Math 439 - Linear Statistical Models - Fall 2010

Statistical methods based on linear algebra --- Prof. Stanley Sawyer

 Topics covered:

Review of matrix theory relevant for the course;  multivariate data;  multivariate normal distributions;  (univariate) multiple linear regressions;  multivariate two-sample and multiple-sample tests (Hotelling's T2 test and MANOVAs);  principal component analysis;  linear discriminant models;  multivariate linear regressions;  canonical correlations;  other topics as time permits.
The computer package SAS will be used for examples and homework problems.
Prerequisites: Math 3200 (or permission of the instructor) and a course in linear algebra, such as Math 309 or 429
Textbook: Methods of Multivariate Analysis, 2nd edn,
by A. C. Rencher, Wiley, 2002   ISBN 978-0471-418894   Old ISBN: 0-471-41889-7 (cloth)
Time and Location: Tues,Thurs 2:30-4:00pm   ---   Eads  Rm 215
Professor: Prof. S. Sawyer   --   Cupples I  Room 107
Phone: (314) 935-6703   --   Send email to Prof Sawyer
Office Hours: MW 3:00-4:00pm    Office:  Rm 107 Cupples I
(Warning: call or email me first to make sure since I may have a conflict.)
(If these times aren't convenient, send me an email and we can set another time,
  or drop by my office anytime I am not talking to someone else.)
Links: Homework Assignments
TAKE-HOME FINAL   DUE  Wed Dec 22, 2010 by 5:30 PM
SAS programs covered or to be covered in class
Guide to using SAS
Notes on using SAS in the ArtSci Computing Lab
Multivariate Linear Models handout
Other handouts that you might find interesting
Click here for Professor Sawyer's home page
Click here for Math 475 home page
Reference Books, including books for reviewing statistics and linear algebra

        There will be four homework sets, an in-class midterm on Tuesday, October 26, and a take-home final. Grades will be based on the homework sets (around 50%), on the midterm (around 20%), and on the takehome final (around 30%). The takehome final will be due on or before Wednesday, December 22. Cr means D or better if you elect ``Credit/No Credit.''

        Collaboration on homework is allowed and can be helpful (and fun). Collaboration on homework is encouraged, both for using the computer and for doing problems. However, you must do all written work by yourself, both computer programs and answers to homework questions. You must also write, enter, and run all programs yourself.
        If you collaborate with someone on a homework, list his or her name in a note at the top of the first page of your homework.

        There should be NO COLLABORATION on takehome tests, other than for the mechanics of using the computer.

        Make a copy of each homework before you hand it in !!
        It may not be returned before you need to refer to it for the next homework (or for the next test).

        If a problem asks you to do a statistical test, EXPLAIN CLEARLY what the problem is and what your answer is. Your answer should include what the null hypothesis H_0 is, what test you used, what the implicit alternative H_1 is for this test, what the P-value is, and whether the data is significant, highly significant, or neither for this hypothesis and test. If you use SAS or a comparable computer program, hand in your homework in the format described below.

        If you use SAS to do a homework problem, then the SAS program and output MUST BE INCLUDED as part of the assignment.
        ALWAYS INCLUDE YOUR NAME in a title statement in your SAS programs, so that your name will appear at the top of each output page.
        ALL HOMEWORKS MUST BE ORGANIZED in the following order:
        (Part 1) First, your answers to all the problems in the homework, whether you use SAS for that problem or not. If the problem asks you to generate a graph or table, refer to the graph or table by page number in the SAS output (see below). Xeroxing a page or two from the SAS output or cutting and pasting into a Word file or TeX source file is also OK, but forward references by page number will usually be sufficient.
        (Part 2) Second, all SAS programs that you used to obtain the output for any of the problems. If possible, similar problems should be done with the same SAS program. (In other words, write one SAS program for several problems if that makes things easier. Better yet would be one SAS program for the entire homework with appropriate title or title2 statements to separate the problems in your output.)
        (Part 3) Third, all output for all the SAS programs in the previous step.
        NOTE: If an answer in Part 1 requires a table or a plot that you need to refer to, make sure that your SAS output has overall increasing (unique) page numbers and make references to Part 3 by page number, such as ``The scatterplot for Problem 2 part (b) is on page #X in the SAS output below.''
        MAKE SURE that the page numbers in your SAS output has increasing page numbers. If you do the entire homework in one SAS file, SAS will provide increasing page numbers in the output. DO NOT say, ``see Page 3 in the SAS output'' if Part 3 has output from several SAS runs, each of which has its own Page 3. In that case, you can either write your own (consecutive, increasing) page numbers on the SAS output, or else (for example) refer to ``Page 2-7 in the SAS output'' (for page 7 in the second set of SAS output) and write page numbers in the format ``2-7'' at the top of pages in your output. Remember that if I can't find your SAS output for a particular question, I can't give you as much partial credit!
        SAS programs should be structured, or have enough comments, so that someone who looks at the program a year from now can easily tell what the program is doing. It is even better if descriptive comments can be put in title (or title2 or title3) statements, since these will appear in the SAS output as well as in the SAS program. SAS programs may be graded for understandability.

REFERENCE BOOKS: A good book for reviewing statistics:
        A. J. Tamhane and D. D. Dunlop, Statistics and Data Analysis from Elementary to Intermediate, Prentice-Hall, 2000.
        This books is often used as the textbook forn Math 3200 at WashU.

Some useful references on using SAS:
        Using the SAS Windowing Environment: A Quick Tutorial, L. Hatcher, SAS Institute Press, 2001.
        The Little SAS Book, Lora Delwiche & Susan Slaughter, SAS Institute Press, 1995.

An excellent advanced book on multivariate statistics:
        T. W. Anderson, An Introduction to Multivarite Statistical Analysis, 3rd edition, John Wiley, 2003.
        This is a good source for more detailed proofs of theorems, proofs of deeper results, and extensions beyond what is in the text.

Click here for Professor Sawyer's home page:

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    Last modified December 14, 2010