### Multivariate Data Analysis

#### Course Description

Multivariate data analysis forms one of the basic pillars of data science and is a generalization of univariate and bivariate statistical methods. Multivariate analysis is intended for simultaneous analysis and visualization of complex datasets with a large number of independent and/or dependent variables that are in different degrees of correlation, and their various effects cannot be interpreted separately. The contents of the course are grouped into three sections. The first part contains the basic concepts and basic techniques that precede the multivariate analysis, the second part relates to various advanced regression techniques and their understanding (with reference to high-dimensional data), and the third to techniques based on matrix decompositions (separation by eigenvalues ​​and separation by singular values).

#### Learning Outcomes

1. Define main notions in the multivariate data analysis
2. Explain mathematical backgrounds of main multivariate statistical procedures
3. Apply linear multiple regression analysis
4. Differentiate between principal component analysis and factor analysis
5. Justify the adequacy of different multivariate statistical methods for various problems
6. Interpret the results of multivariate statistical data analysis and explain their practical meaning

#### Forms of Teaching

Lectures

Exercises

Independent assignments

Laboratory

Continuous Assessment Exam
Laboratory Exercises 50 % 30 % 50 % 30 %
Mid Term Exam: Written 0 % 35 % 0 %
Final Exam: Written 0 % 35 %
Exam: Written 50 % 70 %

#### Week by Week Schedule

1. Introductory concepts, statistical distance, data preparation
2. Random vectors and matrices, matrix decomposition, eigenvalues
3. Sample geometry, random sampling
4. Applied correlation and regression analysis
5. Principal component analysis
6. Exploratory factor analysis
7. Discriminant analysis
8. Midterm exam
9. Multidimensional scaling
10. Correspondence analysis
11. Survival analysis
12. Time Series Analysis
13. The Lasso method for high dimensional data
14. Guest lecture
15. Final exam

#### Study Programmes

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#### Literature

Richard A. Johnson, Dean W. Wichern (2008.), Applied Multivariate Statistical Analysis, Pearson
Barbara G. Tabachnick, Linda S. Fidell (2013.), Using Multivariate Statistics, Pearson
Joseph F. Hair, William C. Black, Barry J. Babin, Rolph E. Anderson (2010.), Multivariate Data Analysis, Pearson

#### General

ID 222481
Summer semester
5 ECTS
L1 English Level
L1 e-Learning
45 Lectures
0 Seminar
15 Exercises
6 Laboratory exercises
0 Project laboratory