Course detail

Mathematics 5 (E)

FAST-NAA024Acad. year: 2022/2023

Parametric and non-parametric problems with one and two random samples, analysis of relationships, regression analysis, introduction to time series, analysis of variance. Use of the EXCEL program.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

prof. Ing. Jiří Vala, CSc.

Department

Institute of Mathematics and Descriptive Geometry (MAT)

Learning outcomes of the course unit

Knowledge of using the statistical programs to apply statistics in regression, analysis of relationships and time series. Knowledge of numerical methods to solve non-linear equations, systems of linear equations, to interpolate functions by polynomials, to differentiate and integrate numerically.

Prerequisites

The basics of the theory of probability and statistics.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Not applicable.

Assesment methods and criteria linked to learning outcomes

Not applicable.

Course curriculum

1. Parametric problems with one random sample.
2. Parametric problems with two random samples.
3. Non-parametric tests. Goodness-of-fit tests.
4. Analysis of relationships of quantitative variables.
5. Analysis of relationships of qualitative variables.
6. Multivariate data analysis.
7. Cluster analysis.
8. Regression analysis. Classical linear model.
9. Choice of a regression model. Nonlinear regression model.
10. Regression polynomial. General linear model.
11. Time series.
12. Decomposition of time series.
13. Analysis of variance.

Work placements

Not applicable.

Aims

Students will learn how to use the EXCEL and STATISTICA programs to apply statistics, study the basic notions of regression, analysis of relationships, analysis of time series. Next they will acquaint themselves with the methods used to solve non-linear equations, iteration methods used to solve systems of linear and non-linear equations, to interpolate functions by polynomials and cubic splines, learning how to numerically differentiate, solve boundary problems in second order ordinary differential equations by the method of grids and by numeric integration.

Specification of controlled education, way of implementation and compensation for absences

Extent and forms are specified by guarantor’s regulation updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ANDĚL, J. Statistické metody. 5. vydání, MatfyzPress, Praha, 2019, 300 s.
ANDĚL, J. Základy matematické statistiky. 3. vydání, MatfyzPress, Praha, 2011. 360 s.
CASELLA, G., BERGER, R.L. Statistical Inference. 2nd ed., Brooks/Cole Cengage Learnign, Belmont, 660 p. ISBN 978-0-534-24312-8.
HASTIE, T., TISHIRANI, R., FRIEDMAN, J. The Elements of Staistical Learning. 2nd ed., Springer, New York, 745 p. ISBN​ 978-0-387-84858-7.
NEUBAUER, J., SEDLAČÍK, M., KŘÍŽ O. Základy statistiky: Aplikace v technických a ekonomických oborech. Grada, Praha, 2012, 240 s.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme NPC-SIE Master's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Mgr. Jana Bulantová, Ph.D.

Syllabus

1. Parametric problems with one random sample. 2. Parametric problems with two random samples. 3. Non-parametric tests. Goodness-of-fit tests. 4. Analysis of relationships of quantitative variables. 5. Analysis of relationships of qualitative variables. 6. Multivariate data analysis. 7. Cluster analysis. 8. Regression analysis. Classical linear model. 9. Choice of a regression model. Nonlinear regression model. 10. Regression polynomial. General linear model. 11. Time series. 12. Decomposition of time series. 13. Analysis of variance.

Exercise

13 hod., compulsory

Teacher / Lecturer

Mgr. Jana Bulantová, Ph.D.
RNDr. Mgr. Lucie Zrůstová, Ph.D.

Syllabus

1. Graphical methods of data files representation I. 2. Graphical methods of data files representation II. 3. Computational methods of data processing I. 4. Computational methods of data processing II. 5. Summary of survey analysis of one-dimensional populations. 6. Two-dimensional data files. 7. Linear regression. 8. Nonlinear regression. 9. Linear forecasting. 10. Multiple correlation and regression. 11. Time series. 12. Interpolation. Numeric differentiating. 13. Tests of hypotheses. Seminar evaluation.