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Regression and ANOVA: An Integrated Approach Using SAS Software

ISBN: 978-0-471-46943-8
592 pages
June 2003
Regression and ANOVA: An Integrated Approach Using SAS Software (0471469432) cover image
The information contained in this book has served as the basis for a graduate-level biostatistics class at the University of North Carolina at Chapel Hill. The book focuses in the General Linear Model (GLM) theory, stated in matrix terms, which provides a more compact, clear, and unified presentation of regression of ANOVA than do traditional sums of squares and scalar equations.

The book contains a balanced treatment of regression and ANOVA yet is very compact. Reflecting current computational practice, most sums of squares formulas and associated theory, especially in ANOVA, are not included. The text contains almost no proofs, despite the presence of a large number of basic theoretical results. Many numerical examples are provided, and include both the SAS code and equivalent mathematical representation needed to produce the outputs that are presented.

All exercises involve only "real" data, collected in the course of scientific research. The book is divided into sections covering the following topics:
* Basic Theory
* Multiple Regression
* Model Building and Evaluation
* ANOVA
* ANCOVA
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Preface.

Examples and Limits of the GLM.

Statement of the Model, Estimation, and Testing.

Some Distributions for the GLM.

Multiple Regression: General Considerations.

Testing Hypotheses in Multiple Regression.

Correlations.

GLM Assumption Diagnostics.

GLM Computation Diagnostics.

Polynomial Regression.

Transformations.

Selecting the Best Model.

Coding Schemes for Regression.

One-Way ANOVA.

Complete, Two-Way Factorial ANOVA.

Special Cases of Two-Way ANOVA and Random Effects Basics.

The Full Model in Every Cell (ANCOVA as a Special Case).

Understanding and Computing Power for the GLM.

Appendix A. Matrix Algebra for Linear Models.

Appendix B. Statistical Tables.

Appendix C. Study Guide for Linear Model Theory.

Appendix D. Homework and Example Data.

Appendix E. Introduction to SAS/IML.

Appendix F. A Brief Manual to LINMOD.

Appendix G. SAS/IML Power Program User's Guide.

Appendix H. Regression Model Selection Data.

References.

Index.

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Keith E. Muller, Ph.D., is Associate Professor of Biostatistics at the University of North Carolina at Chapel Hill. He teaches classes and seminars in the theory and practice of univariate and multivariate linear models with Gaussian errors. A SAS user since 1978, he is best known for his contributions to theory and practice of sample size and power calculations, including SAS/IML programs for power in repeated measures.

Bethel A. Fetterman, M.S., is Director of Clinical Data Processing and Analysis at PharmaLinkFHI in Research Triangle Park, North Carolina. She is currently on leave from the doctoral program in Biostatistics at the University of North Carolina at Chapel Hill. A SAS user since 1989, she uses SAS software in designing, managing, analyzing, and reporting clinical trials of new pharmaceutical.

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“…very useful to applied scientists and for graduate level courses in areas of non-mathematical statistics…” (Zentralblatt Math, Vol.1039, No.8, 2004)
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