In the study of the effect of one or more explanatory variables on a response variable, linear regression and analysis of variance are important techniques. In linear regression we study how a quantitative variable, like the dose of a medicine, influences a quantitative response variable, like blood pressure. In analysis of variance we compare different groups with respect to a quantitative response, e.g. comparing the yields of different corn varieties. The statistical models that underlie these techniques are special cases of the linear model. In this course we discuss linear models with a thorough treatment of the matrix algebra for which the foundation is laid in the first two weeks.
Although linear models are widely used, sometimes alternatives are preferred. 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 discussed in this course are logistic regression for a binary response (assuming a binomial distribution), and log-linear models for counts (using a Poisson distribution). Data are still assumed to be independent. 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.
In the course we will first focus on the linear algebra which will be immediately followed by an exam after 2 weeks. Another exam on the remaining part (linear and generalized linear models) will take place at the end of the course.
Students should understand the basic concepts of linear models (regression, ANOVA, ANCOVA) and generalized linear models, and the proper statistical inference methods. 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, and (3) perform a proper data analysis. Students should know the linear algebra, especially the matrix algebra, that is needed to understand Linear Models.
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Mode of Instruction
Lectures and practicals (partly computer practicals, partly exercises).
Assessment of a student will be based on a written exam in 2 parts (linear algebra and statistics).
Possibly a report on the case study in which students will be asked to analyze a practical data set or study a theoretical topic, will be part of the exam grade. This is yet to be decided upon.
The teacher will inform the students on how the inspection of and follow-up discussion of the exams will take place.
Fox (2008). Applied Regression Analysis and Generalized Linear Models. Sage
Faraway: Practical Regression and ANOVA using R. Text available as PDF at http://cran.r-project.org/doc/contrib/Faraway-PRA.pdf
Faraway (2006). Extending the linear model with R. Generalized linear, mixed effects and nonparametric regression models. Chapman & Hall/CRC
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