STAT 740: LINEAR STATISTICAL MODELS I

COURSE OUTLINE

FALL 2021

Instructor: Paul J. Smith, Statistics Program

Office: MTH 4404

E-mail: pjs@umd.edu

Schedule: MWF 2, MTH 0409.

Office hours: By arrangement using Zoom

Textbooks:

Faraway, J. J. (2005) Linear Models with R. (2nd ed.) Boca Raton, FL: Chapman & Hall/CRC. A preliminary version of the first edition of this book is available on the web here.

Agresti, A. (2015) Foundations of Linear and Generalized Linear Models. Hoboken, NJ: J. Wiley.

Prerequisites: STAT 420 or STAT 700. You will be expected to be proficient with topics in matrix and linear algebra, including orthogonal projection, eigenvalues and eigenvectors.

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 common 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, graphics and interpretation are an essential component of the course, and students will analyze real world data sets, principally using the R statistical computing package (although students may choose to use other packages instead).

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 R procedures for data summary, graphics and regression. Multiple regression, tests and confidence sets. Analysis of residuals, graphical diagnostics, assessment of model fit. Special regression models: polynomial regression and dummy variables. Alternatives to least squares.
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 R. Balanced two way ANOVA, interaction.

Examinations and Grading

Midterm: Friday, October 15, 2:00-2:50 p.m. (tentative), on line.

Final: Saturday, December 18, 1:30-3:30 p.m., MTH 0409.

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

Clarke, B. R. (2008).   Linear Models Hoboken, NJ: J. Wiley.
Cody, R. P. and Smith, J. K. (2006).   Applied Statistics and the SAS Programming Language (5th ed.) Upper Saddle River, NJ: Prentice-Hall.
Christensen, R. (2002).   Plane Answers to Complex Questions: The Theory of Linear Models. (3rd ed.) New York: Springer.
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. (2009).    Analysis of Messy Data, Vol. I: Designed Experiments.   (2nd ed.) New York: CRC Press.
Monahan, J. F. (2008).    A Primer on Linear Models. CRC/Chapman & Hall.
Rencher, A. C. & Schaalje, G. B. (2008).    Linear Models in Statistics.  (2nd ed.) New York: J. Wiley.
Scheffe, H. (2008)   The Analysis of Variance.   Hoboken, NJ: J. Wiley.
Searle, S. R., Casella, G. and McCulloch, C. E. (1992).    Variance Components.   New York: J. Wiley.
Stapleton, J. H. (2009).    Linear Statistical Models.   (2nd ed.) New York: J. Wiley.
Venables, W. N. & Ripley, B. D. (2002).    Modern Applied Statistics with S. (4th ed.) New York: Springer.

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