Introduction to Linear Regression Analysis

Praise for the Fourth Edition "As with previous editions, the authors have produced a leading textbook on regression." — Journal of the American Statistical Association A comprehensive and up-to-date introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including: A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model Tests on individual regression coefficients and subsets of coefficients Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences. This Book Describes Both The Conventional And Less Common Uses Of Linear Regression In The Practical Context Of Today's Mathematical And Scientific Research-- 1. Introduction -- 1.1 Regression And Model Building -- 1.2 Data Collection -- 1.3 Uses Of Regression -- 1.4 Role Of The Computer -- 2. Simple Linear Regression -- 2.1 Simple Linear Regression Model -- 2.2 Least-squares Estimation Of The Parameters -- 2.3 Hypothesis Testing On The Slope And Intercept -- 2.4 Interval Estimation In Simple Linear Regression -- 2.5 Prediction Of New Observations -- 2.6 Coefficient Of Determination -- 2.7 A Service Industry Application Of Regression -- 2.8 Using Sas And R For Simple Linear Regression -- 2.9 Some Considerations In The Use Of Regression -- 2.10 Regression Through The Origin -- 2.11 Estimation By Maximum Likelihood -- 2.12 Case Where The Regressor X Is Random -- 3. Multiple Linear Regression -- 3.1 Multiple Regression Models -- 3.2 Estimation Of The Model Parameters -- 3.3 Hypothesis Testing In Multiple Linear Regression -- 3.4 Confidence Intervals In Multiple Regression -- 3.5 Prediction Of New Observations -- 3.6 A Multiple Regression Model For The Patient Satisfaction Data -- 3.7 Using Sas And R For Basic Multiple Linear Regression -- 3.8 Hidden Extrapolation In Multiple Regression -- 3.9 Standardized Regression Coeffi Cients -- 3.10 Multicollinearity -- 3.11 Why Do Regression Coeffi Cients Have The Wrong Sign? 4. Model Adequacy Checking -- 4.1 Introduction -- 4.2 Residual Analysis -- 4.3 Press Statistic -- 4.4 Detection And Treatment Of Outliers -- 4.5 Lack Of Fit Of The Regression Model -- 5. Transformations And Weighting To Correct Model Inadequacies -- 5.1 Introduction -- 5.2 Variance-stabilizing Transformations -- 5.3 Transformations To Linearize The Model -- 5.4 Analytical Methods For Selecting A Transformation -- 5.5 Generalized And Weighted Least Squares -- 5.6 Regression Models With Random Effect -- 6. Diagnostics For Leverage And Influence -- 6.1 Importance Of Detecting Infl Uential Observations -- 6.2 Leverage -- 6.3 Measures Of Infl Uence: Cook's D -- 6.4 Measures Of Infl Uence: Dffits And Dfbetas -- 6.5 A Measure Of Model Performance -- 6.6 Detecting Groups Of Infl Uential Observations -- 6.7 Treatment Of Infl Uential Observations -- 7. Polynomial Regression Models -- 7.1 Introduction -- 7.2 Polynomial Models In One Variable -- 7.3 Nonparametric Regression -- 7.4 Polynomial Models In Two Or More Variables -- 7.5 Orthogonal Polynomials 8. Indicator Variables -- 8.1 General Concept Of Indicator Variables -- 8.2 Comments On The Use Of Indicator Variables -- 8.3 Regression Approach To Analysis Of Variance -- 9. Multicollinearity -- 9.1 Introduction -- 9.2 Sources Of Multicollinearity -- 9.3 Effects Of Multicollinearity -- 9.4 Multicollinearity Diagnostics -- 9.5 Methods For Dealing With Multicollinearity -- 9.6 Using Sas To Perform Ridge And Principal-component Regression -- 10. Variable Selection And Model Building -- 10.1 Introduction -- 10.2 Computational Techniques For Variable Selection -- 10.3 Strategy For Variable Selection And Model Building -- 10.4 Case Study: Gorman And Toman Asphalt Data Using Sas -- 11. Validation Of Regression Models -- 11.1 Introduction 372 11.2 Validation Techniques -- 11.3 Data From Planned Experiments -- 12. Introduction To Nonlinear Regression -- 12.1 Linear And Nonlinear