# Introduction to linear regression analysis

Douglas C. Montgomery (Author), Elizabeth A. Peck (Author), G. Geoffrey Vining (Author)
"This book describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research"-- Provided by publisher
Print Book, English, 2012
Fifth edition View all formats and editions
Wiley : A John Wiley & Sons, Inc., Hoboken, NJ, 2012
xvi, 645 pages : illustrations ; 27 cm.
9780470542811, 9781119180173, 0470542810, 1119180171
775329531
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. Contents note continued: Machine generated contents note
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