Methods and Applications of Linear Models: Regression and the Analysis of Variance / Edition 3

Hardcover (Print)
Buy Used
Buy Used from
(Save 41%)
Item is in good condition but packaging may have signs of shelf wear/aging or torn packaging.
Condition: Used – Good details
Used and New from Other Sellers
Used and New from Other Sellers
from $72.50
Usually ships in 1-2 business days
(Save 50%)
Other sellers (Hardcover)
  • All (13) from $72.50   
  • New (9) from $95.20   
  • Used (4) from $72.50   


The new edition of this "essential desktop reference book . . . [that] should definitely be on your bookshelf" (Technometrics) features a newly reorganized approach to linear regression that promotes the understanding of theory and models concurrently, featuring newly-developed topics in the field and the use of software applications. It includes:
• numerous exercises
• graphics and computations developed using JMP software
• a new chapter on recent developments with the distribution of linear and quadratic forms
• new topical coverage of least squares, the cell means model, and more

Read More Show Less

Editorial Reviews

A summary of the concepts and methodologies of linear models, containing chapter exercises and real-world examples. Offers a unified treatment of linear regression and the analysis of variance, focusing on the appropriate interpretation of results, with material on mixed models that has not previously appeared in the literature. Features a data-based approach to development and analysis, use of the cell means model, and an introduction to the AVE model. For upper-level undergraduate and graduate students . Annotation c. Book News, Inc., Portland, OR (
From the Publisher
“...presents a thorough treatment of the concepts and methods of linear model analysis and illustrates them with numerical and conceptual examples...” (Quarterly of Applied Mathematics, Vol. LXII, No. 1, March 2004)

" essential desktop reference should definitely be on your bookshelf." (Technometrics, Vol. 45, No. 4, November 2003)

Read More Show Less

Product Details

Meet the Author

RONALD R. HOCKING, PhD, is Professor Emeritus in the Department of Statistics and Founder of the Ronald R. Hocking Lecture Series at Texas A&M University. A Fellow of the American Statistical Association, Dr. Hocking is the recipient of numerous honors in the statistical community including the Shewell Award, the Youden Award, the Wilcoxon Award, the Snedecor Award, and the Owen Award.

