Statistical Modelling

Autumn semester 2019

General information

Lecturer	Christina Heinze-Deml
Assistants	Jinzhou Li, Drago Plecko
Lectures	Wed 8-10 HG G 5
	Thu 13-15 HG D 1.2
Course catalogue data	>>

Course content

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.

Announcements

October 31st 2019:
In December, there will be some deviations from the usual schedule:
- December 5th: Lecture instead of exercise class
- December 11th + 18th: No class
- December 12th: Exercise class
- December 19th: Question hour - questions can be sent to the assistants beforehand
September 17th 2019:
We will be using the ETH EduApp during the lectures for clicker questions. Please install it on your phone or tablet (iOS, Android). If this is not possible, you can also access the EduApp via the Web App if you bring a laptop to class.
August 23rd 2019:
Starting on September 26th, 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 Wednesdays 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 18th.

Course materials

The datasets used in the R scripts shown during the lectures can be found here.

Week	Topic
Week 1 - I	Introduction Slides (annotated) R code: 1, 2; Data Reading: Fahrmeir et al.: 1.2, 2.1 – 2.2.1, 3.1 – 3.1.1
Week 1 - II	Classical linear model Slides (annotated) R code Reading: Fahrmeir et al.: 2.2.2, 3.1.2, 3.1.3
Week 2	Classical linear model Slides (annotated) Reading: Fahrmeir et al.: 3.2.1 - 3.2.2; ESL: 3.2.3
Week 3 - I	Classical linear model Slides (annotated) R code Reading: Fahrmeir et al.: 3.2.3
Week 3 - II	Classical linear model Slides (annotated) Reading: Fahrmeir et al.: 3.2.3
Week 4	Hypothesis testing Slides (annotated) Reading: Fahrmeir et al.: 3.2.3 – 3.3.1
Week 5 - I	Hypothesis testing and confidence intervals Slides (annotated) R code Reading: Fahrmeir et al.: 3.3
Week 5 - II	Confidence intervals and model selection Slides (annotated; updated 04/11) R code (updated 04/11) Reading: Fahrmeir et al.: 3.4.1
Week 6	Model selection Slides (annotated) R code (updated 23/10) Reading: Fahrmeir et al.: 3.4.1 - 3.4.3; ISLR: 6.1
Week 7 - I	Model diagnostics Slides (annotated) R code (updated 31/10) Reading: Fahrmeir et al.: 3.4.4, 4.1.3, 4.1.4; Weisberg: 7.1, 7.3, 8.3.1
Week 7 - II	Model diagnostics Slides (annotated) R code Datasets Reading: Fahrmeir et al.: 3.4.4, 4.1.3, 4.1.4
Week 8	General linear model, weighted least squares and instrumental variables Slides R code Reading: Fahrmeir et al.: 4.1
Week 9 - I	Instrumental variables and penalized regression Slides (annotated) R code (updated 15/11) Reading: Fahrmeir et al.: 4.2.1, 4.2.2; ESL: 3.4.1
Week 9 - II	Penalized regression Slides (updated 03/02) R code Reading: Fahrmeir et al.: 4.2.1 - 4.2.4; ESL: 3.4.1 - 3.4.3; ISLR: 6.2.2
Week 10	Robust regression Slides (annotated, updated 03/02) R code (updated 20/11) Reading: Robust regression handout
Week 11 - I	Generalized linear models Slides (updated 06/12) R code Reading: Fahrmeir et al.: 2.3, 5.1, B.4.2
Week 11 - II	Generalized linear models Slides (updated 06/12) R code Reading: Fahrmeir et al.: 5.1, 5.2, 5.4, 6.1 - 6.3.1, B.4
Week 12 - I	Generalized linear models and nonparametric regression Slides R code Reading: Fahrmeir et al.: 2.5, 6.3.1, 8.1.1 - 8.1.4
Week 12 - II	Nonparametric regression Slides (updated 06/12) R code Reading: Fahrmeir et al.: 2.5, 8.1.7 - 8.1.9

Software

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

Exercise classes will take place every other week on Thursdays. The first exercise class on September 26th will feature an R tutorial with some exercises. Please install R and RStudio and bring your laptop to the exercise classes.

Series

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.

Exercises	Solutions	Due date
Series 1	Solutions 1	08.10.2019
Series 2	Solutions 2	20.10.2019
Series 3	Solutions 3	5.11.2019
Series 4	Solutions 4	20.11.2019
Series 5	Solutions 5	11.12.2019
Series 6	Solutions 6	19.12.2019

Literature

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.
S. Weisberg (2005). Applied Linear Regression. 3rd edition, Wiley.