Multivariate Statistical Analysis

Lecturer

Dr Sharon Lee

Synopsis

Multivariate data naturally arise in a wide range of scientific and applied contexts, including engineering, computer science, finance, medicine, and the social sciences. Understanding and analysing such data require statistical techniques that extend beyond univariate methods to capture the complexity of multidimensional structures.

This course provides a rigorous introduction to classical multivariate statistical methods, with a focus on both theoretical foundations and practical implementation. Topics include multivariate generalizations of familiar univariate techniques, as well as methods uniquely suited to high-dimensional data. Students will develop a solid mathematical understanding of the underlying principles and gain hands-on experience applying these techniques to real data using the R programming language.

Course Overview

This course is designed to cover the core topics from Applied Multivariate Statistical Analysis by Johnson and Wichern (6th ed.). Each week combines theoretical development with practical application using R.

Week 1: Foundations of Multivariate Analysis

• Introduction to multivariate data and visualization
• Multivariate distributions and the geometry of multivariate space
• Sampling distributions and the multivariate normal distribution

Week 2: Inference for Multivariate Means and Regression

• Inference for a single multivariate population
• Comparison of multiple populations (Hotelling’s T², MANOVA)
• Multivariate linear regression

Week 3: Covariance Structure and Dimension Reduction

• Principal Component Analysis (PCA)
• Factor Analysis
• Canonical Correlation Analysis

Week 4: Classification, Clustering, and Multidimensional Techniques

• Discriminant Analysis
• Cluster Analysis (hierarchical, k-means, and mixture models)
• Multidimensional Scaling (MDS)
• Correspondence Analysis

Prerequisites