Syllabus for |
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MVE190 - Linear statistical models
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| Syllabus adopted 2014-02-13 by Head of Programme (or corresponding) |
| Owner: MPENM |
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7,5 Credits |
| Grading: TH - Five, Four, Three, Not passed |
| Education cycle: Second-cycle |
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Major subject: Mathematics
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Department: 11 - MATHEMATICAL SCIENCES
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Teaching language: English
Open for exchange students
| Course module |
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Credit distribution |
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Examination dates |
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Sp1 |
Sp2 |
Sp3 |
Sp4 |
Summer course |
No Sp |
| 0108 |
Examination |
7,5 c |
Grading: TH |
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7,5 c
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14 Jan 2016 am M, |
Contact examiner, |
25 Aug 2016 pm SB
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In programs
TKITE SOFTWARE ENGINEERING, Year 3 (compulsory elective)
MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (elective)
Examiner:
Professor
Rebecka Jörnsten
Go to Course Homepage
Eligibility:
In order to be eligible for a second cycle course the applicant needs to fulfil the general and specific entry requirements of the programme that owns the course. (If the second cycle course is owned by a first cycle programme, second cycle entry requirements apply.)
Exemption from the eligibility requirement:
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling these requirements.
Course specific prerequisites
MVE155 Statistical Inference or a similar course
Aim
The course covers the following topics:
- multidimensional normal distributions
- general linear models in linear algebra terms
- statistical analysis of general linear models using algebraic tools like projections,
generalized matrix inverses and quadratic forms
- the duality of hypothesis tests and confidence sets
- Sheffe's and Tukey's methods for multiple tests and confidence intervals
- noncentral t- and F-distributions and their use for test power computations
- tolerance and prediction intervals
- graphical methods for model validation
- introduction to generalizations towards general heteroscedastic and covariance structures
- generalized linear models with link function for some exponential families
- estimation algorithms for various link functions.
- hypothesis testing and confidence intervals for linear combinations of parameters in
the generalized linear models: the binomial, Poisson and multinomial distribution cases
- generalized residuals and their use.
Learning outcomes (after completion of the course the student should be able to)
Build a general linear model for practical applications and perform the statistical analysis, mostly multiple linear regression by some statistical software.
Describe and analyze linear models using matrix algebra.
Content
- general linear models
in linear algebra terms
- model validation
- transformation
- interaction
- multicollinearity
- predictor selections
- generalized linear models (briefly)
Organisation
Lectures, mathematical exercises, computer labs,
practical work in groups with real data
Literature
Applied Regression Analysis 3rd ed, Draper and Smith,
Wileys series in probability and statistics
Examination
Written examination, assignments