Course detail

Probability and Statistics II

FSI-SP2Acad. year: 2007/2008

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

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

doc. RNDr. Jaroslav Michálek, CSc.

Department

Institute of Mathematics (ÚM)

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 applicable.

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: regression analysis, ANOVA, nonparametric tests, categorial analysis, principal components) using the summary of formula; 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

Not applicable.

Work placements

Not applicable.

Aims

The course objective is to make students majoring in Mathematical Engineering acquainted with methods of multivariate statistical analysis, ANOVA, nonparametric tests, categorial analysis, and with their realization on PC using systems Statistica, MATLAB. Students prepare for independent developing stochastic models of real technical phenomena and processes.

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

Anděl, J.: Matematická statistika. Praha : SNTL, 1978. (CS)
Montgomery, D. C. - Runger, G.: Applied Statistics and Probability for Engineers, John Wiley & Sons, New York. 2002. (EN)
Lamoš, F. - Potocký, R.: Pravdepodobnosť a matematická štatistika. Bratislava : Alfa, 1989.

Recommended reading

Karpíšek, Z.: Matematika IV. Statistika a pravděpodobnost. Brno : FSI VUT v CERM, 2014. (CS)
Anděl, J.: Statistické metody. Praha : Matfyzpress, 2007. (CS)
Hebák, P. et al.: Vícerozměrné statistické metody (1), (2). Praha : Informatorium, 2004, 2005. (CS)

Classification of course in study plans

  • Programme B3901-3 Bachelor's

    branch B3910-00 , 3. year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hours, optionally

Teacher / Lecturer

doc. RNDr. Jaroslav Michálek, CSc.

Syllabus

Multidimensional normal distribution - properties.
Introduction to the regression analysis (regression function, classification, properties, skedasticity).
Multidimensional linear regression model (assumptions, point and interval estimates of coefficients, variance and functional values).
Testing hypotheses concerning linear regression model (particular and simultaneous tests of coefficients, tests of model).
Multicolinearity and ridge regression, heteroskedasticity and autocorrelation of linear model, transformation and weights, orthogonalization.
Nonlinear regression model (problems, point and interval estimates, tests of hypotheses).
Analysis of variance with one factor (test of factor, homogeneity test, tests of contrasts).
Multifactor analysis of variance without and with interactions (tests of factors and interactions, homogeneity test, tests of contrasts).
Nonparametric methods of testing statistical hypotheses (sign test, Wilcoxon tests, Kruskal-Wallis test).
Nonparametric methods of testing statistical hypotheses (Friedman test, Spearman and Kendall coefficient of rank correlation).
Introduction to analysis of categorial data (contingency, chi-square test, measures of association, Fisher test).
Correlation analysis (data matrix, covariance and correlation matrix, total and group independency).
Principal component method (components, geometrical consequence, properties, interpretation).

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer

doc. RNDr. Jaroslav Michálek, CSc.

Syllabus

Defining the regression function profile. Identification of statistical software on PC.
Point and interval estimates of coefficients, variance and values of linear regression function.
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.
ANOVA 1: tests of factor, homogeneity and contrasts.
ANOVA 2 without and with interaction: tests of factors, interaction, homogeneity and contrasts.
ANOVA on PC.
Nonparametric methods of testing statistical hypotheses: sign test, test of randomness, Wilcoxon tests.
Nonparametric methods of testing statistical hypotheses: Kruskal-Wallis test, Friedman test, test of rank correlation.
Analysis of categorial data: contingency table, chi-square test, Fisher test.
Nonparametric tests and analysis of categorial data on PC.
Principal component method: eigenvalues, principal components, application.
Principal component method and cluster analysis on PC.