Introduction to Linear Regression Analysis

Informationen zum Autor 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). Klappentext Praise for the Fourth Edition"As with previous editions, the authors have produced a leading textbook on regression."--Journal of the American Statistical AssociationA comprehensive and up-to-date introduction to the fundamentals of regression analysisIntroduction 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 dataIn 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, and a related FTP site features the presented data sets, extensive problem solutions, software hints, and PowerPoint slides to facilitate instructional use of the book.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 biolog...

List of contents

PREFACE xiii1. INTRODUCTION 11.1 Regression and Model Building 11.2 Data Collection 51.3 Uses of Regression 91.4 Role of the Computer 102. SIMPLE LINEAR REGRESSION 122.1 Simple Linear Regression Model 122.2 Least-Squares Estimation of the Parameters 132.3 Hypothesis Testing on the Slope and Intercept 222.4 Interval Estimation in Simple Linear Regression 292.5 Prediction of New Observations 332.6 Coeffi cient of Determination 352.7 A Service Industry Application of Regression 372.8 Using SAS and R for Simple Linear Regression 392.9 Some Considerations in the Use of Regression 422.10 Regression Through the Origin 452.11 Estimation by Maximum Likelihood 512.12 Case Where the Regressor x is Random 523. MULTIPLE LINEAR REGRESSION 673.1 Multiple Regression Models 673.2 Estimation of the Model Parameters 703.3 Hypothesis Testing in Multiple Linear Regression 843.4 Confidence Intervals in Multiple Regression 973.5 Prediction of New Observations 1043.6 A Multiple Regression Model for the Patient Satisfaction Data 1043.7 Using SAS and R for Basic Multiple Linear Regression 1063.8 Hidden Extrapolation in Multiple Regression 1073.9 Standardized Regression Coeffi cients 1113.10 Multicollinearity 1173.11 Why Do Regression Coeffi cients Have the Wrong Sign? 1194. MODEL ADEQUACY CHECKING 1294.1 Introduction 1294.2 Residual Analysis 1304.3 PRESS Statistic 1514.4 Detection and Treatment of Outliers 1524.5 Lack of Fit of the Regression Model 1565. TRANSFORMATIONS AND WEIGHTING TO CORRECT MODEL INADEQUACIES 1715.1 Introduction 1715.2 Variance-Stabilizing Transformations 1725.3 Transformations to Linearize the Model 1765.4 Analytical Methods for Selecting a Transformation 1825.5 Generalized and Weighted Least Squares 1885.6 Regression Models with Random Effect 1946. DIAGNOSTICS FOR LEVERAGE AND INFLUENCE 2116.1 Importance of Detecting Infl uential Observations 2116.2 Leverage 2126.3 Measures of Infl uence: Cook's D 2156.4 Measures of Infl uence: DFFITS and DFBETAS 2176.5 A Measure of Model Performance 2196.6 Detecting Groups of Infl uential Observations 2206.7 Treatment of Infl uential Observations 2207. POLYNOMIAL REGRESSION MODELS 2237.1 Introduction 2237.2 Polynomial Models in One Variable 2237.3 Nonparametric Regression 2367.4 Polynomial Models in Two or More Variables 2427.5 Orthogonal Polynomials 2488. INDICATOR VARIABLES 2608.1 General Concept of Indicator Variables 2608.2 Comments on the Use of Indicator Variables 2738.3 Regression Approach to Analysis of Variance 2759. MULTICOLLINEARITY 2859.1 Introduction 2859.2 Sources of Multicollinearity 2869.3 Effects of Multicollinearity 2889.4 Multicollinearity Diagnostics 2929.5 Methods for Dealing with Multicollinearity 3039.6 Using SAS to Perform Ridge and