ST813: Statistical Modelling
Students taking the course are expected to:
- Have knowledge of linear algebra, calculus, basic statistics
- Be able to use the statistical software R
mathematical structure of linear and generalized linear models,
including experience in recognizing such models from a given statistical
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
In relation to the competence profile of the degree it is the explicit focus of the course to:
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
- 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:
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
- 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;
the importance of and the difference between regression and dispersion
parameters, and use this knowledge in practical and theoretical
- carry out practical data analysis using statistical
modeling, including investigation of a model’s adequacy using residual
- 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.
- 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.
- 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.
Exam element a)
2 take-home assignments, graded overall
To be announced during the course
Indicative number of lessons
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.
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