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Introduction to Linear Regression Analysis, 5th Edition

Name: Introduction to Linear Regression Analysis, 5th Edition
ISBN: 9780470542811

by Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining

April 2012

Beginner

672 pages

17h 39m

English

Wiley

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Cover Page
Title Page
Copyright
Contents
PREFACE
CHAPTER 1: INTRODUCTION
1.1 REGRESSION AND MODEL BUILDING1.2 DATA COLLECTION1.3 USES OF REGRESSION1.4 ROLE OF THE COMPUTER
CHAPTER 2: SIMPLE LINEAR REGRESSION
2.1 SIMPLE LINEAR REGRESSION MODEL2.2 LEAST-SQUARES ESTIMATION OF THE PARAMETERS2.3 HYPOTHESIS TESTING ON THE SLOPE AND INTERCEPT2.4 INTERVAL ESTIMATION IN SIMPLE LINEAR REGRESSION2.5 PREDICTION OF NEW OBSERVATIONS2.6 COEFFICIENT OF DETERMINATION2.7 A SERVICE INDUSTRY APPLICATION OF REGRESSION2.8 USING SAS® AND R FOR SIMPLE LINEAR REGRESSION2.9 SOME CONSIDERATIONS IN THE USE OF REGRESSION2.10 REGRESSION THROUGH THE ORIGIN2.11 ESTIMATION BY MAXIMUM LIKELIHOOD2.12 CASE WHERE THE REGRESSOR x IS RANDOMPROBLEMS
CHAPTER 3: MULTIPLE LINEAR REGRESSION
3.1 MULTIPLE REGRESSION MODELS3.2 ESTIMATION OF THE MODEL PARAMETERS3.3 HYPOTHESIS TESTING IN MULTIPLE LINEAR REGRESSION3.4 CONFIDENCE INTERVALS IN MULTIPLE REGRESSION3.5 PREDICTION OF NEW OBSERVATIONS3.6 A MULTIPLE REGRESSION MODEL FOR THE PATIENT SATISFACTION DATA3.7 USING SAS AND R FOR BASIC MULTIPLE LINEAR REGRESSION3.8 HIDDEN EXTRAPOLATION IN MULTIPLE REGRESSION3.9 STANDARDIZED REGRESSION COEFFLCIENTS3.10 MULTICOLLINEARITY3.11 WHY DO REGRESSION COEFFICIENTS HAVE THE WRONG SIGN?PROBLEMS
CHAPTER 4: MODEL ADEQUACY CHECKING
4.1 INTRODUCTION4.2 RESIDUAL ANALYSIS4.3 PRESS STATISTIC4.4 DETECTION AND TREATMENT OF OUTLIERS4.5 LACK OF FIT OF THE REGRESSION MODELPROBLEMS
CHAPTER 5: TRANSFORMATIONS AND WEIGHTING TO CORRECT MODEL INADEQUACIES
5.1 INTRODUCTION5.2 VARIANCE-STABILIZING TRANSFORMATIONS5.3 TRANSFORMATIONS TO LINEARIZE THE MODEL5.4 ANALYTICAL METHODS FOR SELECTING A TRANSFORMATION5.5 GENERALIZED AND WEIGHTED LEAST SQUARES5.6 REGRESSION MODELS WITH RANDOM EFFECTSPROBLEMS

