This is a master’s / advanced undergraduate level course in linear regression methods.
Text:
Required:
4th Ed., by Kutner, Nachtsheim, and Neter. McGraw-Hill, 2004.
Strongly recommended:
Pattern Recognition and Machine LearningChristopher M. Bishop. Springer, 2006.
Prerequisite: Calculus; probability and statistics at the level of W4150, or W4105 and W4107 taken concurrently.
Corequisite: Linear algebra.
Grading: Grades will be assigned on a curve, using the following percentages: 35% Homework, 25% Midterm, 35% Final Project, 5% Participation.
Homework will include a mix of paper and computer problems, and will be assigned in class as we go along; the assignments and due dates will be posted on this webpage. No late homework will be accepted.
Midterm: The midterm will be during class hours.
Final project: The final project will be a small group project of your choice, selected just after the midterm examination.
Computing: You will be required to use Matlab to complete your homework assignments. Software of your choice may be used to complete the final project. See the ACIS page for information on software and computing labs.
Scope: This class is about the theory and practice of regression analysis. The theory will be approached from both the frequentist and Bayesian perspectives and use of the computer to analyze data will be emphasized. The first part of the course will focus on the basic techniques with one-dimensional data, and will assume familiarity with the following topics from statistics (see appendix A in the book for a quick review, or e.g. Rice or a similar textbook for more details):
- Gaussian distributions
- Joint, conditional distributions
- Law of large numbers, central limit theorem
- Estimation
- Bias, variance, covariance
- Maximum likelihood
- Hypothesis testing
- Confidence intervals
The second part of the course will look specifically at the challenges posed by multivariate data. We will do a very brief linear algebra review, but it will be essential to be familiar with the following topics from linear algebra:
- Vectors, matrices
- Linear transformations, bases
- Matrix inverse
- Eigenvalues, eigenvectors
- Quadratic forms
- Determinants