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Multivariate Data Analysis, 7.5 Credits

Swedish name: Multivariat dataanalys

This syllabus is valid: 2017-08-07 and until further notice

Course code: 5MS056

Credit points: 7.5

Education level: Second cycle

Main Field of Study and progress level: Mathematical Statistics: Second cycle, has only first-cycle course/s as entry requirements

Grading scale: TH teknisk betygsskala

Responsible department: Department of Mathematics and Mathematical Statistics

Established by: Faculty Board of Science and Technology, 2017-06-30


The course covers the multivariate normal distribution, Hotelling's T2 test, multivariate analysis of variance (MANOVA), principal component analysis (PCA), factor analysis, models for regression analysis with colinear explanatory variables such as principal component regression (PCR) and PLS, analysis of data from experiments with repeated measurements, discriminant analysis and cluster analysis.

Element 1 (5 hp): Theory and applications
The element covers multivariate distributions with special emphasis on the multivariate normal distribution and its properties. Further, methods for inference concerning mean vectors, and variance and correlation matrices are treated, along with methods for projections and classification.

Element 2 (2,5 hp): Multivariat data analysis with suitable statistical software.
The element includes written and oral presentation of results.

Expected learning outcomes

For a passing grade, the student must be able to

Knowledge and understanding
  • derive the most important properties of the multivariate normal distribution
  • decide the distribution of linear combinations of multivariate normal distributions
  • analyze multivariate data sets with the methods included in the course
  • evaluate the results from multivariate analyses and with a scientific touch present the results orally and in written form
  • summarize the most important results from a scientific report on some area in multivariate analysis
Judgment and approach
  • evaluate the applicability of different models from a scientific perspective, and judge what multivariate analysis methods that are suitable to use in different situations

Required Knowledge

The course requires 90 ECTS including courses in Mathematical Statistics, minimum 15 ECTS, or courses in Statistics, minimum 75 ECTS and in both cases a course in Basic Calculus, 7,5 ECTC and a course in Linear algebra, 7,5 ECTS. Proficiency in English equivalent to Swedish upper secondary course English A/5. Where the language of instruction is Swedish, applicants must prove proficiency in Swedish to the level required for basic eligibility for higher studies.


Form of instruction

The teaching is mainly in the form of lectures and lessons.

Examination modes

The examination consists of written reports, oral presentations and a written exam. The oral presentations are awarded with one of the following judgments: Fail (U), or Pass (G). The written reports are awarded with one of the following judgments: Fail (U), or Pass (G), and with points. Element 1 is awarded with one of the following grades: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). The grade is based on the total score, where the written reports has 1/3, and the written exam 2/3 of the total score. Element 2 is awarded with one of the following grades: Fail (U), or Pass (G). In order to get the grade G, all the oral and written presentations must be awarded with the judgment G. For the course as a whole, one of the following grades is awarded: Fail (U), Pass (3), Pass with merit (4), Pass with distinction (5). The grade for the whole course is determined by the grade given for Element 1. To pass the whole course, all elements must have been passed. The grade is only set once all compulsory elements have been assessed. Scores on written reports can be used on later occasions for examination.

A student who has been awarded a passing grade for the course cannot be reassessed for a higher grade. Students who do not pass a test or examination on the original date are given another date to retake the examination. A student who has sat two examinations for a course or a part of a course, without passing either examination, has the right to have another examiner appointed, provided there are no specific reasons for not doing so (Chapter 6, Section 22, HEO). The request for a new examiner is made to the Head of the Department of Mathematics and Mathematical Statistics. Examinations based on this course syllabus are guaranteed to be offered for two years after the date of the student's first registration for the course.

Credit transfer
All students have the right to have their previous education or equivalent, and  their working life experience evaluated for possible consideration in the corresponding education at Umeå university. Application forms should be adressed to Student services/Degree evaluation office. More information regarding credit transfer can be found on the student web pages of Umeå university,, and in the Higher Education Ordinance (chapter 6). If denied, the application can be appealed (as per the Higher Education Ordinance, chapter 12) to Överklagandenämnden för högskolan. This includes partially denied applications

Other regulations

In a degree, this course may not be included together with another course with a similar content. If unsure, students should ask the Director of Studies in Mathematics and Mathematical Statistics. The course can also be included in the subject area of computational science and engineering.


Valid from: 2017 week 34

Applied multivariate statistical analysis
Johnson Richard Arnold, Wichern Dean W.
Sixth edition, Pearson New International edition. : ii, 770 pages :
ISBN: 1292024941
Search Album, the University Library catalogue