Multivariate Statistics: Concepts, Models, and Applications
David W. Stockburger

About Multivariate Statistics: Concepts, Models, and Applications

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The book, Multivariate Statistics: Concepts, Models, and Applications, is an extension of my web text, Introductory Statistics: Concepts, Models, and Applications. An understanding of the concepts presented in the introductory text is necessary to grasp the concepts presented in this text. In my one-semester graduate course, I spend the first third of the course reviewing the material in the introductory text. The book is designed for the last two-thirds of a one-semester course in multivariate statistics for first year graduate or advanced undergraduates.

It has been said that some texts are written to impress one's colleagues and others are written for students. This one is written for students. It is neither a mathematical treatise nor a cookbook. Instead of complicated mathematical proofs I have attempted to write a book about mathematical ideas. I have substituted examples for proofs and require that the reader "believe!" on more than one occasion. The result is a text that can be understood by students. A grasp of the fundamental ideas presented in this text will prepare the student for a much more thorough treatment of multivariate statistics in a later course.

In some ways I hesitate to call this a "multivariate" text. Univariate statistical methods are expanded gradually, first thoroughly exploring bivariate statistical methods (linear transformations with two variables, multiple regression with two independent variables) and culminating with multiple regression models. Analysis of Variance is approached as a special case of multiple regression. The goal is to provide a path from the simple case leading to the complex. The complex case is rarely presented in this text. The issues surrounding the complex case, however, will be familiar to any reader who masters this material.

In the summer of 1996 I attended a four-week multivariate statistics course in Ann Arbor, Michigan. The textbook used for the course was Johnson and Wickren's (1992) Multivariate Statistics. I watched as my fellow graduate students (some of the best from around the world) struggled with matrix theory and operations. I knew that as much as I would like to teach my graduate statistics course in a similar manner, most of my students simply did not have the mathematical background to deal with a course of this level of difficulty. This text is an attempt to explain multivariate statistical concepts in a way that is accessible to graduate students with a background of a single undergraduate statistics course.

This is not an argument against a matrix approach to multivariate statistics. In many ways, I believe that only through matrix operations can the interrelationships between the various multivariate methods be truly appreciated. My goal is to present the material in a manner such that the student can develop a feeling about what and how the various multivariate statistical methods achieve their goal. My hope is that I can treat the material in such a way that the student who wants to go on is better prepared for the experience.

My guess is that students will use this text in an unofficial capacity more often than an official one. If so, I have partially succeeded in my goal.

The major features of the text include:

• An emphasis on mathematical concepts.
• Use of interactive graphics to illustrate multivariate concepts. For example, by rotating a two-dimensional scatterplot and examining the effect on the variances of the resulting variables, the idea of what eigenvectors and eigenvalues mean becomes clear. The ability to view a three-dimensional scatterplot with a plane drawn through the points illustrates conceptually how multiple regression models work.
• There are numerous small assignments associated with each chapter. Each assignment is designed to illustrate a single concept. The assignments are individualized for each student and presented as web pages. Active server programs grade the assignments and return an answer key.

## Restrictions

The following books are placed in the public domain and may be copied with the following restrictions:

• The restrictions must be posted with the work.
• No profit may be made from the works.
• If any portion of the materials is used I must appear as an author.
• If over fifty percent of the completed work is from the following sources I must appear as first author.

Enjoy,
David W. Stockburger