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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 2015 to 2016
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:	http://msekce.karlin.mff.cuni.cz/~komarek/vyuka/nmsa407.html

Guarantor:	doc. RNDr. Arnošt Komárek, Ph.D.
Class:	M Mgr. PMSE M Mgr. PMSE > Povinné
Classification:	Mathematics > Probability and Statistics
Incompatibility :	NSTP194
Interchangeability :	NSTP194
Is pre-requisite for:	NMST431, NMEK450, NMST432, NMST450, NMST531, NMST438, NMFM404, NMST434, NMEK432
Is interchangeable with:	NSTP195, NSTP194

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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.

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. RNDr. Arnošt Komárek, Ph.D. (02.10.2020)

Lecture+exercises.

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.