Read More Show Less

Table of Contents

Preface to the Third Edition xvii

Preface to the Second Edition xix

Preface to the First Edition xxi


1 Introduction to Linear Models 3

1.1 Background Information, 3

1.2 Mathematical and Statistical Models, 5

1.3 Definition of the Linear Model, 8

1.4 Examples of Regression Models, 13

1.5 Concluding Comments, 21

Exercises, 21

2 Regression on Functions of One Variable 23

2.1 The Simple Linear Regression Model, 23

2.2 Parameter Estimation, 25

2.3 Properties of the Estimators and Test Statistics, 34

2.4 The Analysis of Simple Linear Regression Models, 39

2.5 Examining the Data and the Model, 50

2.6 Polynomial Regression Models, 63

Exercises, 72

3 Transforming the Data 81

3.1 The Need for Transformations, 81

3.2 Weighted Least Squares, 82

3.3 Variance Stabilizing Transformations, 85

3.4 Transformations to Achieve a Linear Model, 86

3.5 Analysis of the Transformed Model, 92

Exercises, 95

4 Regression on Functions of Several Variables 99

4.1 The Multiple Linear Regression Model, 99

4.2 Preliminary Data Analysis, 100

4.3 Analysis of the Multiple Linear Regression Model, 103

4.4 Partial Correlation and Added-Variable Plots, 113

4.5 Variable Selection, 119

4.6 Model Specification, 130

Exercises, 137

5 Collinearity in Multiple Linear Regression 142

5.1 The Collinearity Problem, 142

5.2 An Example with Collinearity, 150

5.3 Collinearity Diagnostics, 156

5.4 Remedial Solutions: Biased Estimators, 166

Exercises, 178

6 Influential Observations in Multiple Linear Regression 182

6.1 The Influential Data Problem, 182

6.2 The Hat Matrix, 183

6.3 The Effects of Deleting Observations, 188

6.4 Numerical Measures of Influence, 192

6.5 The Dilemma Data, 197

6.6 Plots for Identifying Unusual Cases, 201

6.7 Robust/Resistant Methods in Regression Analysis, 209

Exercises, 213

7 Polynomial Models and Qualitative Predictors 216

7.1 Polynomial Models, 216

7.2 The Analysis of Response Surfaces, 220

7.3 Models with Qualitative Predictors, 225

Exercises, 247

8 Additional Topics 254

8.1 Nonlinear Regression Models, 254

8.2 Nonparametric Model-Fitting Methods, 260

8.3 Generalized Linear Models, 265

8.4 Random Input Variables, 274

8.5 Errors in the Inputs, 276

8.6 Calibration, 277

Exercises, 278


9 Classification Models I: Introduction 285

9.1 Background Information, 285

9.2 The One-Way Classification Model, 286

9.3 The Two-Way Classification Model: Balanced Data, 304

9.4 The Two-Way Classification Model: Unbalanced Data, 322

9.5 The Two-Way Classification Model: No Interaction, 334

9.6 Concluding Comments, 347

Exercises, 347

10 The Mathematical Theory of Linear Models 359

10.1 The Distribution of Linear and Quadratic Forms, 359

10.2 Estimation and Inference for Linear Models, 368

10.3 Tests of Linear Hypotheses on β, 380

10.4 Confidence Regions and Intervals, 392

Exercises, 395

11 Classification Models II: Multiple Crossed and Nested Factors 405

11.1 The Three-Factor Cross-Classified Model, 406

11.2 A General Structure for Balanced, Factorial Models, 412

11.3 The Twofold Nested Model, 417

11.4 A General Structure for Balanced, Nested Models, 426

11.5 A Three-Factor, Nested-Factorial Model, 429

11.6 A General Structure for Balanced, Nested-Factorial Models, 434

Exercises, 438

12 Mixed Models I: The AOV Method with Balanced Data 443

12.1 Introduction, 443

12.2 Examples of the Analysis of Mixed Models, 444

12.3 The General Analysis for Balanced, Mixed Models, 464

12.4 Additional Examples, 479

12.5 Alternative Developments of Mixed Models, 487

Exercises, 493

13 Mixed Models II: The AVE Method with Balanced Data 499

13.1 Introduction, 499

13.2 The Two-Way Cross-Classification Model, 500

13.3 The Three-Factor, Cross-Classification Model, 511

13.4 Nested Models, 515

13.5 Nested-Factorial Models, 518

13.6 A General Description of the AVE Table, 524

13.7 Additional Examples, 531

13.8 The Computational Procedure for the AVE Method, 537

Exercises, 537

14 Mixed Models III: Unbalanced Data 543

14.1 Introduction, 543

14.2 Parameter Estimation: Likelihood Methods, 545

14.3 ML and REML Estimates with Balanced Data, 554

14.4 The EM Algorithm for REML Estimation, 558

14.5 Diagnostic Analysis with the EM Algorithm, 572

14.6 Models with Covariates, 581

14.7 Summary, 585

Exercises, 585

15 Simultaneous Inference: Tests and Confidence Intervals 591

15.1 Simultaneous Tests, 591

15.2 Simultaneous Confidence Intervals, 610

Exercises, 612

Appendix A Mathematics 615

A.I Matrix Algebra, 615

A.I.1 Notation, 615

A.I.2 The Rank of a Matrix, 616

A.I.3 The Trace of a Matrix, 617

A.I.4 Eigenvalues and Eigenvectors, 617

A.I.5 Quadratic Forms and Definite Matrices, 618

A.I.6 Special Matrices, 619

A.I.7 The Diagonalization of Matrices, 620

A.I.8 Kronecker Products of Matrices, 620

A.I.9 Factorization of Matrices, 621

A.I.10 Matrix Inversion, 622

A.I.11 The Solution of Linear Equations, 624

A.I.12 Generalized Inverses, 627

A.I.13 Cauchy–Schwartz Inequalities, 630

A.II Optimization, 630

A.II.1 The Differentiation of Matrices and Determinants, 630

A.II.2 The Differentiation of a Function with Respect to a Vector, 631

A.II.3 The Optimization of a Function, 632

Appendix B Statistics 634

B.I Distributions, 634

B.I.1 The Normal Distribution, 634

B.I.2 The χ2-Distribution, 637

B.I.3 The t-Distribution, 638

B.I.4 The F-distribution, 639

B.II The Distribution of Quadratic Forms, 639

B.III Estimation, 642

B.III.1 Maximum Likelihood Estimation, 642

B.III.2 Constrained Maximum Likelihood Estimation, 642

B.III.3 Complete, Sufficient Statistics, 643

B.IV Tests of Hypotheses and Confidence Regions, 643

B.IV.1 Tests of Hypotheses, 643

B.IV.2 Confidence Intervals and Regions, 644

Appendix C Data Tables 645

C.I Downloading Data Files from FTP Server, 645

C.II Listing of Data Set Files, 645

Appendix D Statistical Tables 660

References 669

Index 677

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)