Introduction to Linear Regression Analysis

Name: Introduction to Linear Regression Analysis
Price: 6.71 USD
Availability: InStock
ISBN: 9780471058502

ISBN-10: 0471058505

ISBN-13: 9780471058502

Edition: 1982

Authors: Douglas C. Montgomery, Elizabeth A. Peck

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Book details

List price: $54.95
Copyright year: 1982
Publisher: Wiley & Sons, Incorporated, John
Binding: Hardcover
Pages: 504
Size: 4.65" wide x 11.30" long
Weight: 1.914
Language: English

Preface	p. xiii
Introduction	p. 1
Regression and Model Building	p. 1
Data Collection	p. 7
Uses of Regression	p. 11
Role of the Computer	p. 12
Simple Linear Regression	p. 13
Simple Linear Regression Model	p. 13
Least-Squares Estimation of the Parameters	p. 14
Estimation of [beta subscript 0] and [beta subscript 1]	p. 14
Properties of the Least-Squares Estimators and the Fitted Regression Model	p. 20
Estimation of [sigma superscript 2]	p. 22
An Alternate Form of the Model	p. 24
Hypothesis Testing on the Slope and Intercept	p. 24
Use of t-Tests	p. 25
Testing Significance of Regression	p. 26
The Analysis of Variance	p. 28
Interval Estimation in Simple Linear Regression	p. 32
Confidence Intervals on [beta subscript 0], [beta subscript 1], and [sigma superscript 2]	p. 32
Interval Estimation of the Mean Response	p. 34
Prediction of New Observations	p. 37
Coefficient of Determination	p. 39
Some Considerations in the Use of Regression	p. 41
Regression Through the Origin	p. 44
Estimation by Maximum Likelihood	p. 50
Case Where the Regressor x is Random	p. 52
x and y Jointly Distributed	p. 52
x and y Jointly Normally Distributed: The Correlation Model	p. 53
Problems	p. 58
Multiple Linear Regression	p. 67
Multiple Regression Models	p. 67
Estimation of the Model Parameters	p. 71
Least-Squares Estimation of the Regression Coefficients	p. 71
A Geometrical Interpretation of Least Squares	p. 81
Properties of the Least-Squares Estimators	p. 82
Estimation of [sigma superscript 2]	p. 82
Inadequacy of Scatter Diagrams in Multiple Regression	p. 84
Maximum-Likelihood Estimation	p. 85
Hypothesis Testing in Multiple Linear Regression	p. 87
Test for Significance of Regression	p. 87
Tests on Individual Regression Coefficients	p. 91
Special Case of Orthogonal Columns in X	p. 96
Testing the General Linear Hypothesis	p. 98
Confidence Intervals in Multiple Regression	p. 101
Confidence Intervals on the Regression Coefficients	p. 102
Confidence Interval Estimation of the Mean Response	p. 103
Simultaneous Confidence Intervals on Regression Coefficients	p. 104
Prediction of New Observations	p. 108
Hidden Extrapolation in Multiple Regression	p. 109
Standardized Regression Coefficients	p. 112
Multicollinearity	p. 117
Why Do Regression Coefficients have the Wrong Sign?	p. 120
Problems	p. 122
Model Adequacy Checking	p. 131
Introduction	p. 131
Residual Analysis	p. 132
Definition of Residuals	p. 132
Methods for Scaling Residuals	p. 132
Residual Plots	p. 138
Partial Regression and Partial Residual Plots	p. 146
Other Residual Plotting and Analysis Methods	p. 150
The PRESS Statistic	p. 152
Detection and Treatment of Outliers	p. 154
Lack of Fit of the Regression Model	p. 158
A Formal Test for Lack of Fit	p. 158
Estimation of Pure Error from Near-Neighbors	p. 162
Problems	p. 166
Transformations and Weighting to Correct Model Inadequacies	p. 173
Introduction	p. 173
Variance-Stabilizing Transformations	p. 174
Transformations to Linearize the Model	p. 178
Analytical Methods for Selecting a Transformation	p. 186
Transformations on y: The Box-Cox Method	p. 186
Transformations on the Regressor Variables	p. 189
Generalized and Weighted Least Squares	p. 193
Generalized Least Squares	p. 193
Weighted Least Squares	p. 195
Some Practical Issues	p. 196
Problems	p. 200
Diagnostics for Leverage and Influence	p. 207
Importance of Detecting Influential Observations	p. 207
Leverage	p. 209
Measures of Influence: Cook's D	p. 210
Measures of Influence: DFFITS and DFBETAS	p. 213
A Measure of Model Performance	p. 216
Detecting Groups of Influential Observations	p. 217
Treatment of Influential Observations	p. 218
Problems	p. 219
Polynomial Regression Models	p. 221
Introduction	p. 221
Polynomial Models in One Variable	p. 221
Basic Principles	p. 221
Piecewise Polynomial Fitting (Splines)	p. 228
Polynomial and Trigonometric Terms	p. 236
Nonparametric Regression	p. 237
Kernel Regression	p. 238
Locally Weighted Regression (Loess)	p. 239
Final Cautions	p. 243
Polynomial Models in Two or More Variables	p. 244