Principal-Component Regression 32110. VARIABLE SELECTION AND MODEL BUILDING 32710.1 Introduction 32710.2 Computational Techniques for Variable Selection 33810.3 Strategy for Variable Selection and Model Building 35110.4 Case Study: Gorman and Toman Asphalt Data Using SAS 35411. VALIDATION OF REGRESSION MODELS 37211.1 Introduction 37211.2 Validation Techniques 37311.3 Data from Planned Experiments 38512. INTRODUCTION TO NONLINEAR REGRESSION 38912.1 Linear and Nonlinear Regression Models 38912.2 Origins of Nonlinear Models 39112.3 Nonlinear Least Squares 39512.4 Transformation to a Linear Model 39712.5 Parameter Estimation in a Nonlinear System 40012.6 Statistical Inference in Nonlinear Regression 40912.7 Examples of Nonlinear Regression Models 41112.8 Using SAS and R 41213. GENERALIZED LINEAR MODELS 42113.1 Introduction 42113.2 Logistic Regression Models 42213.3 Poisson Regression 44413.4 The Generalized Linear Model 45014. REGRESSION ANALYSIS OF TIME SERIES DATA 47414.1 Introduction to Regression Models for Time Series Data 47414.2 Detecting Autocorrelation: The Durbin-Watson Test 47514.3 Estimating the Parameters in Time Series Regression Models 48015. OTHER TOPICS IN THE USE OF REGRESSION ANALYSIS 50015.1 Robust Regression 50015.2 Effect of Measurement Errors in the Regressors 51115.3 Inverse Estimation--The Calibration Problem 51315.4 Bootstrapping in Regression 51715.5 Classifi cation and Regression Trees (CART) 52415.6 Neural Networks 52615.7 Designed Experiments for Regression 529APPENDIX A. STATISTICAL TABLES 541APPENDIX B. DATA SETS FOR EXERCISES 553APPENDIX C. SUPPLEMENTAL TECHNICAL MATERIAL 574C.1 Background on Basic Test Statistics 574C.2 Background from the Theory of Linear Models 577C.3 Important Results on SSR and SSRes 581C.4 Gauss-Markov Theorem, Var(epsilon) = sigma2I 587C.5 Computational Aspects of Multiple Regression 589C.6 Result on the Inverse of a Matrix 590C.7 Development of the PRESS Statistic 591C.8 Development of S2 (i) 593C.9 Outlier Test Based on R-Student 594C.10 Independence of Residuals and Fitted Values 596C.11 Gauss-Markov Theorem, Var(epsilon) = V 597C.12 Bias in MSRes When the Model Is Underspecifi ed 599C.13 Computation of Infl uence Diagnostics 600C.14 Generalized Linear Models 601APPENDIX D. INTRODUCTION TO SAS 613D.1 Basic Data Entry 614D.2 Creating Permanent SAS Data Sets 618D.3 Importing Data from an EXCEL File 619D.4 Output Command 620D.5 Log File 620D.6 Adding Variables to an Existing SAS Data Set 622APPENDIX E. INTRODUCTION TO R TO PERFORM LINEAR REGRESSION ANALYSIS 623E.1 Basic Background on R 623E.2 Basic Data Entry 624E.3 Brief Comments on Other Functionality in R 626E.4 R Commander 627REFERENCES 628INDEX 642

Report

"The book can be used for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. It also serves as a resource for professionals in the fields of engineering, life and biological sciences, and the social sciences." ( Zentralblatt MATH , 1 October 2013)

Product details

• Authors: Montgomery, Douglas Montgomery, Douglas C. Montgomery, Douglas C. Peck Montgomery, MONTGOMERY DOUGLAS C PECK ELIZA, Elizabeth Peck, Elizabeth A. Peck, G Vining, G. Geoffrey Vining
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 30.03.2012
• EAN: 9780470542811
• ISBN: 978-0-470-54281-1
• No. of pages: 672
• Series: Wiley Series in Probability and Statistics; Wiley Series in Probability an; Wiley Series in Probability and Statistics; Wiley Series in Probability an
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics