SubjectsSubjects(version: 901)
Course, academic year 2021/2022
Linear Regression - NMSA407
Title: Lineární regrese
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2020 to 2021
Semester: winter
E-Credits: 8
Hours per week, examination: winter s.:4/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Additional information:
Guarantor: doc. RNDr. Arnošt Komárek, Ph.D.
Class: M Mgr. PMSE
M Mgr. PMSE > Povinné
Classification: Mathematics > Probability and Statistics
Is pre-requisite for: NMST432, NMST531, NMST438, NMFM404, NMST434, NMEK432, NMST450, NMST431, NMEK450
Is interchangeable with: NSTP194, NSTP195
Annotation -
Last update: T_KPMS (02.05.2014)
Linear regression model, also without classical assumptions (normality, constant variance, uncorrelated errors), simultaneous testing, residual analysis and regression diagnostics.
Aim of the course -
Last update: T_KPMS (16.05.2013)

To teach students how to model the dependence of the expected value of continuous random variables on both quantitative and qualitative variables.

Course completion requirements -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (02.10.2020)

The subject is finalized by a course credit and exam. To be able to take exam, it is necessary to obtain a course credit first.

Course credit requirements:

  • Homework assignments: Each student needs to submit, within pre-specified deadlines, solutions to all homework assignments. All solutions must be graded as "acceptable" by the lecturer.

  • Final test: Each student needs to get at least 60% of the points from the final test. Each student gets exactly two possibilities to write the final test at moments being pre-specified by the lecturer. Absence to any of those two occasions (for arbitrary reasons) does not imply possibility to write the test during additional occasion.

The nature of these requirements precludes any possibility of additional attempts to obtain the exercise class credit.

Literature - Czech
Last update: T_KPMS (20.04.2016)
KHURI, A. I. Linear Model Methodology. Chapman & Hall/CRC: Boca Raton, 2010, xx+542 s. ISBN: 978-1-58488-481-1.

ZVÁRA, K. Regrese. Matfyzpress: Praha, 2008, 253 s. ISBN: 978-80-7378-041-8.

Doporučená doplňková
DRAPER, N. R., SMITH, H. Applied Regression Analysis, Third Edition. John Wiley & Sons: New York, 1998, xx+706 s. ISBN: 0-471-17082-8.

SEBER, G. A. F., LEE, A. J. Linear Regression Analysis, Second Edition. John Wiley 7 Sons: Hoboken, 2003, xvi+557 s. ISBN: 0-471-41540-5.

WEISBERG, S. Applied Linear Regression, Third Edition. John Wiley & Sons: Hoboken, 2005, xvi+310 s. ISBN: 0-471-66379-4.

ANDĚL, J. Základy matematické statistiky, druhé opravené vydání. Matfyzpress: Praha, 2007, 358 s. ISBN: 80-7378-001-1.

CIPRA, T. Finanční ekonometrie. Ekopress: Praha, 2008, 538 s. ISBN: 978-80-86929-43-9.

ZVÁRA, K. Regresní analýza. Academia: Praha, 1989, 245 s. ISBN: 80-200-0125-5.

Teaching methods -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (02.10.2020)

Distant learning, off-line combined with live discussions run by the mean of the ZOOM application.

Materials and additional instructions to the lecture are gradually published here:

pro cvičení (všechny skupiny) zde:

Requirements to the exam -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (27.09.2018)

Exam is composed of two parts

  • written part composed of theoretical and semi-practical assignments (no computer analysis);
  • oral part with questions corresponding to topics covered by lecture and exercise classes.

Problems assigned during exam are based on topics presented during lectures and also correspond to topics covered by exercise classes. Assigned problems correspond to the syllabus into extent covered by lectures.

Exam grade will be based on point evaluation of the written part and evaluation of the oral part.

Syllabus -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (03.12.2020)

1. Linear model: projection and least squares estimates (LSE), Gauss-Markov theorem, estimable parameters.

2. Normal linear model: LSE properties under the normality, tests of linear hypotheses, confidence intervals and regions, prediction.

3. Submodel, tests on submodels, coefficient of determination.

4. General linear model and generalized least squares (GLS).

5. Parameterizations of numeric and categorical regressors, interpretation of a linear regression model.

6. Residual analysis and regression diagnostics: residual plots, standardized, studentized and partial residuals, leverage, outlying and influential observations, selected tests on assumptions of a linear model.

7. Consequences of a problematic regression space, multicollinearity, effect of model misspecification.

8. Strategies of model building.

9. Selected models of analysis of variance.

10.Simultaneous inference: multiple comparison procedures, methods of Tukey, Hothorn-Bretz-Westfall, confidence bands for the regression function.

11. Maximum likelihood estimates (MLE) in the normal linear model: properties of MLE, relationship to LSE.

12. Method of least squares without satisfied classical assumptions: asymptotic properties of the LSE without assumed normality and without homoscedasticity, sandwich (White) estimate of the variance of the LSE, robustness of classical confidence intervals and tests.

Entry requirements -
Last update: doc. RNDr. Arnošt Komárek, Ph.D. (25.05.2018)
  • Vector spaces, matrix calculus;
  • Probability space, conditional probability, conditional distribution, conditional expectation;
  • Elementary asymptotic results (laws of large numbers, central limit theorem for i.i.d. random variables and vectors, Cramér-Wold theorem, Cramér-Slutsky theorem);
  • Foundations of statistical inference (statistical test, confidence interval, standard error, consistency);
  • Basic procedures of statistical inference (asymptotic tests on expected value, one- and two-sample t-test, one-way analysis of variance, chi-square test of independence);
  • Maximum-likelihood theory including asymptotic results and the delta method;
  • Working knowledge of R, a free software environment for statistical computing and graphics (
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