Academic year 2023/2024 |
Supervisor: | doc. Mgr. Zuzana Hübnerová, Ph.D. | |||
Supervising institute: | ÚM | |||
Teaching language: | Czech | |||
Aims of the course unit: | ||||
The course objective is to make students majoring in Mathematical Engineering acquainted with theoretical background of regression analysis and with real applications of regression methods in technical practice. | ||||
Learning outcomes and competences: | ||||
Students acquire needed knowledge from important parts of the probability theory and mathematical statistics, which will enable them to evaluate and develop stochastic models of technical phenomena and processes based on these methods and apply them on PC. |
||||
Prerequisites: | ||||
Rudiments of descriptive statistics, probability theory and mathematical statistics. | ||||
Course contents: | ||||
This course is concerned with the following topics: multidimensional normal distribution, linear regression model (estimates, tests of hypotheses, regression diagnostics), nonlinear regression model, introduction to ANOVA, correlation analysis, basic methods of categorical analysis. Students learn about the applicability of those methods and available software for computations. | ||||
Teaching methods and criteria: | ||||
The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures. | ||||
Assesment methods and criteria linked to learning outcomes: | ||||
Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing all written exams, and semester assignment acceptance. Preparing and defending a project. Examination: written form of the exam (70 points) and oral part (30 points): a practical written part (4 tasks related to random vectors, conditional distribution, multivariate normal distribution, regression analysis, correlation analysis, categorical data analysis); theoretical oral part (4 tasks related to basic notions, their properties, sense and practical use, and proofs of two theorems); evaluation according to the total number of points (scoring 0 points for any of 4 practical tasks or whole theoretical part means failing the exam): excellent (90 - 100 points and both proofs), very good (80 - 89 points and both proofs), good (70 - 79 points and one proof), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points). |
||||
Controlled participation in lessons: | ||||
Participation in the exercise is mandatory and the teacher decides on the compensation for absences. | ||||
Type of course unit: | ||||
Lecture | 13 × 2 hrs. | optionally | ||
Computer-assisted exercise | 13 × 2 hrs. | compulsory | ||
Course curriculum: | ||||
Lecture | Random vector, moment characteristics. |
|||
Computer-assisted exercise | Random vector, variance-covariance matrix, correlation matrix. Conditional distribution, conditional expectation, conditional variance. Characteristic function - examples, properties. Properties of the multivariate normal distribution, linear transformation. Distributions of quadratic forms - examples for normal distribution. Point and interval estimates of coefficients, variance and values of linear regression function. Statistical software on PC Testing hypotheses concerning linear regression functions: particular and simultaneous tests of coefficients, tests of model. Multidimensional linear and nonlinear regression functions and diagnostics on PC. Correlation coefficients, partial and multiple correlations. Goodness of fit tests on PC. Analysis of categorical data: contingency table, chi-square test, Fisher test. |
|||
Literature - fundamental: | ||||
1. Anděl, J.: Matematická statistika. Praha : SNTL, 1978. | ||||
2. Montgomery, D. C. - Runger, G.: Applied Statistics and Probability for Engineers, John Wiley & Sons, New York. 2002. | ||||
3. Lamoš, F. - Potocký, R.: Pravdepodobnosť a matematická štatistika. Bratislava : Alfa, 1989. | ||||
4. Anděl, J.: Základy matematické statistiky. Praha : Matfyzpress, 2005. | ||||
Literature - recommended: | ||||
1. Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2014. | ||||
2. Anděl, J.: Statistické metody. Praha : Matfyzpress, 2007. | ||||
3. Hebák, P. et al.: Vícerozměrné statistické metody (1), (2). Praha : Informatorium, 2004, 2005. | ||||
4. Zvára, K.: Regrese. Praha: Matfyzpress. 2008. |
The study programmes with the given course: | |||||||||
Programme | Study form | Branch | Spec. | Final classification | Course-unit credits | Obligation | Level | Year | Semester |
B-MAI-P | full-time study | --- no specialisation | -- | Cr,Ex | 4 | Compulsory | 1 | 3 | S |
Faculty of Mechanical Engineering
Brno University of Technology
Technická 2896/2
616 69 Brno
Czech Republic
+420 541 14n nnn
+420 726 81n nnn – GSM Telef. O2
+420 604 07n nnn – GSM T-mobile
Operator: nnnn = 1111