Math 6266

Spring 1999

Professor Spruill

Office hours: Mon. 10-11 A.M., Weds. 11-12 A.M.

Your grade for the course will be determined by your performance on a midterm exam, a final exam, and problem sets. Each will count one third.

Text (optional) : A Course in Probability and Statistics, by C. Stone, Duxbury.

• Problems I
• Vector and inner product spaces
• Change of Bases
• Distributions

Some References
(1) Albert,A. Regression and the Moore-Penrose Pseudoinverse 
(2) Arnold, Steven F.  The Theory of Linear Models and Multivariate Analysis.
(3) Graybill,F. Theory and Application of the Linear Model
(4) Hicks, C. Fundamental Concepts in the Design of Experiments
(5) Hogg,R. and Craig,A. Introduction to Mathematical Statistics
(6) Rao,C.R. Linear Statistical Inference
(7) Scheffe, H. The Analysis of Variance

Summary of Topics for Linear Statistical Models

Examples of statistical problems covered by the general linear model including regression, ANOVA, and ANCOVA; geometry, projections, and the Moore-Penrose inverse; estimability, the Gauss-Markov theorem, least squares estimators; testing linear hypotheses, distributional results for the likelihood ratio and the Wald statistic, application of results to data sets through canned programs like SAS and through Matlab or other specialized programs; traditional formulas via Cochran's theorem; individual comparisons.

• Some data sets
  • Example 0.1 .
  • Example 0.2 .
  • Example 0.4 .
  • A three way classification where the columns contain, from left to right, the levels of factors A, B, C, and the observation of the variable Y. Find, if possible, a parsimonious model which yields good predictions of the variable Y given the levels of the other factors.
  The final homework grade distribution is 0 87 101 114 122 165 165 167 177 187 199 202 203.