Course detail

Probability and Statistics 2

FP-Vps2PAcad. year: 2013/2014

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, categorial analysis, selected multivariate methods (correlation analysis). Students learn of the applicability of those methods and disposable software for computations.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

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.

Co-requisites

Not applied.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations.

Assesment methods and criteria linked to learning outcomes

Course-unit credit requirements: active participation in seminars, mastering the subject matter, passing both written exams and semester assignment acceptance. Preparing and defending a project. Examination (written form) consists of two parts: a practical part (4 tasks related to: random vectors, conditional distribution, multivariate normal distribution, regression analysis, categorial data analysis); theoretical part (4 tasks related to basic notions, their properties, sense and practical use, and proofs of two theorems); evaluation: each task 0 to 20 points and each theoretical question 0 to 5 points; evaluation according to the total number of points (scoring 0 points for any theoretical part task means failing the exam): excellent (90 - 100 points), very good (80 - 89 points), good (70 - 79 points), satisfactory (60 - 69 points), sufficient (50 - 59 points), failed (0 - 49 points).

Course curriculum

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 case 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 categorial data (contingency, chi-square test, measures of association, Fisher test).
Correlation analysis

Work placements

Not applicable.

Aims

The course objective is to make students from 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

Attendance at seminars is controlled and the teacher decides on the compensation for absences.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Not applicable.

Recommended reading

Not applicable.

Classification of course in study plans

  • Programme BAK-KME Bachelor's

    branch BAK-MME , 2 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Exercise

26 hod., compulsory

Teacher / Lecturer