SubjectsSubjects(version: 949)
Course, academic year 2021/2022
Multivariate data analysis - AM413004
Title: Multivariate data analysis
Guaranteed by: Department of Mathematics, Informatics and Cybernetics (446)
Faculty: Faculty of Chemical Engineering
Actual: from 2021 to 2022
Semester: summer
Points: summer s.:5
E-Credits: summer s.:5
Examination process: summer s.:
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
Language: English
Teaching methods: full-time
Teaching methods: full-time
For type: Master's (post-Bachelor)
Note: course can be enrolled in outside the study plan
enabled for web enrollment
Guarantor: Kříž Pavel Ing. Mgr. Ph.D.
Zikmundová Markéta Mgr. Ph.D.
Šnupárková Jana RNDr. Ph.D.
Interchangeability : M413004, N413040
Is interchangeable with: M413004
This subject contains the following additional online materials
Annotation -
Last update: Zikmundová Markéta Mgr. Ph.D. (18.12.2023)
Basic principles of selected statistical methods for analysing multidimensional data will be outlined with focus on reconciliation of the assumptions of the methods and interpretation of their results. Students will learn how to perform corresponding calculations in statistical software R.
Aim of the course -
Last update: Kubová Petra Ing. (22.01.2018)

Students will know:

1. Understand basic principles of selected statistical methods for multivariate data analysis

2. Reconcile assumptions of particular methods.

3. Understand the results of the methods.

4. Perform essential calculations with specific data in specialized software (R).

Literature -
Last update: Kříž Pavel Ing. Mgr. Ph.D. (30.05.2019)

R: Härdle W. K., Simar L.: Applied Multivariate Statistical Analysis, Springer 2015, ISBN 978-3-662-45171-7.

R: Rencher A. C., Christensen W. F.: Methods of Multivariate Analysis, John Wiley & Sons 2012, ISBN: 978-0-470-17896-6.

A: Meloun M., Militký J., Hill M.: Počítačová analýza vícerozměrných dat v příkladech, Academia, Praha 2012, ISBN: 978-80-200-2071-0.

A: Hendl J.: Přehled statistických metod, Portál, Praha 2015, ISBN: 978-80-262-0981-2.

Learning resources -
Last update: Kříž Pavel Ing. Mgr. Ph.D. (30.05.2019)

Lecture notes on e-learning

Statistická analysa dat v R (lecture notes by Doc. Spiwok, VSCHT, in Czech)

Teaching methods -
Last update: Kubová Petra Ing. (22.01.2018)

Lectures and seminars.

Syllabus -
Last update: Kříž Pavel Ing. Mgr. Ph.D. (30.05.2019)

1. Data vector, data matrix and matrix algebra (multiplication, inverse matrix, eigenvalues and eigenvectors), covariance matrix.

2. Vizualisation of multidimensional data.

3. Exploratory data analysis (EDA).

4. Cluster analysis.

5. Principal component analysis (PCA).

6. Multidimensional scaling.

7. Multidimensional parameter estimation and hypothesis testing. Bayesian statistics.

8. Multivariate analysis of variance (MANOVA).

9. Regression methods 1 - multiple linear regression.

10. Regression methods 2 - principal component regression (PCR), generalized linear models (GLM).

11. Discriminant analysis.

12. Canonical correlation analysis.

13. Factor analysis (FA).

Entry requirements -
Last update: Řehák Karel doc. Ing. CSc. (08.03.2023)

Students are expected to have either completed at least one of the prerequisite courses Applied Statistics or Statistical Data Analysis or possess the equivalent knowledge on probability theory and statistics prior to enrolling in the course.

For successful completion of the course, basic knowledge of probability and mathematical statistics is required at a level corresponding to the syllabus of the Applied Statistics course:

1. Random events, probability and its properties, independence of random events, conditional probability

2. Random variables, their probability distribution and characteristics

3. Fundamental types of probability distributions (especially normal distribution)

4. Random vectors and their distributions, correlation and independence of random variables

5. Sum of large number of random variables — Central Limit Theorem, Law of Large Numbers

6. Random sample, point estimate of expectation and variance, Maximum Likelihood and Bayesian estimators

7. Confidence intervals — calculation and interpretation

8. Testing of statistical hypotheses — basic principle, type I and II errors, interpretation of results (p-value), basic parametric and nonparametric tests


10. Test of independence of quantitative random variables (correlation test)

11. Goodness-of-fit testing, test of independence in contingency tables

12. Fundaments of regression analysis — linear, multiple, nonlinear Futher, knowledge of at least basic R software and eigenvalues and eigenvectors of matrices is recommended.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (06.05.2019)

No requirements.

Course completion requirements -
Last update: Kříž Pavel Ing. Mgr. Ph.D. (09.02.2018)

Credit for seminar project. Oral exam.

Teaching methods
Activity Credits Hours
Účast na přednáškách 1 28
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi 0.5 14
Práce na individuálním projektu 1 28
Příprava na zkoušku a její absolvování 1.5 42
Účast na seminářích 1 28
5 / 5 140 / 140