Course Details

Mathematics 5 (E)

Academic Year 2024/25

NAA024 course is part of 1 study plan

​ NPC-SIE Winter Semester 1st year

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.

Credits

4 credits

Language of instruction

Czech

Semester

winter

Course Guarantor

prof. Ing. Jiří Vala, CSc.

Institute

Institute of Mathematics and Descriptive Geometry

Forms and criteria of assessment

course-unit credit and examination

Entry Knowledge

The basics of the theory of probability and statistics.

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.


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.

Basic Literature

ANDĚL, J. Základy matematické statistiky. 3. vydání, MatfyzPress, Praha, 2011. 360 s.
ANDĚL, J. Statistické metody. 5. vydání, MatfyzPress, Praha, 2019, 300 s.
NEUBAUER, J., SEDLAČÍK, M., KŘÍŽ O. Základy statistiky: Aplikace v technických a ekonomických oborech. Grada, Praha, 2012, 240 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.

Offered to foreign students

Not to offer

Course on BUT site

https://www.vut.cz/en/students/courses/detail/281783

Lecture

13 weeks, 2 hours/week, elective

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 weeks, 1 hours/week, compulsory

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.