# Study-Unit Description

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CODE SOR3210

TITLE Multivariate Analysis 1

LEVEL 03 - Years 2, 3, 4 in Modular Undergraduate Course

ECTS CREDITS 5

DEPARTMENT Statistics and Operations Research

DESCRIPTION - Sampling from a Multivariate Normal Distribution
- Wishart Distribution and its Properties
- Hotelling's T2 Distribution and its Properties
- Distribution of Sample Mean and Covariance Matrix
- Inference about Mean Vectors
- Confidence Regions and Simultaneous Comparisons
- Comparing Two Populations, Profile Analysis
- Estimation
- Hypothesis Testing
- Principal Components
- Factor Analysis

Study-unit Aims:

The main aim of this study-unit is that of familiarizing the students with the theoretical and practical framework underlying the analysis of any data set that involves more than one variable.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will:
- Be able to understand the role that the multivariate normal distribution plays in estimation and hypothesis testing of mean vectors and variance covariance matrices in a multivariate setting;
- Be familiar with various techniques that may be used in multivariate hypothesis testing, with special consideration being given to the likelihood ratio test;
- Have developed a sound background in multivariate estimation theory;
- Have a better appreciation of the role which matrix algebra plays, particularly in analysing covariance structures.

2. Skills:

By the end of the study-unit the student will be able to:
- Use their theoretical knowledge and various statistical packages to perform simulations and to analyse real multivariate data;
- Use the material learnt to understand the theoretical and practical importance of multivariate techniques which have not been covered in this study-unit.

Main Text/s and any supplementary readings:

- Mardia, K.V., Kent, J.T. and Bibby, J.M. (1995) Multivariate Analysis, Academic.
- Knight, K. (1999) Mathematical Statistics, Chapman & Hall.
- Srivastava, M.S. and Khatri, C.G. (1979) An Introduction to Multivariate Statistics, North Holland.
- Johnson, R.A. and Wichern, D.W. (1992) Applied Multivariate Statistical Analysis, Prentice Hall Inc.
- Flury, B. (1997) A First Course in Multivariate Statistics, Springer.
- Hair J., Anderson R., Tatham R. and Black W., (1998) Multivariate Data Analysis, Prentice Hall I.

ADDITIONAL NOTES Pre-requisite Study-units: SOR1110, SOR2210 & SOR2220

STUDY-UNIT TYPE Lecture and Practical

METHOD OF ASSESSMENT
 Assessment Component/s Assessment Due Resit Availability Weighting Computer-based Examination (2 Hours) SEM2 Yes 100%

LECTURER/S Fiona Sammut

The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2020/1. It may be subject to change in subsequent years.

https://www.um.edu.mt/course/studyunit