M6120 Linear statistical models II

Faculty of Science
Spring 2025
Extent and Intensity
2/2/0. 4 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
doc. PaedDr. RNDr. Stanislav Katina, Ph.D. (lecturer)
Mgr. Vojtěch Šindlář (seminar tutor)
Guaranteed by
doc. PaedDr. RNDr. Stanislav Katina, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
M5120 Linear Models in Statistics I
Linear regression model: at the level of the course M5120. 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 also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
In the first part, the course offers a detailed study of selected special cases of the linear model. In the second part, an overview of a broad spectrum of generalizations of the linear model is provided; the focus is on the applications of these methods and connections between them. The students are also made aware of the master courses and literature offering more detailed information on the studied modelling techniques.
Learning outcomes
Student will be able:
- to test statistical hypotheses in LRM;
- to build up and explain suitable LRM;
- to apply LRM on real data;
- to implement LRM in R.
Syllabus
  • Asymptotic statistical tests as Linear Regression Mode (LRM)
  • One-way analysis of variance (ANOVA) with fixed effects (homogeneity and inhomogeneity of variances)
  • Two-way and hierarchical ANOVA with fixed effects.
  • Analysis of covariance (ANCOVA).
  • Quadratic and polynomial LRM.
  • Joint and conditional multivariate normal disrtribution.
  • Correlation analysis.
  • LRM (homogeneity and inhomogeneity of variances), LRM with fixed effects and correlated errors, weighted least squares.
  • Orthogonal regression model.
  • Implementations in R.
Literature
    recommended literature
  • KATINA, Stanislav, Miroslav KRÁLÍK and Adéla HUPKOVÁ. Aplikovaná štatistická inferencia I. Biologická antropológia očami matematickej štatistiky (Applied statistical inference I). 1. vyd. Brno: Masarykova univerzita, 2015, 320 pp. ISBN 978-80-210-7752-2. info
  • HARRELL, Frank E. Regression modeling strategies : with applications to linear models, logistic and ordinal regression, and survival analysis. Second edition. Heidelberg: Springer, 2015, xxiii, 582. ISBN 9783319194240. info
  • FARAWAY, Julian James. Linear models with R. Second edition. Boca Raton, FL: CRC Press/Taylor & Francis Group, 2014, xii, 274. ISBN 9781439887332. info
  • RAO, C. Radhakrishna and Helge TOUTENBURG. Linear models : least squares and alternatives. New York: Springer-Verlag, 1995, 352 s. ISBN 0387945628. info
Teaching methods
Lectures: theoretical explanation with practical examples.
Exercises: practicals focused on data analysis in R. On-line using MS Teams or full-time according to the according to the development of the epidemiological situation and the applicable restrictions.
Assessment methods
Conditions: semestral data project, oral final exam. The conditions may be specified according to the development of the epidemiological situation and the applicable restrictions.
Language of instruction
Czech
Further comments (probably available only in Czech)
The course is taught annually.
The course is taught: every week.
Teacher's information
https://is.muni.cz/auth/el/1431/jaro2017/M6120/index.qwarp
Přednášky budou probíhat prezenčně dle rozvrhu. V IS bude vždy k dispozici záznam textu přednášky v PDF (přednášející text píše elektronickým perem na obrazovce tabletu a tento se zobrazuje na plátně) a slajdy v PDF s TeXovaným textem. Záznamy se budou sdílet až po dané přednášce a před další přednáškou.

K získání zápočtu je potřeba aktivní účast na cvičeních (povolené jsou 2 neomluvené absence). Za omluvenou absenci se považuje výhradně absence omluvená na studijním oddělení a zavedená do informačního systému v řádném termínu (do 5 pracovních dnů od termínu konání výuky). Je to v souladu se studijním řádem, kde se v čl.9 odstavci (7) píše, že (7) Student je povinen písemně omluvit na studijním oddělení fakulty svou neúčast do 5 pracovních dnů od termínu konání výuky, jež je omlouvána.

The course is also listed under the following terms Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024.
  • Enrolment Statistics (Spring 2025, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2025/M6120