# ST813: Statistical Modelling

## Comment

## Entry requirements

## Academic preconditions

Students taking the course are expected to:

- Have knowledge of linear algebra, calculus, basic statistics
- Be able to use the statistical software R

## Course introduction

mathematical structure of linear and generalized linear models,

including experience in recognizing such models from a given statistical

problem.

The course builds on the knowledge acquired in the courses

ST521: Mathematical Statistics and on knowledge of linear algebra

corresponding to the course MM538: Algebra and Linear Algebra, and gives

an academic basis for advanced courses in statistics and master thesis

projects.

In relation to the competence profile of the degree it is the explicit focus of the course to:

- have

an overview of the various types of linear and generalized linear

models and the main examples of these, as well as to identify which

problems can be solved by means of such models; - be skilled at

manipulating the mathematical and statistical elements of linear and

generalized linear models and to clearly distinguish between exact and

asymptotic results; - know how to securely apply the theoretical

results for linear and generalized linear models to concrete examples

and explain the practical interpretation of the results - have familiarity with the statistical package R, and routine in its use for statistical modeling.

## Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

- recognize

the different types of statistical models and describe their

similarities and differences, and explain the role that the response

variable, explanatory variables, variance function and link function

play for statistical modeling; - be able to manipulate the

mathematical and statistical elements of linear and generalized linear

models, such as parameters and principles of estimation, the derivation

of statistical tests based on standard errors deviance and residual sum

of squares; - obtain an overview of the most important examples of

linear and generalized linear models, and to derive theoretical

properties of new models based on the general theory; - recognize

the importance of and the difference between regression and dispersion

parameters, and use this knowledge in practical and theoretical

contexts: - carry out practical data analysis using statistical

modeling, including investigation of a model’s adequacy using residual

analysis; - perform the statistical analysis using the statistical

software R, including the ability to identify and interpret relevant

information in the program output; - document the results of a statistical analysis in the form of a written report.

## Content

- Linear models, simple and multiple regression.
- Parameter estimation, hypothesis tests and confidence regions.
- Residual analysis.
- Transformation of variables, polynomial regression.
- The one-way ANOVA model.
- Model building and variable selection.
- Prediction.
- Natural exponential families; moment generating functions; variance functions;
- Dispersion models;
- Likelihood theory;
- Chi -square, F- and t-tests; analysis of deviance;
- Iterative least- squares algorithm;
- Normal-theory linear models,
- Logistic regression,
- Analysis of count data, positive data.

## Literature

## Examination regulations

## Exam element a)

## Timing

## Tests

## 2 take-home assignments, graded overall

## EKA

## Censorship

## Grading

## Identification

## Language

## Examination aids

To be announced during the course

## ECTS value

## Additional information

## Indicative number of lessons

## Teaching Method

In the intro phase a modified version of the classical lecture is employed, where the terms and concepts of the topic are presented, from theory as well as from examples based on actual data. In these hours there is room for questions and discussions. In the training phase the students work with data-based problems and discussion topics, related to the content of the previous lectures in the intro phase. In these hours there is a possibility of working specifically with selected difficult concepts. In the study phase the students work independently with problems and the understanding of the terms and concepts of the topic. Questions from the study phase can afterwards be presented in either the intro phase hours or the training phase hours.

Educational activities

The students are expected to:

- Work with the new concepts and terms introduced.
- Increase their understanding of the topics covered during the lectures.
- Solve relevant exercises.
- Read the text book chapters and the scientific journal articles provided as support for the lectures