Foundation of Regression - NMFM334
Title: Základy regrese
Guaranteed by: Department of Probability and Mathematical Statistics (32-KPMS)
Faculty: Faculty of Mathematics and Physics
Actual: from 2024 to 2024
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech
Teaching methods: full-time
Guarantor: doc. RNDr. Michal Pešta, Ph.D.
doc. RNDr. Matúš Maciak, Ph.D.
Teacher(s): doc. RNDr. Zdeněk Hlávka, Ph.D.
doc. RNDr. Matúš Maciak, Ph.D.
RNDr. Jan Vávra, Ph.D.
Class: M Bc. FM
M Bc. FM > Povinně volitelné
Classification: Mathematics > Probability and Statistics
Pre-requisite : NMFM301, NMMA341
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Annotation -
Basic statistic course for Financial Mathematics students.
Last update: Zichová Jitka, RNDr., Dr. (10.05.2021)
Aim of the course -

To explain basics of regression models.

Last update: Zichová Jitka, RNDr., Dr. (04.06.2021)
Course completion requirements -

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:

  • Presence in class: at least 75%.
  • Homework assignment: Each student needs to submit, within the pre-specified deadline, a solution to the homework assignment. The solution must be graded as "acceptable" by the lecturer.

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

Last update: Pešta Michal, doc. RNDr., Ph.D. (24.01.2022)
Literature -

JAMES, G.; WITTEN, D.; HASTIE, T.; TIBSHIRANI, R. An Introduction to Statistical Learning (with Applications in R), 2nd edition. Springer: New York, NY, 2021, xv+607 s. ISBN: 978-1-0716-1417-4.

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.

Last update: Pešta Michal, doc. RNDr., Ph.D. (24.01.2022)
Teaching methods -

Lecture + exercises.

Last update: Zichová Jitka, RNDr., Dr. (10.05.2021)
Requirements to the exam -

Exam is oral and it is composed of two parts:

  • questions corresponding to topics covered by lecture and exercise classes;
  • discussions about the written course credit homework.

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 course credit homework and evaluation of the oral part.

Last update: Pešta Michal, doc. RNDr., Ph.D. (24.01.2022)
Syllabus -

Linear regression model.

Least squares method.

Coefficient of determination.

Quantitative and qualitative regressors, interactions and their interpretations.

Analysis of residuals a regression diagnostics.

Submodel testing, model building.

Logistic regression.

Last update: Pešta Michal, doc. RNDr., Ph.D. (24.01.2022)
Entry requirements -
  • 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 (https://www.r-project.org).

Last update: Pešta Michal, doc. RNDr., Ph.D. (24.01.2022)