Introduction to Linear Regression Analysis, 3rd Edition

by Douglas C. Montgomery (Arizona State Univ.); Elizabeth A. Peck (The Coca-Cola Company); G. Geoffrey Vining (Virginia Polytechnic and State Univ.)

• ISBN13: 9780471315650
• ISBN10: 0471315656
• Edition: 3rd
• Format: Hardcover
• Copyright: 2001-04-01
• Publisher: Wiley-Interscience

Summary

With its new exercises and structure, this book is highly recommended for upper-undergraduate and beginning graduate students in mathematics, engineering, and natural sciences. Scientists and engineers will find the book to be an excellent choice for reference and self-study.

Author Biography

DOUGLAS C. MONTGOMERY is Professor in the Department of Industrial Engineering, Arizona State University. <p> ELIZABETH A. PECK is Logistics Modeling Specialist at the Coca-Cola Company in Atlanta, Georgia. <p> G. GEOFFREY VINING is Professor and Head of the Department of Statistics, Virginia Tech.

Table of Contents

Preface	xiii
Introduction	1	(12)
Regression and Model Building	1	(6)
Data Collection	7	(4)
Uses of Regression	11	(1)
Role of the Computer	12	(1)
Simple Linear Regression	13	(54)
Simple Linear Regression Model	13	(1)
Least-Squares Estimation of the Parameters	14	(10)
Estimation of β0 and β1	14	(6)
Properties of the Least-Squares Estimators and the Fitted Regression Model	20	(2)
Estimation of σ2	22	(2)
An Alternate From of the Model	24	(1)
Hypothesis Testing on the Slope and Intercept	24	(8)
Use of t-Tests	25	(1)
Testing Significance of Regression	26	(2)
The Analysis of Variance	28	(4)
Interval Estimation in Simple Linear Regression	32	(5)
Confidence Intervals on β0, β1 and σ2	32	(2)
Interval Estimation of the Mean Response	34	(3)
Prediction of New Observations	37	(2)
Coefficient of Determination	39	(2)
Some Considerations in the Use of Regression	41	(3)
Regression Through the Origin	44	(6)
Estimation by Maximum Likelihood	50	(2)
Case Where the Regressor x is Random	52	(15)
x and y Jointly Distributed	52	(1)
x and y Jointly Normally Distributed: The Correlation Model	53	(5)
Problems	58	(9)
Multiple Linear Regression	67	(64)
Multiple Regression Models	67	(4)
Estimation of the Model Parameters	71	(16)
Least-Squares Estimation of the Regression Coeficients	71	(10)
A Geometrical Interpretation of Least Squares	81	(1)
Properties of the Least-Squares Estimators	82	(1)
Estimation of σ2	82	(2)
Inadequacy of Scatter Diagrams in Multiple Regression	84	(1)
Maximum-Likelihood Estimation	85	(2)
Hypothesis Testing in Multiple Linear Regression	87	(14)
Test for Significance of Regression	87	(4)
Tests on Individual Regression Coefficients	91	(5)
Special Case of Orthogonal Columns in X	96	(2)
Testing the General Linear Hypothesis	98	(3)
Confidence Intervals in Multiple Regression	101	(7)
Confidence Intervals on the Regression Coefficients	102	(1)
Confidence Interval Estimation on the Mean Response	103	(1)
Simultaneous Confidence Intervals on Regression Coefficients	104	(4)
Prediction of New Observations	108	(1)
Hidden Extrapolation in Multiple Regression	109	(3)
Standardized Regression Coefficients	112	(5)
Multicollinearity	117	(3)
Why Do Regression Coefficients have the Wrong Sign?	120	(11)
Problems	122	(9)
Model Adequacy Checking	131	(42)
Introduction	131	(1)
Residual Analysis	132	(20)
Definition of Residuals	132	(1)
Methods for Scaling Residuals	132	(6)
Residual Plots	138	(8)
Partial Regression and Partial Residual Plots	146	(4)
Other Residual Plotting and Analysis Methods	150	(2)
The Press Statistic	152	(2)
Detection and Treatment of Outliers	154	(4)
Lack of Fit of the Regression Model	158	(15)
A Formal Test for Lack of Fit	158	(4)
Estimation of Pure Error from Near-Neighbors	162	(4)
Problems	166	(7)
Transformations and Weighting to Correct Model Inadequacies	173	(34)
Introduction	173	(1)
Variance-Stabilizing Transformations	174	(4)
Transformations to Linearize the Model	178	(8)
Analytical Methods for Selecting a Transformation	186	(7)
Transformations on y: The Box-Cox Method	186	(3)
Transformations on the Regressor Variables	189	(4)
Generalized and Weighted Least Squares	193	(14)
Generalized Least Squares	193	(2)
Weighted Least Squares	195	(1)
Some Practical Issues	196	(4)
Problems	200	(7)
Diagnostics for Leverage and Influence	207	(14)
Importance of Detecting Influential Observations	207	(2)
Leverage	209	(1)
Measures of Influence: Cook's D	210	(3)
Measures of Influence: DFFITS and DFBETAS	213	(3)
A Measure of Model Performance	216	(1)
Detecting Groups of Influential Observations	217	(1)
Treatment of Influential Observations	218	(3)
Problems	219	(2)
Polynomial Regression Models	221	(44)
Introduction	221	(1)
Polynomial Models in One Variable	221	(16)
Basic Principles	221	(7)
Piecewise Polynomial Fitting (Splines)	228	(8)
Polynomial and Trigonometric Terms	236	(1)
