M5120 Linear Models in Statistics I

Faculty of Science
Autumn 2015
Extent and Intensity
2/1/0. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
Mgr. Ondřej Pokora, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 M1,01017
  • Timetable of Seminar Groups:
M5120/01: Wed 14:00–14:50 MP1,01014, O. Pokora
M5120/02: Wed 13:00–13:50 MP1,01014, O. Pokora
M5120/03: Wed 15:00–15:50 MP1,01014, O. Pokora
Prerequisites
KREDITY_MIN(30) && ( M4122 Probability and Statistics II || M6130 Computational statistics )
Basics of probability and statistics, theory of estimation, testing statistical hypotheses. Calculus and linear algebra. Computer exercices: basis knowledge of R language at the level of the course M4130 "Mathematical Software".
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of the course the student should be able to understand and use basic methods of statistical regression analysis, which are explained by a matrix approach. Programming environment R is used in the exercises for the basic statistical analysis.
Syllabus
  • Basic knowledge of matrix algebra: positive definite matrix, idempotent matrix, generalized inverse of matrix
  • Normal distribution: n-dimensional normal distribution and its properties, distribution of quadratic forms
  • Regression: regular linear regression model, least squares method and estimators of model's parameters, properties of the estimators, testing hypotheses about the parameters and confidence intervals for parameters, basic of regression diagnostics
  • Correlation: correlation coefficient, multiple correlation coefficient, partial correlation coefficient, their sampling opposites and tests for them
  • Exercises: estimation of parameters using maximum likelihood and moment method; random vectors and matrix calculus; variance-covariance matrix; linear regression model; sample correlations; practical computations in R software.
Literature
  • ANDĚL, Jiří. Matematická statistika. Vyd. 2. Praha: SNTL - nakladatelství technické literatury, Alfa, vydavatelstvo technickej a ekonomickej literatury, 1985, 346 s. URL info
  • RAO, C. Radhakrishna. Lineární metody statistické indukce a jejich aplikace. Translated by Josef Machek. Vyd. 1. Praha: Academia, 1978, 666 s. URL info
Teaching methods
Lectures: theoretical explanation with practical examples Exercises: solving problems for understanding of basic concepts and theorems, contains also more complex problems.
Assessment methods
Conditions: active participation in seminars, individual homeworks, 1 test on computer. Evaluation: written (weight 50 %) and oral (weight 50 %) final examination, at least 50 % of points is needed to pass.
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2015, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2015/M5120