639-3021/01 – Foundations of Mathematical Statistics (ZMS)
| Gurantor department | Department of Quality Management | Credits | 4 |
| Subject guarantor | Ing. Filip Tošenovský, Ph.D. | Subject version guarantor | Ing. Filip Tošenovský, Ph.D. |
| Study level | undergraduate or graduate | Requirement | Compulsory |
| Year | 1 | Semester | winter |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FMT | Intended for study types | Follow-up Master |
Subject aims expressed by acquired skills and competences
Knowledge of basic statistical methods
Analysis of real data
Ability to process correctly experimental data
Managing work with Excel
Teaching methods
Lectures
Tutorials
Summary
The primary aim of the subject is an exposition of the theory of estimation of population parameters, hypothesis testing, modelling of technological processes with regression models and their assessment by correlation analysis. Multivariate regression is taught under the required theoretical conditions. Correlation analysis shows ways of measuring dependence for various types of variables.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Two tests in the course of the semester, where the score is counted towards the cumulative credit points.
One project, where the score is counted towards the cumulative credit points.
The examination is in written form.
E-learning
Other requirements
80% attendance in seminars
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Introduction to statistics – explanation of its use in metallurgy. Graphical representation of data samples, assessment of data type. General principles of testing.
2. Confirmation of data sample homogeneity using graphs. Outliers – their depiction, detection (box plot) and solution.
3. Confirmation of data independence using graphs. Effect of data dependence on quality of data sample processing.
4. Confirmation of normality: normal distribution, Gauss curve and its parameters, empirical histogram. Reasons why normality is required, and procedures to be followed if the normality condition is not met.
5. Descriptive characteristics of location, variability, skewness and kurtosis. The notion of robustness of numerical characteristics.
6. Student’s distribution, Fisher’s distribution, Pearson’s distribution and their graphs. Examples of using the distributions. Use of tables of quantiles and critical values.
7. Point estimation and confidence intervals. „Confidence level“ and „nivel of test“.
8. Analysis of two data samples. Testing the difference of expected values and variances. Two-sample t-test, F-test.
9. Evaluating a measure of dependence (correlation) of two variables: Pearson’s correlation coefficient, Spearman’s rank correlation coefficient.
10. Regression analysis – simple (paired) linear regression. Estimation of regression coefficients by least squares. Assessment of significance and quality of the regression function. Simple nonlinear regression models (power, exponential, logarithmic, quadratic and polynomial models).
11. Regression analysis – multivariate linear regression. Assessment of significance of the model and its regression coefficients. Use of multivariate regression.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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