STAT 740: LINEAR STATISTICAL MODELS I

COURSE OUTLINE

FALL 2008

Instructor: Paul J. Smith, Statistics Program

Office: MTH 1107

Telephone: (301) 405-5061

E-mail: pjs@math.umd.edu

Schedule: Fall 2008, MWF 10, MTH 0302

Textbook: Rencher, A. C. & Schaalje, G. B. (2008). Linear Models in Statistics. (2nd ed.) New York: J. Wiley.

Prerequisites: STAT 420 or STAT 700.

The goal of applied statistics is to model relationships between variables and to perform inferences on real world situations based on statistical models. Regression analysis and analysis of variance are the main techniques to model quantitative response variables; these are examples of linear statistical models, in which a response variable is modeled as a linear function of predictors plus a random error term. Linear models are analyzed using least squares, nowadays using statistical software packages like SAS or R/S-Plus.

STAT 740-741 is a year long sequence dealing with linear models and some of their extensions. The material covered in these courses is central to applied statistical methodology and is also part of the Graduate Written Examination in Applied Statistics. The first semester deals mainly with least squares, regression analysis and basic analysis of variance models. The second semester deals with more complex analysis of variance models, random and mixed effects models, and generalized linear models for discrete response variables.

These courses are primarily applied, although theoretical topics will be treated as necessary. Data analysis and interpretation are an essential component of the course, and students will analyze real world data sets using the SAS statistical computing package.

STAT 740 Topics:

Linear Statistical Models: Motivating examples: straight line regression and comparison of group means. General linear model: matrix formulation, geometric formulation, least squares, estimable functions. Confidence sets, tests of linear hypotheses under normality, connection with likelihood-based methods. Review of normal-theory sampling distributions as required.
Regression Analysis: Model formulation, least squares estimates, distribution theory, ANOVA table. Introduction to SAS procedures for regression. Multiple regression, tests and confidence sets. Analysis of residuals, graphical diagnostics, assessment of model fit. Special regression models: polynomial regression and dummy variables.
Introduction to Analysis of Variance: Comparison of means and one way analysis of variance (ANOVA), full rank and reduced rank models, estimable functions and contrasts, multiple comparisons, use of SAS. Two way ANOVA, interaction.
Nonlinear Least Squares: Distribution theory, computational issues, reparameterization.

Examinations and Grading

Midterm: Friday, October 24.

Final: Saturday, December 20, 8-10 a.m.

Homework: Frequent problem sets will be assigned. These will be a mix of theoretical and applied problems involving analysis of real data sets on the computer. Click here for homework assignments.

Grading: The midterm and final will each count for approximately 30% of the grade and the homework will count for approximately 40%.

References

Cody, R. P. and Smith, J. K. (2006).   Applied Statistics and the SAS Programming Language (5th ed.) Upper Saddle River, NJ: Prentice-Hall.
Daniel, C. and Wood, F. S. (1980).   Fitting Equations to Data (2nd ed.) New York: J. Wiley.
Draper, N. R. and Smith, H. (1998).   Applied Regression Analysis (3rd ed.) New York: J. Wiley.
Hocking, R. (1996).    Methods and Applications of Linear Models.   New York: J. Wiley.
McCullagh, P. and Nelder, J. A. (1989).   Generalized Linear Models. (2nd ed.) New York: Chapman and Hall.
McCulloch, C. E., Searle, S. R. and Neuhaus, J. M. (2008).   Generalized, Linear and Mixed Models. (2nd ed.) New York: Wiley.
Milliken, G. and Johnson, D. (1984).    Analysis of Messy Data, Vol. I: Designed Experiments.   New York: Van Nostrand Reinhold.
Rao, P. S. R. S. (1997).    Variance Components Estimation.   New York: Chapman and Hall.
Scheffe, H. (1958).    The Analysis of Variance.   New York: J. Wiley.
Searle, S. R., Casella, G. and McCulloch, C. E. (1992).    Variance Components.   New York: J. Wiley.
Stapleton, J. H. (1995).    Linear Statistical Models.   New York: J. Wiley.