# SF2950 Applied Mathematical Statistics 7.5 credits

The overall purpose of the course is that the student should be well acquainted with statistical modelling and analysis of observd and experimental data and provide insight in statistical design of experiments, sampling methods and concepts in statistical quality control. During the course regression and variance analysis models are applied to real problems.

### Offering and execution

Course offering missing for current semester as well as for previous and coming semesters

## Course information

### Content and learning outcomes

#### Course contents *

Theory of the common linear model: Estimation, confidence intervals and hypothesis testing.

Regression analysis: Multiple regression analysis.

Modelling: selection bias, simultaneity, heteroskedasticity, multikollinearity and estimation methods for such problems. The LOGIT model.

Variance analysis: One, two and multi way variance analysis, hierarchical splitting. Systematical and stochastic components.

Experimental planning: Factor trial, totally randomised tests, randomised blocks, Latin squares totally and fractional 2k-experiments.

Sample theory: Simple random samples, stratified samples.

Statistical quality control: Differentiating and guided control.

Non parametric methods.

#### Intended learning outcomes *

To pass the course, the student should be able to do the following:

• analyse and model real data with statistical computer software
• analyse and apply the theory of the general linear model on real problems by estimating the parameters in the general model and quantify the uncertainty in those estimates and determine how this affect the conclusions when testing statistical hypothesis
• perform multiple regression analysis and determine the applicability of the model on a real problem
• Understand problems with observed data, such as simultaneity and sample selection bias, and know  how to use instrumental variables.
• perform a one and two sided variance analysis and distinguish between systematic and random factor models in real modelling situations
• analyse and judge different choices of experimental plans, i.e., distinguish between completely randomised experiments, randomised blocks and Latin squares when planning and modelling experiments. Judge the applicability of randomised and stratified sampling.
• apply full and fractional 2k designs on concrete problems
• decide and apply nonparametric methods on real problems based on different modelling aspects

• Combine all the concepts and methods mentioned above in order to solve more complex problems.

#### Course Disposition

No information inserted

### Literature and preparations

#### Specific prerequisites *

Previous knowledge is assumed equivalent to Mathematical Statistics SF1906 (5B1506) and Linear Algebra SF1604 (5B1109).

#### Recommended prerequisites

No information inserted

#### Equipment

No information inserted

#### Literature

Material from the department.

### Examination and completion

A, B, C, D, E, FX, F

#### Examination *

• LAB1 - Laboratory Work, 1.5 credits, Grading scale: P, F
• TEN1 - Examination, 6.0 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

#### Other requirements for final grade *

Assignment (LAB1; 1,5 university credits), written exam (TEN1; 6 university credits).

#### Opportunity to complete the requirements via supplementary examination

No information inserted

#### Opportunity to raise an approved grade via renewed examination

No information inserted

### Further information

#### Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2950

SCI/Mathematics

Mathematics

Second cycle