Mathematics 304/604-01 - Linear Models

Instructor: John Liukkonen
Office: 405 Gibson Hall
Telephone: 862-3440
E-mail: jrl@math.tulane.edu

Course Description

The course consists of two parts. We first develop the theoretical and conceptual background for linear regression, based upon the classical Gauss-Markov assumptions of independent normal errors with equal variances. In particular we will review the linear algebra of orthogonality, orthogonal projections, and least squares solutions to overdetermined systems. Next we will go over the multivariate normal distribution and see how chi-squared, t, and F distributions arise from a multivariate normal distribution. Using all this we will develop all the standard tests and confidence intervals for linear regression in the classical Gauss-Markov context.

We will then move to regression diagnostics, in which we go through graphical and other techniques aimed at checking the whether the Gauss-Markov assumptions hold for specific data sets, and at remediating deviations from these assumptions. This part of the course will include several data analysis problems to be using SAS, S-Plus, R, or other major statistical package. No previous experience with such a package is necessary.

Prerequisites

Math 301/601(Introduction to Probability and Statistics) or equivalent
Math 309 (Linear Algebra) or equivalent.

Course Materials

Textbook: Weisberg, Applied Linear Regression
Optional SAS Computer Reference: Elliott, Learning SAS in the Computer Lab
Optional SAS Computer Reference: Littell, Freund, and Spector, SAS System for Linear Models
Optional S-Plus or R Computer Reference: Fox, An R and S-Plus Companion to Applied Regression
Optional S-Plus or R Computer Reference: Venables and Ripley, Modern Applied Statistics with S
Optional Linear Algebra Reference: Strang, Linear Algebra with Applications, Ch 3, on reserve in math library
Background Notes: handed out in class, and also available here: Click here

Note: To use this link you will need Acrobat Reader, available by free download from www.adobe.com.

Final Exam:

Sunday May 9 from 8AM to noon.

Tests:

Wednesday, February 18
Wednesday, April 7

Homework:

This will include data analysis assignments and count 40% of your grade. The assignments will be posted here as the term goes on.

Note: The problem set files are pdf files and so require Acrobat Reader.

Problem Set I due January 23. To view, click here.
Problem Set II due February 6. To view, click here.
Problem Set III, due February 16. To view, click here.

Data Analysis Assignment I, due March 8. To view, click here.
Data Analysis Assignment II, due March 15. To view, click here.
Data Analysis Assignment III, due March 24. To view, click here.
Data Analysis Assignment IV, due April 5. To view, click here.
Data Analysis Assignment V, due April 23. To view, click here.

Data Sets

Here are data sets for problems from Weisberg's text. They are text files (not requiring Acrobat Reader); you should save them to your directory for use in the data analysis assignments.

Exercise 1.1	Exercise 1.2	Forbes Data
Exercise 2.1, boys, part I	Exercise 2.1, boys, part II	Exercise 2.1, girls, part I
Exercise 2.1, girls, part II	Exercise 2.8	Exercise 4.6
Exercise 5.1	Exercise 5.2	Exercise 6.4
Exercise 6.5	Exercise 7.9, gothic data	Exercise 7.9, roman data
fuel0210	Exercise 7.11