Regression Models -- 12.2 Origins Of Nonlinear Models -- 12.3 Nonlinear Least Squares -- 12.4 Transformation To A Linear Model -- 12.5 Parameter Estimation In A Nonlinear System -- 12.6 Statistical Inference In Nonlinear Regression -- 12.7 Examples Of Nonlinear Regression Models -- 12.8 Using Sas And R 13. Generalized Linear Models -- 13.1 Introduction -- 13.2 Logistic Regression Models -- 13.3 Poisson Regression -- 13.4 The Generalized Linear Model -- 14. Regression Analysis Of Time Series Data -- 14.1 Introduction To Regression Models For Time Series Data -- 14.2 Detecting Autocorrelation: The Durbin-watson Test -- 14.3 Estimating The Parameters In Time Series Regression Models -- 15. Other Topics In The Use Of Regression Analysis -- 15.1 Robust Regression -- 15.2 Effect Of Measurement Errors In The Regressors -- 15.3 Inverse Estimation -- The Calibration Problem -- 15.4 Bootstrapping In Regression -- 15.5 Classifi Cation And Regression Trees (cart) -- 15.6 Neural Networks -- 15.7 Designed Experiments For Regression -- Appendix A. Statistical Tables -- Appendix B. Data Sets For Exercises -- Appendix C. Supplemental Technical Material -- C.1 Background On Basic Test Statistics -- C.2 Background From The Theory Of Linear Models -- C.3 Important Results On Ssr And Ssres -- C.4 Gauss-markov Theorem, Var(epsilon) = Sigma2i C.5 Computational Aspects Of Multiple Regression -- C.6 Result On The Inverse Of A Matrix -- C.7 Development Of The Press Statistic -- C.8 Development Of S2 (i) -- C.9 Outlier Test Based On R-student -- C.10 Independence Of Residuals And Fitted Values -- C.11 Gauss -- Markov Theorem, Var(epsilon) = V -- C.12 Bias In Msres When The Model Is Underspecified -- C.13 Computation Of Infl Uence Diagnostics -- C.14 Generalized Linear Models -- Appendix D. Introduction To Sas -- D.1 Basic Data Entry -- D.2 Creating Permanent Sas Data Sets -- D.3 Importing Data From An Excel File -- D.4 Output Command -- D.5 Log File -- D.6 Adding Variables To An Existing Sas Data Set -- Appendix E. Introduction To R To Perform Linear Regression Analysis -- E.1 Basic Background On R -- E.2 Basic Data Entry -- E.3 Brief Comments On Other Functionality In R -- E.4 R Commander. Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining. Includes Bibliographical References (p. 628-641) And Index. DOUGLAS C. MONTGOMERY, PhD, is Regents Professor of Industrial Engineering and Statistics at Arizona State University. Dr. Montgomery is a Fellow of the American Statistical Association, the American Society for Quality, the Royal Statistical Society, and the Institute of Industrial Engineers and has more than thirty years of academic and consulting experience. He has devoted his research to engineering statistics, specifically the design and analysis of experiments, statistical methods for process monitoring and optimization, and the analysis of time-oriented data. Dr. Montgomery is the coauthor of Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition and Introduction to Time Series Analysis and Forecasting, both published by Wiley. ELIZABETH A. PECK, PhD, is Logistics Modeling Specialist at the Coca-Cola Company in Atlanta, Georgia. G. GEOFFREY VINING, PhD, is Professor in the Department of Statistics at Virginia Polytechnic and State University. He has published extensively in his areas of research interest, which include experimental design and analysis for quality improvement, response surface methodology, and statistical process control. A Fellow of the American Statistical Association and the American Society for Quality, Dr. Vining is the coauthor of Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition (Wiley) * This Fifth Edition introduces and features the use of R and JMP software. SAS, S-Plus, and Minitab continue to be employed in this new edition, and the output from all of these packages can be found throughout the book.