Orthogonal Polynomials	p. 253
Problems	p. 258
Indicator Variables	p. 265
The General Concept of Indicator Variables	p. 265
Comments on the Use of Indicator Variables	p. 279
Indicator Variables versus Regression on Allocated Codes	p. 279
Indicator Variables as a Substitute for a Quantitative Regressor	p. 280
Regression Approach to Analysis of Variance	p. 281
Problems	p. 287
Variable Selection and Model Building	p. 291
Introduction	p. 291
The Model-Building Problem	p. 291
Consequences of Model Misspecification	p. 292
Criteria for Evaluating Subset Regression Models	p. 296
Computational Techniques for Variable Selection	p. 302
All Possible Regressions	p. 302
Stepwise Regression Methods	p. 310
Some Final Recommendations for Practice	p. 317
Problems	p. 318
Multicollinearity	p. 325
Introduction	p. 325
Sources of Multicollinearity	p. 325
Effects of Multicollinearity	p. 328
Multicollinearity Diagnostics	p. 334
Examination of the Correlation Matrix	p. 334
Variance Inflation Factors	p. 337
Eigensystem Analysis of X'X	p. 339
Other Diagnostics	p. 343
Methods for Dealing with Multicollinearity	p. 345
Collecting Additional Data	p. 345
Model Respecification	p. 346
Ridge Regression	p. 348
Other Methods	p. 363
Comparison and Evaluation of Biased Estimators	p. 375
Problems	p. 378
Robust Regression	p. 382
The Need for Robust Regression	p. 382
M-Estimators	p. 386
Properties of Robust Estimators	p. 400
Breakdown Point	p. 400
Efficiency	p. 401
Survey of Other Robust Regression Estimators	p. 401
High-Breakdown-Point Estimators	p. 401
Bounded Influence Estimators	p. 406
Other Procedures	p. 407
Computing Robust Regression Estimators	p. 409
Problems	p. 410
Introduction to Nonlinear Regression	p. 414
Linear and Nonlinear Regression Models	p. 414
Linear Regression Models	p. 414
Nonlinear Regression Models	p. 415
Nonlinear Least Squares	p. 416
Transformation to a Linear Model	p. 420
Parameter Estimation in a Nonlinear System	p. 423
Linearization	p. 423
Other Parameter Estimation Methods	p. 431
Starting Values	p. 432
Computer Programs	p. 433
Statistical Inference in Nonlinear Regression	p. 434
Examples of Nonlinear Regression Models	p. 437
Problems	p. 438
Generalized Linear Models	p. 443
Introduction	p. 443
Logistic Regression Models	p. 444
Models with a Binary Response Variable	p. 444
Estimating the Parameters in a Logistic Regression Model	p. 447
Interpretation of the Parameters in a Logistic Regression Model	p. 450
Hypothesis Tests on Model Param6ters	p. 453
Poisson Regression	p. 459
The Generalized Linear Model	p. 466
Link Functions and Linear Predictors	p. 467
Parameter Estimation and Inference in the GLM	p. 468
Prediction and Estimation with the GLM	p. 472
Residual Analysis in the GLM	p. 474
Overdispersion	p. 475
Problems	p. 477
Other Topics in the Use of Regression Analysis	p. 488
Regression Models with Autocorrelation Errors	p. 488
Source and Effects of Autocorrelation	p. 488
Detecting the Presence of Autocorrelation	p. 489
Parameter Estimation Methods	p. 494
Effect of Measurement Errors in the Regressors	p. 500
Simple Linear Regression	p. 501
The Berkson Model	p. 502
Inverse Estimation--The Calibration Problem	p. 503
Bootstrapping in Regression	p. 508
Bootstrap Sampling in Regression	p. 509
Bootstrap Confidence Intervals	p. 510
Classification and Regression Trees (CART)	p. 516
Neural Networks	p. 518
Designed Experiments for Regression	p. 521
Problems	p. 524
Validation of Regression Models	p. 529
Introduction	p. 529
Validation Techniques	p. 530
Analysis of Model Coefficients and Predicted Values	p. 530
Collecting Fresh Data--Confirmation Runs	p. 532
Data Splitting	p. 534
Data from Planned Experiments	p. 545
Problems	p. 545
Statistical Tables	p. 549
Data Sets For Exercises	p. 567
Supplemental Technical Material	p. 582
Background on Basic Test Statistics	p. 582
Background from the Theory of Linear Models	p. 585
Important Results on SS[subscript R] and SS[subscript Res]	p. 588
The Gauss-Markov Theorem, Var([varepsilon]) = [sigma superscript 2]I	p. 594
Computational Aspects of Multiple Regression	p. 595
A Result on the Inverse of a Matrix	p. 597
Development of the PRESS Statistic	p. 598
Development of S[superscript 2 subscript (i)]	p. 600
An Outlier Test Based on R-Student	p. 601
The Gauss-Markov Theorem, Var([varepsilon]) = V	p. 604
The Bias in MS[subscript Res] When the Model is Underspecified	p. 606
Computation of Influence Diagnostics	p. 608
Generalized Linear Models	p. 610
References	p. 621
Index	p. 637
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