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# Multivariate Analysis - MAT00021H

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• Department: Mathematics
• Module co-ordinator: Dr. Agostino Nobile
• Credit value: 10 credits
• Credit level: H
• Academic year of delivery: 2022-23
• See module specification for other years: 2021-22

## Related modules

• None

### Prohibited combinations

Pre-requisite modules for Natural Sciences students: Statistics Option MAT00033I.

## Module will run

Occurrence Teaching period
A Spring Term 2022-23

## Module aims

To introduce the main ideas of multivariate statistical analysis; that is, the analysis of sets of data where there are several measurements on each of a number of individuals.

## Module learning outcomes

• A knowledge and understanding of models and methods for multivariate data.

• A reasonable degree of familiarity with some of the main techniques of multivariate analysis.

• Apply appropriate techniques to different sets of data.

• Use the statistical package R to analyse multivariate data by various techniques.

## Module content

Syllabus

• Introduction: Aims of multivariate analysis, descriptive statistics, graphical representation, basic concepts of vectors and matrices, use of the R program for matrix algebra and multivariate analysis.
• The Multivariate Normal Distribution: Properties of the multivariate normal, contours of constant density, marginal and conditional distribution, checking normality.
• Hotelling's T-squared test: One-sample tests, two-sample tests, large sample inference.
• Multvariate Analysis of Variance (MANOVA): One-way and two-way MANOVA, Wilks' Lambda and other criteria.
• Principal component analysis: Principal components, principle component analysis by correlation matrix, choosing the number of components.
• Factor analysis: The idea of factor analysis, estimation of loadings, choosing the number of factors.
• Cluster analysis: Hierarchical cluster methods, dendrogram, non-hierarchical cluster methods.

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Multivariate Analysis
2 hours 100

None

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Multivariate Analysis
2 hours 100

## Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.