Multivariate Statistics
This course will teach you key multivariate procedures such as multivariate analysis of variance (MANOVA), principal components, factor analysis, and classification.
Overview
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 Statistics.com cover areas not included in this course. See our “Related Courses” below for more information on these courses.
Our Instructors
Dr. Robert LaBudde
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
2025
Instructors: Dr. Robert LaBudde
Instructors: Dr. Robert LaBudde
Instructors: Dr. Robert LaBudde
Prerequisites
You should be familiar R software.
Multivariate statistics is a wide field, and many courses at Statistics.com 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
- Skill: Intermediate, Advanced
- Credit Options: CEU
Private: Cluster Analysis
- Skill: Intermediate, Advanced
- Credit Options: CEU
Private: Logistic Regression
- Skill: Intermediate, Advanced
- Credit Options: CEU
Private: Campaign Analytics for Marketing
- Skill: Intermediate, Advanced
- Credit Options: CEU
Deep Learning
- Skill: Intermediate, Advanced
- Credit Options: CEU
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Additional Information
Homework
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.
Software
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
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