chapter 1.
4. Paired comparisons for means. New material on comparing two population means using a paired difference experiment is now included in Chapter 1 (Sec. 1.10).
5. Reorganization of multiple regression models. The multiple regression models presented in Chapter 4 have been reorganized according to order and complexity. First-order models are presented first, followed by interaction and second-order models.
6. Model validation. The section on external model validation (previously presented as a special topic in Chapter 9) has been moved to the model building chapter (Chapter 5). Several new examples are presented.
7. Variable screening methods. Stepwise regression and the all-possible-regressions-selection procedure are now included in a separate chapter (Chapter 6).
8. Spline regression. Spline regression methods are now discussed in the section on robust regression (Sec. 9.8) in Chapter 9: Special Topics.
9. Case study 13: Residential property sale price data updated. The data set for the case study on predicting sale prices of residential properties has been updated to reflect current economic trends.

Numerous less obvious changes in details have been made throughout the text in response to suggestions by current users of the earlier editions.