Applied Multivariate Statistics (Fall 2022 TA)

Teaching Assistant

My primary responsibilities were grading homework assignments (12) and exams (3), providing solutions and detailed feedback on student work, monitoring discussion board (12 Modules), and promptly replying to posts. Additionally, I provided handouts with detailed solutions to example questions. To ensure effective communication and support, I maintained a high level of organization and ensured that the students’ grades were accurate. I made myself readily available to students by responding promptly to emails, offering virtual office hours, and providing assistance both during and outside of scheduled office hours. Additionally, I closely monitored students’ progress throughout the semester and scheduled Zoom meetings with students to address any questions or concerns that arose during the course.

Textbooks

• Required Textbooks:
  • Richard A. Johnson and Dean W. Wichern, “Applied Multivariate Statistical Analysis”
  • Alvin C. Rencher and William F. Christensen, “Methods of Multivariate Analysis”

Course Description

Multivariate Statistics is the study of dependent variables. The main objective of this course is to equip students with the traditional and modern multivariate statistical methods. More specifically, we will learn the motivation behind these methods, how to apply them and interpret the results obtained. Most of the theory, including the distributional results, is mathematically involved and we will focus mainly on understanding and applying them rather than their technical derivations. Matrix algebra is very useful in multivariate statistics. Matrix algebra is summarized in Chapter 2 (and its supplement) of the textbook. Anyone who masters this chapter (and the supplement) will have a reasonable competency in this area. The course will start with classical multivariate statistical analysis, including multivariate normal distribution and related sampling distributions, parameter estimation, hypotheses testing about the mean and regressions, all of which are direct generalizations of univariate methods. The second half of the course will be on methods that arise with multivariate data; for example, detection of structures, dimension reduction, classification and clustering.

Student Learning Outcomes

The primary goals of this course are:

• Data reduction and simplification.
• Grouping units based on their similarity on measured variables.
• Explaining the nature of dependence or relationship between variables in simpler terms.
• Using multivariate models for prediction of variables or group membership.
• Formulating multivariate models for multivariate methods.
• Carrying out multivariate analysis using the statistical software R.
• Interpreting results from multivariate methods.

Software

R and/or JMP.