Mathematics, Statistics & Computer Science Department
COURSE NO./TITLE:
CREDITS:
STAT-740 Multivariate Statistical Analysis
3
COURSE DESCRIPTION: Aspects of multivariate analysis, matrix algebra, random vectors,
graphical techniques and descriptive statistics for multivariate data, multivariate normal, Wishart
distribution, inference about mean vectors, confidence regions and simultaneous comparisons of
component means, comparison of several multivariate means, multivariate linear regression,
principle component and factor analysis, classification-discriminants analysis, clustering and
trees.
Prerequisite: STAT-640
TEXTBOOK: TBD
COURSE OBJECTIVES: Upon successful completion of this course, a student will be able to:
1. Understand and explain what multivariate statistical analysis is and when its application
is appropriate.
2. Derive various statistics for random vectors via matrix algebra.
3. Graphically display multivariate data.
4. Demonstrate thorough familiarity with multivariate distributions, and in particular
multivariate normal and Wishart distributions.
5. Demonstrate knowledge in drawing inferences about mean vectors and comparison of
several multivariate means.
6. Devise and analyze multivariate regression models.
7. Condense information contained in a large number of variables into a smaller set of
factors using principle component and factor analysis.
8. Search for distinguishable groups of objects using various classification techniques.
9. Implement all of the above using standard statistical packages (e.g., SPSS)
10. Reproduce the results obtained in statistical packages (e.g., SPSS) using spreadsheets
(e.g., Excel).
COURSE OUTLINE:
1. Introduction and application of multivariate techniques (Objective 1)
2. Data displays and pictorial representations (Objectives 3, 9)
3. Random vectors (Objective 2)
4. Sample geometry and random sampling (Objective 2)
5. The multivariate normal, Hotelling’s T2, and Wishart distributions (Objective 4)
6. Assessing the assumption of normality (Objectives 4, 5, 9)
7. Inference about mean vectors (Objectives 5, 9)
8. Simultaneous confidence intervals (Objectives 5, 9)
9. Comparisons of several multivariate means-MANOVA (Objectives 5, 9)
10. Multivariate linear regression models (Objective 6)
11. Inference about regression models and likelihood ratio tests (Objective 6)
12. Principle components, factor analysis and orthogonal models (Objective 7)
13. Separation of distinct sets of objects (Objective 8)
14. Discriminant analysis, clustering and trees (Objective 8)
15. Research project presentations (Objective 10)
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