M5VM05 Statistical modelling

Faculty of Science
autumn 2017
Extent and Intensity
2/1/0. 3 credit(s) (fasci plus compl plus > 4). 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
Contact Person: doc. Mgr. Jan Koláček, Ph.D.
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 18. 9. to Fri 15. 12. Thu 10:00–11:50 M4,01024
  • Timetable of Seminar Groups:
M5VM05/01: Mon 18. 9. to Fri 15. 12. Thu 12:00–12:50 M4,01024, J. Koláček
Prerequisites
KREDITY_MIN(80)||TYP_STUDIA(N)
Basic terms from theory of probability and statistics. Basic knowledge of R language.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The course focuses on basic statistical methods and models. In the beginning, 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, how to use these results for specific models, understand the relationships between different types of models, interpret their results.
Syllabus
  • 1.Exploratory data analysis. Number characteristics of data sample, diagnostics graphs - boxplot,N-P plot, Q-Q plot, P-P plot, histogram.
  • 2.Basic terms of mathematical statistics: random sampling, basic statistics and their properties, testing of hypotheses. The empirical distribution function and survival function.
  • 3.Basics of regression and correlation analysis: the term of regression and correlation, correlation coefficient, multiple correlation coefficient, partial correlation coefficient.
  • 4.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.
  • 5.Analysis of variance. Construction of the model and testing the hypothesis about sample means equality. Sample variance equality tests. Multiple comparisons methods.
  • 6.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.
  • 7.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
  • ANDĚL, Jiří. Matematická statistika. Praha: SNTL - Nakladatelství technické literatury, 1985. info
  • RAO, C. Radhakrishna. Lineární metody statistické indukce a jejich aplikace. Translated by Josef Machek. Vyd. 1. Praha: Academia, 1978, 666 s. URL info
Teaching methods
Lectures: theoretical explanation with practical examples, Excercises: computer excercises focused on acquirement of basic concepts, solving simple tasks in R language
Assessment methods
Lectures and exercises. Active work in exercises. One computer test within the semester. The test consists of 2-3 examples and is for 30 points. 50% of points is needed to pass fulfilling requirements. Examination consists of two parts: written and oral. Written part consists of 8 theoretical questions, each for 10 points. The final result is corrected by the oral part. Final grade: A: 72 - 80 points B: 63 - 71 points C: 54 - 62 points D: 45 - 53 points E: 36 - 44 points F: 0 - 35 points
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2011 - acreditation, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, Autumn 2018, Autumn 2019.
  • Enrolment Statistics (autumn 2017, recent)
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