Second Course in Statistics, A: Regression Analysis

William Mendenhall / Terry Sincich  
Total pages
November 2013
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Second Course in Statistics, A: Regression Analysis
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The Second Course in Statistics is an increasingly important offering since more students are arriving at college having taken AP Statistics in high school. Mendenhall/Sincich’s A Second Course in Statistics is the perfect book for courses that build on the knowledge students gain in AP Statistics, or the freshman Introductory Statistics course.


A Second Course in Statistics: Regression Analysis, Seventh Edition, focuses on building linear statistical models and developing skills for implementing regression analysis in real situations. This text offers applications for engineering, sociology, psychology, science, and business. The authors use real data and scenarios extracted from news articles, journals, and actual consulting problems to show how to apply the concepts. In addition, seven case studies, now located throughout the text after applicable chapters, invite students to focus on specific problems, and are suitable for class discussion.


  • Readability was a main goal of the authors, whose intent was to create a teaching text rather than a reference text. Concepts are explained in a logical, intuitive manner with worked-out examples.
  • Model building is fundamental to any regression analysis and is introduced in Chapters 4—8, then emphasized throughout the text.
  • Development of regression skills: in addition to teaching basic concepts and methodology, this text stresses its usage in solving applied problems.
  • Real data is used in examples and exercises to maintain the applied nature of this text.
    • Examples illustrate the important aspects of model construction, data analysis, and the interpretation of results.
    • Exercises are located at the end of every section and chapter. Nearly every exercise is based on data and research extracted from news or journal articles.
  • Seven case studies address real-life research problems and are suitable for class discussion. While working through these, students can see how regression analysis is used to answer practical questions, and can then formulate appropriate statistical models for the analysis and interpretation of sample data.
  • Data sets for all case studies, exercises, and examples are available on the CD-ROM included with the book and on the Pearson Data Sets website (
  • Statistical software instruction includes the latest software packages: SAS®, SPSS®, MINITAB®, and, new to this edition, R. Tutorials are provided on the included CD-ROM and printouts associated with the software are presented and discussed throughout the text.


New to this Edition

  • New and updated case studies: two new case studies (Case Study 1: Legal Advertising–Does it Pay? and Case Study 3: Deregulation of the Trucking Industry) have been added, and another (Case Study 2: Modeling Sale Prices of Residential Properties) has been updated with current data.  Also, all seven of the case studies now follow the relevant chapter material for improved logical flow.
  • Real data exercises have been increased and updated, based on contemporary studies and developments in a variety of fields.
  • Statistical software instruction includes the latest software packages: SAS®, SPSS®, MINITAB®, and, new to the text, R. Tutorials are now provided on the CD-ROM, and printouts associated with the software are presented and discussed throughout the text.
  • More emphasis onp-values reflects the tendency of regression analysts to rely on statistical software to fit and assess models in practice. This prepares students for testing statistical hypothesis theories with technology used by professional statisticians.
  • Updated examples in Chapter 9, Special Topics in Regression, include new examples on piecewise regression, weighted least squares, logistic regression, and ridge regression.
  • Redesigned end-of-chapter summaries are easier to use when reviewing and studying.
    • Flow charts aid in the selection of the appropriate statistical method.
    • Important points are reinforced through boxed notes with key words, formulas, definitions, lists, and key concepts.


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 s2

3.6 Assessing the Utility of the Model: Making Inferences About the Slope ß1

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 s2, the Variance of e

4.6 Testing the Utility of a Model: The Analysis of Variance F-Test

4.7 Inferences About the Individual ß Parameters

4.8 Multiple Coefficients of Determination: R2 and R2adj

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

8.3 Detecting Lack of Fit

8.4 Detecting Unequal Variances

8.5 Checking the Normality Assumption

8.6 Detecting Outliers and Identifying Influential Observations

8.7 Detection of Residual Correlation: The Durbin-Watson Test


Case Study 4: An Analysis of Rain Levels in California

Case Study 5: An Investigation of 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 Ridge Regression

9.8 Robust Regression

9.9 Nonparametric Regression Models


10. Introduction to 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: Reluctance to Transmit Bad News: The MUM Effect


Appendix A: Derivation of the Least Squares Estimates of ß0 and ß1 in Simple Linear Regression

Appendix B: The Mechanics of a Multiple Regression Analysis

B.1 Introduction

B.2 Matrices and Matrix Multiplication

B.3 Identity Matrices and Matrix Inversion

B.4 Solving Systems of Simultaneous Linear Equations

B.5 The Least Squares Equations and Their Solution

B.6 Calculating SSE and s2

B.7 Standard Errors of Estimators, Test Statistics, and Confidence Intervals for ß0, ß1, ... , ßk

B.8 A Confidence Interval for a Linear Function of the ß Parameters; A Confidence Interval for E(y)

B.9 A Prediction Interval for Some Value of y to be Observed in the Future


Appendix C: A Procedure for Inverting a Matrix


Appendix D: Statistical Tables

Table D.1: Normal Curve Areas

Table D.2: Critical Values for Student's t

Table D.3: Critical Values for the F Statistic: F.10

Table D.4: Critical Values for the F Statistic: F.05

Table D.5: Critical Values for the F Statistic: F.025

Table D.6: Critical Values for the F Statistic: F.01

Table D.7: Random Numbers

Table D.8: Critical Values for the Durbin-Watson d Statistic (a =.05)

Table D.9: Critical Values for the Durbin-Watson d Statistic (a =.01)

Table D.10: Critical Values for the X2-Statistic

Table D.11: Percentage Points of the Studentized Range, q(p,v), Upper 5%

Table D.12: Percentage Points of the Studentized Range, q(p,v), Upper 1%


Appendix E: File Layouts for Case Study Data Sets



Answers to Selected Odd Numbered Exercises


Technology Tutorials: SAS, SPSS, MINITAB, and R (on CD)