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Linear Regression - NMSA407

Title:	Lineární regrese
Guaranteed by:	Department of Probability and Mathematical Statistics (32-KPMS)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2023
Semester:	winter
E-Credits:	8
Hours per week, examination:	winter s.:4/2, C+Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	English, Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	https://www2.karlin.mff.cuni.cz/~kulich/vyuka/linreg/index.html

Guarantor:	doc. Mgr. Michal Kulich, Ph.D.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinné
Classification:	Mathematics > Probability and Statistics
Is pre-requisite for:	NMST432, NMST436, NMST564, NMST434, NMST531, NMST431, NMST438, NMEK432, NMST511, NMST422, NMFM404, NMEK511, NMST424, NMST412, NMST444, NMSA562, NMST450, NMEK450
Is interchangeable with:	NSTP194, NSTP195
In complex pre-requisite:	NMFP406
Is complex co-requisite for:	NMST545

Opinion survey results Examination dates WS schedule Noticeboard

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. Mgr. Michal Kulich, Ph.D. (07.09.2022)

The subject is finalized by a tutorial credit and an exam. Only the students who have obtained the tutorial credit can attempt to take the exam. The exam has two parts: written and oral.

Tutorial credit requirements:

1. Regular small assignments: A student needs to prepare acceptable solutions to at least 10 out of 12 tutorial class assignments. An assignment can be solved either during the corresponding tutorial class or the solution needs to be submitted within a pre-specified deadline.

2. Project: A student needs to submit a project satisfying the requirements given in the assignment. A corrected version of an unsatisfactory project can be resubmitted once.

The nature of these requirements precludes any possibility of additional attempts to obtain the tutorial credit (with the exceptions listed above).

Literature - Czech

Last update: T_KPMS (20.04.2016)

Základní
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. Mgr. Michal Kulich, Ph.D. (03.09.2022)

This course requires personal presence, no distant teaching components will be available.

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. Mgr. Michal Kulich, Ph.D. (02.08.2023)

1. Introduction - Simple linear regression

2. Linear regression model, least squares method

3. Properties of LS estimates

4. Statistical inference in LR model

5. Predictions

6. Model Checking and Diagnostic Methods (residuals)

7. Transformation of the response

8. Parametrization of a single covariate

9. Interactions

10. Analysis of variance (ANOVA) models

11. Multiple tests and simultaneous confidence intervals

12. Regression model with multiple covariates

13. Regression Models With Heteroskedastic Data (weighted least squares, sandwich estimation)

14. Sources of Bias in Regression Estimation (Covariate measurement errors, sampling bias)

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 (https://www.r-project.org).