Course detail
Probability and Statistics II
FSI-SP2 Acad. year: 2021/2022 Summer semester
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.
Language of instruction
Czech
Number of ECTS credits
4
Supervisor
Department
Learning outcomes of the course unit
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 realize them on PC.
Prerequisites
Rudiments of descriptive statistics, probability theory and mathematical statistics.
Planned learning activities and teaching methods
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: semester assignment (10 points) and written form of the exam (90 points) consisting of two parts: a practical part (4 tasks related to random vectors, conditional distribution, multivariate normal distribution, regression analysis, correlation analysis, categorical data analysis); theoretical part (4 tasks related to basic notions, their properties, sense and practical use, and proofs of two theorems); evaluation: 0 to 70 points for the practical part and 0 to 20 points for the theoretical part; 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).
Aims
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.
Specification of controlled education, way of implementation and compensation for absences
Participation in the exercise is mandatory and the teacher decides on the compensation for absences.
The study programmes with the given course
Programme B-MAI-P: Mathematical Engineering, Bachelor's, compulsory
Type of course unit
Lecture
26 hours, optionally
Teacher / Lecturer
Syllabus
Random vector, moment characteristics.
Conditional distribution.
Characteristic function.
Multidimensional normal distribution – properties.
Distribution of quadratic forms.
Linear regression model (LRM) and parameter estimates in LRM.
Testing hypotheses concerning linear regression model.
Special cases of LRM (regression line, regression parabola, polynomial regression, ANOVA models).
Weighted regression, an introduction into regression diagnostic and linearized regression model.
Goodness of fit tests with known and unknown parameters
Introduction to analysis of categorical data (chi-square test, measures of association, Fisher factorial test).
Correlation analysis
Computer-assisted exercise
26 hours, compulsory
Teacher / Lecturer
Syllabus
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.