In regression analysis, we examine the relationship between a random response variable and several other explanatory variables. In this class, we consider the theory of linear regression with one or more explanatory variables. Moreover, we also study robust methods, generalized linear models, model choice, high-dimensional linear models, nonlinear models and nonparametric methods. Several numerical examples will illustrate the theory. You will learn to perform a regression analysis and interpret the results correctly. We will use the statistical software R to get hands-on experience with this. You will also learn to interpret and critique regression analyses done by others.
Starting on September 24th, the exercise classes will take place every second Thursday. The first exercise session will include an introduction to the statistical programming language R with some exercises. In the exercise sessions, you can solve the R problems, the series and ask questions. You need to bring your own laptop for solving the R questions. On Tuesdays there will be a lecture every week and the class on Thursday will alternate between lectures and exercise sessions (exceptions will be announced). Please check this course website regularly for announcements regarding the schedule. The first lecture will be on September 15th.
Starting from November 5th, the exercise classes will take place via zoom. Please join by using the zoom details provided on the course's moodle page 1.
The datasets used in the R scripts shown during the lectures can be found here.
Two old Exams are made available here.
|Week 1 - I||Introduction|
|Week 1 - II||Classical linear model|
|Week 2||Classical linear model
|Week 3 - I||Classical linear model
|Week 3 - II||Classical linear model
|Week 4||Hypothesis testing
|Week 5 - I||Hypothesis testing and confidence intervals
|Week 5 - II||Confidence intervals and model selection
|Week 6||Model selection and the Gauss-Markov theorem
|Week 7 - I||Model selection and Logistic regression
|Week 7 - II||Logistic regression
|Week 8||Generalized linear models
|Week 9 - I||Nonlinear least squares and hypothesis testing
|Week 9 - II||Non-parametric regression
|Week 10||Non-parametric regression and cross-validation
|Week 11 - I||Non-parametric regression|
|Week 11 - II||QA-session|
|Week 12 - I||Lasso
|Week 13 - I||QA-session and Lasso|
|Week 13 - II||Lasso and robust regression|
|Week 14 - I||Robust regression|
Examples in the lecture as well as solutions to the exercises will be based on the statistical software R. R is a freely available open source program that works on all platforms and has become worldwide standard for data analysis. It can be downloaded from CRAN. An R Tutorial can be found here. The most commonly used editor for R is RStudio which can be downloaded from here.
Exercise classes will take place every other week on Thursdays. The first exercise class on September 24th will feature an R tutorial with some exercises. Please install R and RStudio and bring your laptop to the exercise classes.
If you are a PhD student who needs ETH credit points, the submission of four exercise series is mandatory. If this applies to you, please email your solutions to the assistants or place them in the corresponding tray in HG J 68. Students who need ECTS credit points have to take the exam.
|Series 1||Solutions 1||08.10.2020|
|Series 2<||Solutions 2||22.10.2020|
|Series 3||Solutions 3||5.11.2020|
|Series 4-->||Solutions 4||19.11.2020|
|Series 5||Solutions 5||3.12.2020|
|Series 6||Solutions 6||17.12.2020|
|Week 4||Hypothesis testing
|Week 6||Model selection|
|Week 8||Hypothesis testing and GLMs|
|Week 10||Residual analysis and outliers|
|Week 12||Nonparametric regression and cross-validation|
|Week 12||Model selection and instrumental variable estimators
- L. Fahrmeir, T. Kneib, S. Lang and B. Marx (2013), Regression - Models, Methods and Applications. Springer.
- T. Hastie, R. Tibshirani, and J. Friedman (2009), The Elements of Statistical Learning [ESL]. 2nd edition, Springer.
- G. James, D. Witten, T. Hastie, R. Tibshirani. An Introduction to Statistical Learning: with Applications in R [ISLR]. Springer.
- Script by Peter Bühlmann, Nicolai Meinshausen and Hans-Rudolf Künsch.
- additional Notes by Peter Bühlmann on Heteroscedastic errors and robust inference.
- S. Weisberg (2005). Applied Linear Regression. 3rd edition, Wiley.