Linear models : the theory and application of analysis of variance / Brenton R. Clarke.
This graduate-level book succinctly describes the role of analysis of variance (ANOVA) in the study of linear models. Applications to linear regression (both simple and multiple) and to experimental design are included in order to help explain the theory behind and the analysis of ANOVA techniques.
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| Main Author: | |
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| Format: | Ebook |
| Language: | English |
| Published: |
Hoboken, N.J. :
Wiley,
[2008]
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| Series: | Wiley series in probability and statistics.
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| Subjects: | |
| Online Access: | Wiley Online Library Table of contents Publisher description |
| Summary: | This graduate-level book succinctly describes the role of analysis of variance (ANOVA) in the study of linear models. Applications to linear regression (both simple and multiple) and to experimental design are included in order to help explain the theory behind and the analysis of ANOVA techniques. Linear Models explores the theory of linear models and the dynamic relationships that these models have with Analysis of Variance (ANOVA), experimental design, and random and mixed-model effects. This one-of-a-kind book emphasizes an approach that clearly explains the distribution theory of linear models and experimental design starting from basic mathematical concepts in linear algebra. The author begins with a presentation of the classic fixed-effects linear model and goes on to illustrate eight common linear models, along with the value of their use in statistics. From this foundation, subsequent chapters introduce concepts pertaining to the linear model, starting with vector space theory and the theory of least-squares estimation. An outline of the Helmert matrix is also presented, along with a thorough explanation of how the ANOVA is created in both typical two-way and higher layout designs, ultimately revealing the distribution theory. Other important topics covered include: vector space theory, the theory of least squares estimation, Gauss-Markov theorem, Kronecker products, diagnostic and robust methods for linear models; and likelihood approaches to estimation. A discussion of Bayesian theory is also included for purposes of comparison and contrast, and numerous illustrative exercises assist the reader with uncovering the nature of the models, using both classic and new data sets. Requiring only a working knowledge of basic probability and statistical inference, Linear Models is a valuable book for courses on linear models at the upper-undergraduate and graduate levels. It is also an excellent reference for practitioners who use linear models to conduct research in the fields of econometrics, psychology, sociology, biology, and agriculture. |
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| Physical Description: | 1 online resource (xviii, 241 pages) : illustrations. |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 0470025662 9780470025666 |