M5VM05 Statistical modelling

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/1. 5 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. Mgr. Jan Koláček, Ph.D. (lecturer)
Guaranteed by
doc. Mgr. Jan Koláček, Ph.D.
Department of Mathematics and Statistics – Departments – Faculty of Science
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The course focuses on basic statistical methods and models. In the early parts basic concepts of mathematical statistics are studied. Then a regression analysis is studied, as the first the linear regression model, followed by generalized linear models. It is a course where the practical applications in other fields is immediate and very common. At the end of this course the student will be able to understand the principles of mathematical statistics and data analysis, to learn how to use these results for specific models, to understand the relationships between different types of models, interpret their results.
Syllabus
  • 1.Basic terms of mathematical statistics: random sampling, basic statistics and their properties, testing of hypotheses. The empirical distribution function and survival function. Exploratory Data Analysis.
  • 2.Basics of regression and correlation analysis: the term of regression and correlation, correlation coefficient, multiple correlation coefficient, partial correlation coefficient.
  • 3.Linear regression model: its definition, estimates of unknown parameters, hypothesis testing, verification of the model. Most important applications: two-sided t-test, analysis of variance, standard regression models - linear regression, polynomial and trigonometric regression. Regression models for correlated data.
  • 4.Generalized linear models: description of model components (a linker function, linear predictor, the distribution of exponential type for dependent variables). The most important applications: gamma regression, regression models for the alternative (binary) and binomial data, batch response models, models for nominal and ordinal data, poisson regression, log-linear models.
  • 5.Modeling of dependence between qualitative variables - contingency tables. Testing the independence and homogeneity, four-array contingency tabulars.
Literature
    recommended literature
  • ANDĚL, Jiří. Základy matematické statistiky. Vyd. 1. Praha: Matfyzpress, 2005, 358 s. ISBN 8086732401. info
  • An introduction to generalized linear models. Edited by Annette J. Dobson. 2nd ed. Boca Raton: CRC Press, 2002, vii, 225 s. ISBN 1-58488-165-8. info
  • DUPAČ, Václav and Marie HUŠKOVÁ. Pravděpodobnost a matematická statistika. Praha: Karolinum, 2001, 162 s. ISBN 8024600099. info
  • CLEVELAND, William S. Visualizing data. Murray Hill: AT & T Bell Laboratories, 1993, 360 s. ISBN 0-9634884-0-6. info
  • RAO, C. Radhakrishna. Lineární metody statistické indukce a jejich aplikace. Translated by Josef Machek. Vyd. 1. Praha: Academia, 1978, 666 s. URL info
  • ANDĚL, Jiří. Matematická statistika. 1. vyd. Praha: SNTL/ALFA, 1978, 346 pp. info
Language of instruction
Czech
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2011 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019.