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.

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

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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.

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.

Instructors

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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.
See Instructor Bio

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

2019

Jul 5, 2019 to Aug 2, 2019

2020

Jan 31, 2020 to Feb 28, 2020

2021

No classes scheduled at this time.

Send me reminder for next class

Prerequisites

You should be familiar R software.

Introductory Statistics

We assume you are versed in statistics or have the equivalent understanding of topics covered in our Statistics 1 and Statistics 2 courses. but do not require them as eligibility to enroll in this course. Please review the course description for each of our introductory statistics courses, estimate which best matches your level of understanding of the material covered in these courses, then take the short assessment test for that course. If you can not answer more than half of the questions correctly, we suggest you take our Statistics 1 and Statistics 2 courses prior to taking this course.

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:

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.
Topic: Statistics, Analytics, Marketing Analytics, Statistical Modeling | Skill: Intermediate | Credit Options: ACE, CAP, CEU
Class Start Dates: May 29, 2020

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.
Topic: Data Science, Machine Learning | Skill: Intermediate | Credit Options: ACE, CEU
Class Start Dates: Nov 6, 2020

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.
Topic: Statistics, Statistical Modeling | Skill: Intermediate | Credit Options: CAP, CEU
Class Start Dates: Jan 10, 2020, Jul 17, 2020

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.
Topic: Statistics, Statistical Modeling | Skill: Intermediate | Credit Options: ACE, CAP, CEU
Class Start Dates: Mar 27, 2020, Aug 14, 2020

Regression Analysis

This course will teach you how multiple linear regression models are derived, assumptions in the models, how to test whether data meets assumptions, and develop strategies for building and understanding useful models.
Topic: Statistics, Statistical Modeling | Skill: Intermediate | Credit Options: ACE, CAP, CEU
Class Start Dates: Jan 17, 2020, May 8, 2020, Oct 2, 2020

What Our Students Say​

The material covered here will be indispensable in my work. I can't wait to take other courses. Great work!

Stephen McAllister
Ottawa Public Library

I learned more in the past 6 weeks than I did taking a full semester of statistics in college, and 10 weeks of statistics in graduate school. Seriously.

Amir Aminimanizani
MRR Pharmacy Consulting, Inc

Frequently Asked Questions

What is your satisfaction guarantee and how does it work?

We offer a “Student Satisfaction Guarantee​” that includes a tuition-back guarantee, so go ahead and take our courses risk free. That’s our commitment to student satisfaction. Students may cancel, transfer, or withdraw from a course under certain conditions. If you’re not satisfied with a course, you may withdraw from the course and receive a tuition refund.

Please see our knowledge center for more information.

Who are the instructors at the Institute?

The Institute has more than 60 instructors who are recruited based on their expertise in various areas in statistics. Our faculty members are:

  • Authors of well-regarded texts in their area;
  • Advisory board members;
  • Senior faculty; and
  • Educators who have made important contributions to the field of statistics or online education in statistics.

The majority of our instructors have more than five years of teaching experience online at the Institute.

Please visit our faculty page for more information on each instructor at The Institute for Statistics Education.

Please see our knowledge center for more information.

What type of courses does the Institute offer?

The Institute offers approximately 80 courses each year. Topics include basic survey courses for novices, a full sequence of introductory statistics courses, bridge courses to more advanced topics. Our courses cover a range of topics including biostatistics, research statistics, data mining, business analytics, survey statistics, and environmental statistics.

Please see our course search or knowledge center for more information.

Do your courses have for-credit options?

Our courses have several for-credit options:

  • Continuing education units (CEU)
  • College credit through The American Council on Education (ACE CREDIT)
  • Course credits that are transferable to the INFORMS Certified Analytics Professional (CAP®)

Please see our knowledge center for more information.

Is the Institute for Statistics Education certified?

The Institute for Statistics Education is certified to operate by the State Council of Higher Education for Virginia (SCHEV). For more information visit: http://www.schev.edu

Please see our knowledge center for more information.

Visit our knowledge base and learn more.

FAQs + Knowledge Base

Related Courses

Statistics 1 – Probability and Study Design

This course, the first of a three-course sequence, provides an introduction to statistics for those with little or no prior exposure to basic probability and statistics.
Topic: Statistics, Introductory Statistics | Skill: Introductory | Credit Options: ACE, CAP, CEU

Statistics 2 – Inference and Association

This course, the second of a three-course sequence, will teach you the use of inference and association through a series of practical applications, based on the resampling/simulation approach, and how to test hypotheses, compute confidence intervals regarding proportions or means, computer correlations, and use of simple linear regressions.
Topic: Statistics, Introductory Statistics | Skill: Introductory | Credit Options: ACE, CEU
Class Start Dates: Dec 6, 2019

Additional Course Information

Organization of Course

This course takes place online at The Institute for 4 weeks. During each course week, you participate at times of your own choosing – there are no set times when you must be online. Course participants will be given access to a private discussion board. In class discussions led by the instructor, you can post questions, seek clarification, and interact with your fellow students and the instructor.

At the beginning of each week, you receive the relevant material, in addition to answers to exercises from the previous session. During the week, you are expected to go over the course materials, work through exercises, and submit answers. Discussion among participants is encouraged. The instructor will provide answers and comments, and at the end of the week, you will receive individual feedback on your homework answers.

Time Requirements

This is a 4-week course requiring 10-15 hours per week of review and study, at times of your choosing.

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.

Please order a copy of your course textbook prior to course start date.

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.

Software Uses and Descriptions | Available Free Versions
To learn more about the software used in this course, or how to obtain free versions of software used in our courses, please read our knowledge base article “What software is used in courses?” 

Course Fee & Information

Enrollment
Courses may fill up at any time and registrations are processed in the order in which they are received. Your registration will be confirmed for the first available course date unless you specify otherwise.

Transfers and Withdrawals
We have flexible policies to transfer to another course or withdraw if necessary.

Group Rates
Contact us to get information on group rates.

Discounts
Academic affiliation?  In most courses you are eligible for a discount at checkout.

New to Statistics.com?  Click here for a special introductory discount code.  

Invoice or Purchase Order
Add $50 service fee if you require a prior invoice, or if you need to submit a purchase order or voucher, pay by wire transfer or EFT, or refund and reprocess a prior payment.

Options for Credit and Recognition

This course is eligible for the following credit and recognition options:

No Credit
You may take this course without pursuing credit or a record of completion.

Mastery or Certificate Program Credit
If you are enrolled in mastery or certificate program that requires demonstration of proficiency in this subject, your course work may be assessed for a grade.

CEUs and Proof of Completion
If you require a “Record of Course Completion” along with professional development credit in the form of Continuing Education Units (CEU’s), upon successfully completing the course, CEU’s and a record of course completion will be issued by The Institute upon your request.

Supplemental Information

There is no supplemental content for this course.

Miscellaneous

There is no additional information for this course.

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Multivariate Statistics
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