Math 439 - Linear Statistical Models - Fall 2006

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

 Topics covered:

Multivariate data;  review of linear algebra;  covariance and correlation matrices;  multivariate normal distributions;  linear statistical models with normal errors;  regression models and ANOVAs using the distributions of quadratic forms;  principal components models;  multivariate (vector-valued) Student-t tests, linear regressions, and ANOVAS (ANOVAS with vector-valued data are called MANOVAS);  and other topics as time permits.
SAS will be used for examples and homework problems.
Prerequisites: A course in linear algebra, such as Math 309 or 429 at WashU, and a course in statistics that includes regression, such as Math 320.
Textbooks: Applied Multivariate Statistical Analysis
by R. A. Johnson and D. W. Wichern, 5th edition, Prentice Hall, 2002.
Time and Location: Tuesday-Thursday 2:30-4:00pm   --   Cupples I  Room 207
See Final Exam below for information about the final examination.
Professor: Prof. S. Sawyer   --   Cupples I  Room 107
Phone: (314) 935-6703   --   Send an email
Office Hours: MW 3:00-4:00pm    Office:  Rm 107 Cupples I
(call or email first to be sure since I may have a conflict)
(if these times aren't convenient, send me an email and we can set another time)
Midterm Examination: There will be an examination in class on Thursday, October 26 (2:30-4:00pm)
Links: Take-Home Final due Thu 12-21 by 5:30PM
Homework Assignments
SAS programs covered or to be covered in class
Guide to using SAS    (PDF format)
Multivariate Linear Models handout    (PDF format)
Other Handounts
Click here for Professor Sawyer's home page
Reference Books, including books for reviewing statistics and linear algebra

Exams, Homework Sets, and Grades:
        There will be around five homework sets, the inclass midterm, and a final. Grades will be based on on the homework sets (around 40%), the midterm (around 20%), and the final (around 40%). Cr means D or better if you elect ``Credit/No Credit.''

Final Examination:
        There will be a Take-Home final examination. This will be posted on the Math 439 Web site on the weekend before Reading Period (that is, before Monday, December 11) and will be due Thursday, December 21 before 5:30 PM. However, you can turn it in earlier if you choose.

Collaboration:
        Collaboration on homework is allowed and can be helpful (and fun). However, you must do all written work yourself. If you use SAS on a problem, you must write the SAS program and enter and run it yourself.
        Note: If you collaborate with someone on a homework, list his or her name in a note at the top of the first part of your homework.

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

WARNING:
        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).

Problems:
        If a problem asks you to do a statistical test, EXPLAIN CLEARLY what the null hypothesis H_0 is, what test you used, what the P-value is, and whether the data is significant, highly significant, or neither. If you use SAS, include this as part of your answer in part (i) below.

USING SAS:

SAS PROGRAMS AND ASSIGNMENTS:
        If you use SAS to do a homework problem, then both the SAS program and output must be included as part of the homework that you turn in.
        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.
        If a homework uses SAS, then it MUST BE ORGANIZED in the following order:
       

  • (i) First, your answers to all the problems in the homework, whether they use SAS or not. If you use a computer package to do a homework problem, you must explain your answers in English. If a homework problem asks for a table or a graph, give a page number to later in your homework (see below).
           
  • (ii) 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. (You can 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 statements to separate the problems in your output.)
           
  • (iii) Third, all output for all the SAS programs in the previous step. You should write consecutive page numbers on the output for use in part (i) if the page numbers supplied by SAS in the output are not consecutive.

            If an answer to a problem in part (i) requires a table or a plot, add page numbers to your homework and make references in part (i) by page number, such as ``The scatterplot for part (b) is on page #X in the SAS output below.'' Alternatively, you could Xerox a page or two of your SAS output and include it in part (i) along with annotations as well as in part (iii), but references by page number will usually be enough.

            SAS programs may be graded for understandability. 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.

    REFERENCES:

    A good book for reviewing Linear Algebra and Matrix Theory:
            Bernard Kolman and David Hill, Elementary Linear Algebra, 8th edition, Pearson/Prentice Hall, 2004, ISBN 0-13-045787-6
            This book has been used to teach Math 309 at WashU.

    A good book for Linear Algebra and Statistics:
            Shayle R. Searle, Matrix Algebra Useful for Statistics, John Wiley and Sons, 1982.

    Some good books for reviewing Elementary Statistics:
            R. L. Iman, A Data-Based Approach to Statistics. Duxbury Press, 1994.
            A. J. Tamhane and D. D. Dunlop, Statistics and Data Analysis from Elementary to Intermediate, Prentice-Hall, 2000.
            Both books have been used as textbooks in Math 320 at WashU. The second book (Tamhane et al) is drier but deeper.

    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 the precise statement and proofs of theorems and extensions beyond what is in the text.

    Click here for Professor Sawyer's home page:

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    Last modified December 11, 2006