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Multivariate Statistics

Multivariate Statistics

This course will teach you key multivariate procedures such as multivariate analysis of variance (MANOVA), principal components, factor analysis, and classification.


Multivariate data typically consist of many records, each with readings on two or more variables, with or without an “outcome” variable of interest. This course covers the theoretical foundations of multivariate statistics including multivariate data, common distributions and discriminant analysis. Procedures covered in the course include multivariate analysis of variance (MANOVA), principal components, factor analysis and classification.

  • Intermediate, Advanced
  • 4 Weeks
  • Expert Instructor
  • Tuiton-Back Guarantee
  • 100% Online
  • TA Support

Learning Outcomes

Students completing this course will understand the theoretical foundations of the topic including multivariate data structure, multivariate distributions and inference, multidimensional scaling and discriminant analysis.

  • Describe the multivariate normal distribution
  • Depict multivariate data with scatterplots
  • Specify the form of the Hotelling T2 and Wishart distributions
  • Conduct principal components analysis
  • Conduct correspondence analysis
  • Conduct discriminant analysis

Who Should Take This Course

Students who are planning to take technique-specific courses (e.g. cluster analysis, factor analysis, logistic regression, GLM, mixed models) or domain-specific courses (e.g. data mining) and who need additional background in multivariate theory and practice prior to doing so.

Multivariate statistics is a wide field, and many courses at cover areas not included in this course. See our “Related Courses” below for more information on these courses.

Our Instructors

Dr. Robert LaBudde

Dr. Robert LaBudde

Dr. Robert LaBudde is president and founder of Least Cost Formulations, Ltd., a mathematical software development company specializing in optimization and process control software for manufacturing companies. He has served on the faculties of the University of Wisconsin, Massachusetts Institute of Technology, Old Dominion University and North Carolina State University. Dr. LaBudde is currently Adjunct Professor of Statistics at Old Dominion University.

Course Syllabus

Week 1

Multivariate Data

  • Descriptive Statistics
  • Rows (Subjects) vs. Columns (Variables)
  • Covariances, Correlations and Distances
  • The Multivariate Normal Distribution
  • Scatterplots
  • More than 2 Variable Plots
  • Assessing Normality

Week 2

Multivariate Normal Distribution, MANOVA, & Inference

  • Details of the Multivariate Normal Distribution
  • Wishart Distribution
  • Hotelling T2 Distribution
  • Multivariate Analysis of Variance (MANOVA)
  • Hypothesis Tests on Covariances
  • Joint Confidence Intervals

Week 3

Multidimensional Scaling & Correspondence Analysis

  • Principal Components
  • Correspondence Analysis
  • Multidimensional Scaling

Week 4

Discriminant Analysis

  • Classification Problem
  • Population Covariances Known
  • Population Covariances Estimated
  • Fisher’s Linear Discriminant Function
  • Validation

Class Dates


01/26/2024 to 02/24/2024
Instructors: Dr. Robert LaBudde
07/19/2024 to 08/16/2024
Instructors: Dr. Robert LaBudde


01/24/2025 to 02/21/2025
Instructors: Dr. Robert LaBudde
07/25/2025 to 08/22/2025
Instructors: Dr. Robert LaBudde
10/24/2025 to 11/21/2025
Instructors: Dr. Robert LaBudde


You should be familiar R software.

Multivariate statistics is a wide field, and many courses at cover areas not included in this course. These courses are not required as eligibility to enroll in this course, and are presented here for information purposes only:

Private: Matrix Algebra

This course will teach you the basics of vector and matrix algebra and operations necessary to understand multivariate statistical methods, including the notions of the matrix inverse, generalized inverse and eigenvalues and eigenvectors.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU

Private: Cluster Analysis

This course will teach you how to use various cluster analysis methods to identify possible clusters in multivariate data. Methods discussed include hierarchical clustering, k-means clustering, two-step clustering, and normal mixture models for continuous variables.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU

Private: Logistic Regression

This course will teach you logistic regression ordinary least squares (OLS) methods to model data with binary outcomes rather than directly estimating the value of the outcome, logistic regression allows you to estimate the probability of a success or failure.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU

Private: Campaign Analytics for Marketing

Learn how to put powerful statistical methods to work in your marketing campaigns to yield higher response and more profit.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU

Deep Learning

This course will introduce you to the essential techniques of text mining as the extension of data mining’s standard predictive methods to unstructured text.
  • Skill: Intermediate, Advanced
  • Credit Options: CEU
Karolis Urbonas
Susan Kamp
Stephen McAllister
Amir Aminimanizani
Elena Rose
Leonardo Nagata
Richard Jackson

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Multivariate Statistics

Additional Information


Homework in this course consists of short answer questions to test concepts, guided data analysis problems using software, and guided data modeling problems using software.

In addition to assigned readings, this course also has an end of course data modeling project, and supplemental readings available online.

Course Text

The required text is An Introduction to Applied Multivariate Analysis with R by Brian Everitt, and Torsten Hothorn.  The text may be purchased here

The course will be supplemented by notes supplied by the instructor for topics not covered by the text.


The exercises in this course will require the use of statistical software that can do multivariate analysis (plots, MANOVA, discriminant analysis, correspondence analysis, multidimensional scaling) and standard matrix operations.

Output in the course material and the text is based on the R statistical system and Microsoft Excel, as these are the programs the instructor is familiar with. Other software may be used, but you should be prepared to use your program and interpret its output (in comparison with that given in the course) on your own. If you are planning to use R in this course and are not already familiar with it, please consider taking one of our courses where R is introduced from the ground up:  “Introduction to R: Data Handling,”  “Introduction to R: Statistical Analysis,” or “Introduction to Modeling.” R has a learning curve that is steeper than that of most commercial statistical software.

Supplemental Information

Literacy, Accessibility, and Dyslexia

At, we aim to provide a learning environment suitable for everyone. To help you get the most out of your learning experience, we have researched and tested several assistance tools. For students with dyslexia, colorblindness, or reading difficulties, we recommend the following web browser add-ons and extensions:







  • Navidys (for colorblindness, dyslexia, and reading difficulties)
  • HelperBird for Safari (for colorblindness, dyslexia, and reading difficulties)

Register For This Course

Multivariate Statistics