Instructor:	Prof. Robert Fovell
Office:	7162 Math Sciences
Office hours:	Informal and by appointment
Phone:	(310) 206-9956
E-mail:	fovell@atmos.ucla.edu
Lectures:	Monday and Wednesday, 2-3:20

Texts:

Required:	Gunst and Mason: Regression analysis and its application
Not required:	Jackson: A user's guide to principal components	Expensive
Not required:	Huff: How to lie with statistics	Just for fun!

Grading:

• ``Midterm'' exam 30% [may be quite delayed, though]
• Homework, including class project 35%
• Final exam 35%

Overview:

This course was created in response to student requests. They wanted a concise introduction to basic multivariate analysis, with emphasis placed on practice over theory. This course attempts to cover three basic analytical tools: linear regression, principal component, and cluster analyses. There is no way to do all three in a single quarter without going fast. Yet, the specific tools learned herein are less important than the underlying fundamental concepts. This is very much a hands-on class.

Topic and subtopic outline:

1. Linear regression analysis:
   • Dependent and independent variables
   • Model building vs. prediction
   • Uses and abuses of regression analysis
   • Ordinary least squares (OLS) estimates
   • Analysis of variance (ANOVA) for regression models
   • Matrix formulation of the OLS problem
   • Collinearity
   • Significance tests for models and parameters
   • Errors vs. residuals
   • Testing residuals
   • Model misspecification
   • Deleted and studentized residuals, leverage values, Cook's D
   • Polynomial regression, interaction terms, indicator variables
   • Variable selection strategies
   • Partial correlation and the Extra Sum of Squares Principle
   • Odds and ends

2. Principal components analysis (PCA):
   • Least normal squares
   • Dispersion matrices, eigenvalues and eigenvectors
   • Scaling issues
   • PC ``scores''
   • Principal component regression
   • PCA for variable reduction; truncation tests and rules
   • Rotation of components

3. Cluster analysis:
   • Motivation
   • Concept of ``distance''; various distance measures
   • Redundant and irrelevant information
   • Clustering strategies and algorithms
   • Biases of clustering methods
   • Stopping rules; number of clusters problem