Methods and Applications of Linear Models

Methods and Applications of Linear Models provides a clear and concise summary of the concepts and methodologies of linear models and illustrates the analysis with numerous exercises and real-world examples. Special features include:

• Data sets available on an ftp site
• Graphical illustrations of many of the analyses
• A data-based approach to development and analysis
• Graphical and numerical diagnostic methods in regression
• Use of the cell means model for the analysis of variance
• The introduction of the AVE method for variance component estimation
• A general approach to the analysis of unbalanced mixed models

This novel approach to linear model analysis offers a unified treatment of linear regression and the analysis of variance. The focus is on the appropriate interpretation of results. Carefully chosen examples illustrate the analyses and some of the common sources of confusion in the application of the methods. The treatment of mixed models includes material that has not previously appeared in the literature.

For upper-level undergraduate and graduate students of regression and the analysis of variance, this volume provides simple explanations of the basic methodologies. It is also a valuable professional reference for applied statisticians and researchers.Ronald R. Hocking is Professor Emeritus in the Department of Statistics at Texas A&M University. He received his PhD in mathematics and statistics and is a Fellow of the American Statistical Association.

* Includes material on the AVE method and explains existing information in an even more user-friendly form.

* Includes additional exercises.

* Describes a general approach to the analysis of unbalanced mixed models

* Uses data-based approach to development and analysis.

* An Instructor's Manual presenting detailed solutions to all the problems in the book is available upon request from the Wiley editorial department.

The ready availability of high-speed computers and statistical software encourages the analysis of ever larger and more complex problems while at the same time increasing the likelihood of improper usage. That is why it is increasingly important to educate end users in the correct interpretation of the methodologies involved. Now in its second edition, Methods and Applications of Linear Models: Regression and the Analysis of Variance seeks to more effectively address the analysis of such models through several important changes. Notable in this new edition:

• Fully updated and expanded text reflects the most recent developments in the AVE method
• Rearranged and reorganized discussions of application and theory enhance text’s effectiveness as a teaching tool
• More than 100 new exercises in the areas of regression and analysis of variance

As in the First Edition, the author presents a thorough treatment of the concepts and methods of linear model analysis, and illustrates them with various numerical and conceptual examples, using a data-based approach to development and analysis. Data sets, available on an FTP site, allow readers to apply analytical methods discussed in the book.

Preface to the First Edition.

PART I: REGRESSION MODELS.

Introduction to Linear Models.

Regression on Functions of One Variable.

Transforming the Data.

Regression of Functions of Several Variables.

Collinearity in Multiple Linear Regression.

Influential Observations in Multiple Linear Regression.

Polynomial Models and Qualitative Predictors.

Additional Topics.

PART II: ANALYSIS OF VARIANCE MODELS.

Introduction to Analysis of Variance Models.

Fixed Effects Models I: One-Way Classification of Means.

Fixed Effects Models II: Two-Way Classification of Means.

Fixed Effects Models III: Multiple Crossed and Nested Factors.

Mixed Models I: The AOV Method with Balanced Data.

Mixed Models II: The AVE Method with Balanced Data.

Mixed Models III: Unbalanced Data.

PART III: MATHEMATICAL THEORY OF LINEAR MODELS.

Distribution of Linear and Quadratic Forms.

Estimation and Inference for Linear Models.

Simultaneous Inference: Tests and Confidence Intervals .

Appendix A. Mathematics.

Appendix B. Statistics.

Appendix C. Statistical Tables.

Appendix D. Data Tables.

References.

Index.