CHAPTER 6: DIAGNOSTICS FOR LEVERAGE AND INFLUENCE
6.1 IMPORTANCE OF DETECTING INFLUENTIAL OBSERVATIONS6.2 LEVERAGE6.3 MEASURES OF INFLUENCE: COOK'S D6.4 MEASURES OF INFLUENCE: DFFITS AND DFBETAS6.5 A MEASURE OF MODEL PERFORMANCE6.6 DETECTING GROUPS OF INFLUENTIAL OBSERVATIONS6.7 TREATMENT OF INFLUENTIAL OBSERVATIONSPROBLEMS
CHAPTER 7: POLYNOMIAL REGRESSION MODELS
7.1 INTRODUCTION7.2 POLYNOMIAL MODELS IN ONE VARIABLE7.3 NONPARAMETRIC REGRESSION7.4 POLYNOMIAL MODELS IN TWO OR MORE VARIABLES7.5 ORTHOGONAL POLYNOMIALSPROBLEMS
CHAPTER 8: INDICATOR VARIABLES
8.1 GENERAL CONCEPT OF INDICATOR VARIABLES8.2 COMMENTS ON THE USE OF INDICATOR VARIABLES8.3 REGRESSION APPROACH TO ANALYSIS OF VARIANCEPROBLEMS
CHAPTER 9: MULTICOLLINEARITY
9.1 INTRODUCTION9.2 SOURCES OF MULTICOLLINEARITY9.3 EFFECTS OF MULTICOLLINEARITY9.4 MULTICOLLINEARITY DIAGNOSTICS9.5 METHODS FOR DEALING WITH MULTICOLLINEARITY9.6 USING SAS TO PERFORM RIDGE AND PRINCIPAL-COMPONENT REGRESSIONPROBLEMS
CHAPTER 10: VARIABLE SELECTION AND MODEL BUILDING
10.1 INTRODUCTION10.2 COMPUTATIONAL TECHNIQUES FOR VARIABLE SELECTION10.3 STRATEGY FOR VARIABLE SELECTION AND MODEL BUILDING10.4 CASE STUDY: GORMAN AND TOMAN ASPHALT DATA USING SASPROBLEMS
CHAPTER 11: VALIDATION OF REGRESSION MODELS
11.1 INTRODUCTION11.2 VALIDATION TECHNIQUES11.3 DATA FROM PLANNED EXPERIMENTSPROBLEMS
CHAPTER 12: INTRODUCTION TO NONLINEAR REGRESSION
12.1 LINEAR AND NONLINEAR REGRESSION MODELS12.2 ORIGINS OF NONLINEAR MODELS12.3 NONLINEAR LEAST SQUARES12.4 TRANFORMATION TO A LINEAR MODEL12.5 PARAMETER ESTIMATION IN A NONLINEAR SYSTEM12.6 STATISTICAL INFERENCE IN NONLINEAR REGRESSION12.7 EXAMPLES OF NONLINEAR REGRESSION MODELS12.8 USING SAS AND RPROBLEMS
CHAPTER 13: GENERALIZED LINEAR MODELS
13.1 INTRODUCTION13.2 LOGISTIC REGRESSION MODELS13.3 POISSON REGRESSION13.4 THE GENERALIZED LINEAR MODELPROBLEMS
CHAPTER 14: REGRESSION ANALYSIS OF TIME SERIES DATA
14.1 INTRODUCTION TO REGRESSION MODELS FOR TIME SERIES DATA14.2 DETECTING AUTOCORRELATION: THE DURBIN–WATSON TEST14.3 ESTIMATING THE PARAMETERS IN TIME SERIES REGRESSION MODELSPROBLEMS
CHAPTER 15: OTHER TOPICS IN THE USE OF REGRESSION ANALYSIS
15.1 ROBUST REGRESSION15.2 EFFECT OF MEASUREMENT ERRORS IN THE REGRESSORS15.3 INVERSE ESTIMATION—THE CALIBRATION PROBLEM15.4 BOOTSTRAPPING IN REGRESSION15.5 CLASSIFICATION AND REGRESSION TREES (CART)15.6 NEURAL NETWORKS15.7 DESIGNED EXPERIMENTS FOR REGRESSIONPROBLEMS
APPENDIX A: STATISTICAL TABLES
APPENDIX B: DATA SETS FOR EXERCISES
APPENDIX C: SUPPLEMENTAL TECHNICAL MATERIAL
C.1 BACKGROUND ON BASIC TEST STATISTICSC.2 BACKGROUND FROM THE THEORY OF LINEAR MODELSC.3 IMPORTANT RESULTS ON SS R AND SS RESC.4 GAUSS–MARKOV THEOREM, VAR(ε) = σ2IC.5 COMPUTATIONAL ASPECTS OF MULTIPLE REGRESSIONC.6 RESULT ON THE INVERSE OF A MATRIXC.7 DEVELOPMENT OF THE PRESS STATISTICC.8 DEVELOPMENT OF S2(i)C.9 OUTLIER TEST BASED ON R-STUDENTC.10 INDEPENDENCE OF RESIDUALS AND FITTED VALUESC.11 GAUSS-MARKOV THEOREM, VAR(ε) = VC.12 BIAS IN MS RES WHEN THE MODEL IS UNDERSPECIFIEDC.13 COMPUTATION OF INFLUENCE DIAGNOSTICSC.14 GENERALIZED LINEAR MODELS
APPENDIX D: INTRODUCTION TO SAS
D.1 BASIC DATA ENTRYD.2 CREATING PERMANENT SAS DATA SETSD.3 IMPORTING DATA FROM AN EXCEL FILED.4 OUTPUT COMMANDD.5 LOG FILED.6 ADDING VARIABLES TO AN EXISTING SAS DATA SET
APPENDIX E: INTRODUCTION TO R TO PERFORM LINEAR REGRESSION ANALYSIS
E.1 Basic Background on RE.2 Basic Data EntryE.3 Brief Comments on Other Functionality in RE.4 R Commander
REFERENCES
INDEX

Content preview from Introduction to Linear Regression Analysis, 5th Edition

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 SS_R and SS_Res

C.4 Gauss-Markov Theorem, Var(ε) = σ²I

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(ε) = V

C.12 Bias in MS_Res When the Model Is Underspecified

C.13 Computation of Influence Diagnostics

C.14 Generalized Linear Models

C.1 BACKGROUND ON BASIC TEST STATISTICS

We indicate that Y is a random variable that follows a normal distribution with mean μ and variance σ² by

C.1.1 Central Distributions

Let Y₁, Y₂, …, Y_n be independent normally distributed random variables with E(Y_i) = μ_i and Var(Y_i) = σ²_i. Let a₁, a₂, …, a_n be known constants. If we define the linear combination of the Y_i's by

then

The key point is that linear combinations of normally distributed random variables also follow normal distributions.
If Y ~ N(μ, σ²), then
Z is called the standard normal random variable.
Let Z = (Y – μ)/σ. If Y

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Introduction to Linear Regression Analysis, 5th Edition

by Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining

APPENDIX C

SUPPLEMENTAL TECHNICAL MATERIAL