Multivariate Statistical Analysis

This course develops knowledge of multivariate statistical techniques through theory, proofs, problem solving, and implementations in Excel and R. It covers multivariate distributions, inference, regression, PCA, factor analysis, classification, and clustering, and expects prior knowledge of linear algebra, probability, and statistics.

Syllabus

Multivariate Analysis - Introduction/Theory (Part 0).
Multivariate Analysis - Introduction/Problem Solving (Part 1).
Multivariate Analysis - Introduction/Excel (Part 2).
Multivariate Analysis - Introduction/R (Part 3).
Multivariate Analysis - Sample Geometry and Random Sampling (Part 4).
Multivariate Normal Distribution - Theorems with proofs (Part 5).
Multivariate Normal Distribution - Maximum Likelihood Estimation (Part 6).
Multivariate Normal Distribution - Problem Solving (Part 7).
Multivariate Normal Distribution - Excel (Part 8).
Inferences About a Mean Vector - Excel (Part 9).
Comparisons of Several Multivariate Means - Excel (Part 10).
Introduction to Linear Regression - Simple, Multiple, Multivariate (Part 11).
Ordinary Least Squares and Gauss-Markov Theorem with Proof (Part 12).
Fitting Linear Regression Models - Excel (Part 13).
Principal Components Analysis - PCA Introduction (Part 14).
Factor Analysis - A short introduction in Excel (Part 16).
Clustering - Part 17.