A Second Course in Statistics Regression Analysis

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

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. 

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? 

Appendix A: Derivation of the Least Squares Estimates of β ₀ and β ₁ in Simple Linear Regression

Appendix B: The Mechanics of a Multiple Regression Analysis

  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

Appendix C: A Procedure for Inverting a Matrix

Appendix 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%

Appendix E:  File Layouts for Case Study Data Sets

Answers to Odd Numbered Exercises

Index

Online: 

SAS Tutorial

SPSS Tutorial

MINITAB Tutorial

R Tutorial

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