Course syllabus - Multivariate Statistical Analysis

Objectives

The objective of the course is to give the student the opportunity to become acquainted with the more common multivariate statistical methods in order to make proper interpretations and appropriate analyses of multivariate data.

Learning outcomes

Upon completion of the course, the student is expected to be able to
1. prove the most important properties of the multivariate normal distribution
2. describe and apply multivariate linear models
3. understand and derive multivariate statistical methods, such as principal component analysis, factor analysis, discriminant analysis, cluster analysis and canonical correlation analysis
4. evaluate the applicability of different models from a scientific perspective, and judge what multivariate analysis methods are best suitable to use in different contexts
5. analyse the results from applying multivariate statistical methods and explain its limitations
6. use a statistical software to analyse and compare different multivariate methods and draw adequate conclusions
7. implement some of the models studied, using a software/programming language suitable for a specific problem

Course content

- Introduction to multivariate analysis: descriptive statistics for multivariate data, sample geometry and random sampling
- Multivariate normal distribution and statistical inference based on this distribution
- Multivariate linear models: linear regression and multivariate multiple regression
- Analysis of a covariance structure: principal components and factor analysis
- Classification and grouping techniques: classification, discrimination and cluster analysis

Specific requirements

Calculus of Several Variables, 4 credits, Vector Algebra, 5 credits, Statistics, 3.5 credits, Probability, 3.5 credits, or equivalent. In addition, Swedish B/Swedish 3 and English A/English 6 are required. In cases when the course is offered in English, the requirement for Swedish B/Swedish 3 is excluded.

Examination

INL1, Written assignment, 2.5 credits, written assignments concerning learning outcomes 6-7, grades Fail (U) or Pass (G).
TEN1, Written examination, 5 credits, individual written examination concerning learning outcomes 1-5, grades Fail (U), 3, 4 or 5.

A student who has a certificate from MDU regarding a disability has the opportunity to submit a request for supportive measures during written examinations or other forms of examination, in accordance with the Rules and Regulations for Examinations at First-cycle and Second-cycle Level at Mälardalen University (2020/1655). It is the examiner who takes decisions on any supportive measures, based on what kind of certificate is issued, and in that case which measures are to be applied.

Suspicions of attempting to deceive in examinations (cheating) are reported to the Vice-Chancellor, in accordance with the Higher Education Ordinance, and are examined by the University’s Disciplinary Board. If the Disciplinary Board considers the student to be guilty of a disciplinary offence, the Board will take a decision on disciplinary action, which will be a warning or suspension.

Grade

Grading scale: 5, 4, 3