Linear Statistical Models

Linear Statistical Models Developed and refined over a period of twenty years, the materialin this book offers an especially lucid presentation of linearstatistical models. These models lead to what is usually called"multiple regression" or "analysis of variance" methodology, which,in turn, opens up a wide range of applications to the physical,biological, and social sciences, as well as to business,agriculture, and engineering. Unlike similar books on this topic,Linear Statistical Models emphasizes the geometry of vector spacesbecause of the intuitive insights this approach brings to anunderstanding of the theory. While the focus is on theory, examplesof applications, using the SAS and S-Plus packages, are included.Prerequisites include some familiarity with linear algebra, andprobability and statistics at the postcalculus level. Major topics covered include: * Methods of study of random vectors, including the multivariatenormal, chi-square, t and F distributions, central and noncentral * The linear model and the basic theory of regression analysis andthe analysis of variance * Multiple regression methods, including transformations, analysisof residuals, and asymptotic theory for regression analysis.Separate sections are devoted to robust methods and to thebootstrap. * Simultaneous confidence intervals: Bonferroni, Scheffe, Tukey,and Bechhofer * Analysis of variance, with two- and three-way analysis ofvariance * Random component models, nested designs, and balanced incompleteblock designs * Analysis of frequency data through log-linear models, withemphasis on vector space viewpoint. This chapter alone issufficient for a course on the analysis of frequency data.