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The statistical models that underlie these techniques are special cases of linear models. In this course we discuss linear models with a thorough treatment of the matrix algebra. Although linear models are widely used, sometimes alternatives are preferred.

## Algebra and Number Theory Day – Johns Hopkins University & University of Maryland

Therefore, we discuss how to check the assumptions underlying linear model: independent errors, with a normal distribution and constant variance. When the assumptions of normality and constant variance are violated, the wider class of generalized linear models may be employed. Examples are logistic regression for a binary response assuming a binomial distribution , or log-linear models for counts using a Poisson distribution. Data are still assumed to be independent. Analysis of dependent data will be discussed in the course on mixed and longitudinal modeling.

Emphasis will be on gaining understanding of the models, the kind of data that can be analyzed with these models, and with the statistical analysis of empirical data itself.

## Welcome to the Algebra and Number Theory group at the University of Copenhagen!

Students, when confronted with practical data for a linear or generalized linear model assuming independence should be able 1 understand the statistical analysis of the empirical data itself, 2 check for violations on the assumptions 2 , and perform a proper data analysis. Students should acquaint themselves with the basics of linear algebra, especially the matrix algebra that is needed to understand Linear Models. Case study report: In week four, students will be asked to analyze a practical data set or study a theoretical topic.

A report should be handed and the student will give a 15 minutes short oral presentation on the topic of his or her report.

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The room and building for the exam will be announced on the electronic billboard, to be found at the opposite of the entrance, the content can also be viewed here.