Nonparametric Regression	237	(7)
Kernel Regression	238	(1)
Locally Weighted Regression (Loess)	239	(4)
Final Cautions	243	(1)
Polynomial Models in Two or More Variables	244	(9)
Orthogonal Polynomials	253	(12)
Problems	258	(7)
Indicator Variables	265	(26)
The General Concept of Indicator Variables	265	(14)
Comments on the Use of Indicator Variables	279	(2)
Indicator Variables versus Regression on Allocated Codes	279	(1)
Indicator Variables as a Substitute for a Quantitative Regressor	280	(1)
Regression Approach to Analysis of Variance	281	(10)
Problems	287	(4)
Variable Selection and Model Building	291	(34)
Introduction	291	(11)
The Model-Building Problem	291	(1)
Consequences of Model Misspecification	292	(4)
Criteria for Evaluating Subset Regression Models	296	(6)
Computational Techniques for Variable Selection	302	(15)
All Possible Regressions	302	(8)
Stepwise Regression Methods	310	(7)
Some Final Recommendations for Practice	317	(8)
Problems	318	(7)
Multicollinearity	325	(57)
Introduction	325	(1)
Sources of Multicollinearity	325	(3)
Effects of Multicollinearity	328	(6)
Multicollinearity Diagnostics	334	(11)
Examination of the Correlation Matrix	334	(3)
Variance Inflation Factors	337	(2)
Eigensystem Analysis of X'X	339	(4)
Other Diagnostics	343	(2)
Methods for Dealing with Multicollinearity	345	(37)
Collecting Additional Data	345	(1)
Model Respecification	346	(2)
Ridge Regression	348	(15)
Other Methods	363	(12)
Comparison and Evaluation of Biased Estimators	375	(3)
Problems	378	(4)
Robust Regression	382	(32)
The Need for Robust Regression	382	(4)
M-Estimators	386	(14)
Properties of Robust Estimators	400	(1)
Breakdown Point	400	(1)
Efficiency	401	(1)
Survey of Other Robust Regression Estimators	401	(13)
High-Breakdown-Point Estimators	401	(5)
Bounded Influence Estimators	406	(1)
Other Procedures	407	(2)
Computing Robust Regression Estimators	409	(1)
Problems	410	(4)
Introduction to Nonlinear Regression	414	(29)
Linear and Nonlinear Regression Models	414	(2)
Linear Regression Models	414	(1)
Nonlinear Regression Models	415	(1)
Nonlinear Least Squares	416	(4)
Transformation to a Linear Model	420	(3)
Parameter Estimation in a Nonlinear System	423	(11)
Linearization	423	(8)
Other Parameter Estimation Methods	431	(1)
Starting Values	432	(1)
Computer Programs	433	(1)
Statistical Inference in Nonlinear Regression	434	(3)
Examples of Nonlinear Regression Models	437	(6)
Problems	438	(5)
Generalized Linear Models	443	(45)
Introduction	443	(1)
Logistic Regression Models	444	(15)
Models with a Binary Response Variable	444	(3)
Estimating the Parameters in a Logistic Regression Model	447	(3)
Interpretation of the Parameters in a Logistic Regression Model	450	(3)
Hypothesis Tests on Model Paramoters	453	(6)
Poisson Regression	459	(7)
The Generalized Linear Model	466	(22)
Link Functions and Linear Predictors	467	(1)
Parameter Estimation and Inference in the GLM	468	(4)
Prediction and Estimation with the GLM	472	(2)
Residual Analysis in the GLM	474	(1)
Overdispersion	475	(2)
Problems	477	(11)
Other Topics in the Use of Regression Analysis	488	(41)
Regression Models with Autocorrelation Errors	488	(12)
Source and Effects of Autocorrelation	488	(1)
Detecting the Presence of Autocorrelation	489	(5)
Parameter Estimation Methods	494	(6)
Effect of Measurement Errors in the Regressors	500	(3)
Simple Linear Regression	501	(1)
The Berkson Model	502	(1)
Inverse Estimation-The Calibration Problem	503	(5)
Bootstrapping in Regression	508	(8)
Bootstrap Sampling in Regression	509	(1)
Bootstrap Confidence Intervals	510	(6)
Classification and Regression Trees (CART)	516	(2)
Neural Networks	518	(3)
Designed Experiments for Regression	521	(8)
Problems	524	(5)
Validation of Regression Models	529	(20)
Introduction	529	(1)
Validation Techniques	530	(15)
Analysis of Model Coefficients and Predicted Values	530	(2)
Collecting Fresh Data-Confirmation Runs	532	(2)
Data Splitting	534	(11)
Data from Planned Experiments	545	(4)
Problems	545	(4)
APPENDIX A. Statistical Tables	549	(18)
APPENDIX B. Data Sets For Exercises	567	(15)
APPENDIX C. Supplemental Technical Material	582	(39)
C.1 Background on Basic Test Statistics	582	(3)
C.2 Background from the Theory of Linear Models	585	(3)
C.3 Important Results on SSR and SSRes	588	(6)
C.4 The Gauss-Markov Theorem, Var(&epsis;) = σ2I	594	(1)
C.5 Computational Aspects of Multiple Regression	595	(2)
C.6 A Result on the Inverse of a Matrix	597	(1)
C.7 Development of the PRESS Statistic	598	(2)
C.8 Development of S2(i)	600	(1)
C.9 An Outlier Test Based on R-Student	601	(3)
C.10 The Gauss-Markov Theorem, Var(&epsis;) = V	604	(2)
C.11 The Bias in MSRes When the Model is Underspecified	606	(2)
C.12 Computation of Influence Diagnostics	608	(2)
C.13 Generalized Linear Models	610	(11)
References	621	(16)
Index	637