PřF:M5120 Linear Models in Statistics I - Course Information

M5120 Linear Models in Statistics I

Extent and Intensity

2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).

Teacher(s)

doc. Mgr. David Kraus, Ph.D. (lecturer)
Mgr. Michaela Marčeková (seminar tutor)
Mgr. Tomáš Pompa (seminar tutor)

Guaranteed by

doc. Mgr. David Kraus, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science

Timetable

Mon 14:00–15:50 M4,01024

• Timetable of Seminar Groups:

M5120/01: Tue 16:00–17:50 MP1,01014, T. Pompa
M5120/02: Tue 18:00–19:50 MP1,01014, M. Marčeková

Prerequisites

M4122 Probability and Statistics II
Calculus, linear algebra. Probability and mathematical statistics, in particular theory of estimation and testing statistical hypotheses: at the level of the course M4122. Statistical software R: at the level of the course M4130.

Course Enrolment Limitations

The course is offered to students of any study field.

Course objectives

The course offers an overview of linear statistical models as the fundamental tool of statistical analysis. Within one semester, the students encounter theory, software implementation, applications and interpretation.

Learning outcomes

After the course, the students
- are able to recognize the situations that can be addressed by linear models;
- are able to formulate and implement a model, and interpret the results;
- are aware of the limitations of the model;
- in a given situation, they are able to anticipate possible problems and avoid them by slightly modifying the procedure.

Syllabus

• Problem statement.
• Descriptive statistics and graphical diagnostics.
• Projection, conditional expectation, normal distribution.
• Linear model without the assumption of normality.
• Linear model with the assumption of normality.
• Submodel.
• Residuals and model diagnostics.
• Multicollinearity and rank-defficient models.
• Practical aspects, troubleshooting.

Literature

recommended literature
• ZVÁRA, Karel. Regrese (Regression). Praha, 2008, 253 pp. ISBN 978-80-7378-041-8. info
• WOOD, Simon N. Generalized additive models : an introduction with R. Boca Raton, Fla.: Chapman & Hall/CRC, 2006, xvii, 392. ISBN 1584884746. info
• ANDĚL, J. Základy matematické statistiky. Praha: MFF UK, 2005. info

not specified
• FARAWAY, Julian James. Linear models with R. Second edition. Boca Raton: CRC Press, 2015, 1 online. ISBN 9781439887349. URL info
• Applied multivariate statistical analysis. Edited by Richard Arnold Johnson - Dean W. Wichern. 6th ed. Upper Saddle River, N.J.: Pearson Prentice Hall, 2007, xviii, 773. ISBN 9780131877153. info
• ANDĚL, Jiří. Matematická statistika. Vyd. 2. Praha: SNTL - nakladatelství technické literatury, Alfa, vydavatelstvo technickej a ekonomickej literatury, 1985, 346 s. URL info
• RAO, C. Radhakrishna. Lineární metody statistické indukce a jejich aplikace. Translated by Josef Machek. Vyd. 1. Praha: Academia, 1978, 666 s. URL info

Teaching methods

Lectures: theoretical explanation with practical examples.
Exercises: exercises focused on in-depth understanding of the theory and on practical data analysis

Assessment methods

Conditions: semestral data project, written final exam, potentially with a bonus for an optional written midterm exam.

Language of instruction

Czech

Follow-Up Courses

• M6120 Linear statistical models II
• M7222 Generalized linear models

Further Comments

Study Materials
The course is taught annually.

Listed among pre-requisites of other courses

• M6120 Linear statistical models II
  M5120  

Teacher's information

https://is.muni.cz/auth/el/sci/podzim2023/M5120/index.qwarp

• Enrolment Statistics (Autumn 2023, recent)
  
• Permalink: https://is.muni.cz/course/sci/autumn2023/M5120