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

Course Materials

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

Final Exam:

Tests:

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.

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 dataExercise 7.9, roman data
fuel0210Exercise 7.11