Regression

Outline:

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, and nonparametric methods. Several numerical examples will illustrate the theory. The main goals for this class are:

• That you 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.
• That you learn to interpret and critique regression analyses done by others. This is important because regression analysis is one of the most widely used statistical methods.

Schedule / Exercises:

Wednesdays there will be lectures every week (exceptions will be announced). Fridays will alternate between lectures and exercise sessions. The first exercise session is on February 21 and will be an introduction to the statistical programming language R. All exercises take place in computer rooms, where you can solve the R questions and ask questions. You can also bring your own laptop if you prefer. Please check this course website regularly for announcements regarding the schedule.

Text:

• Text by Prof. Künsch (english)
  
• Practical regression with R by Julian R. Faraway (2002) with R-code

Additional material:

An Introduction to R

R reference card by Tom Short

R-Scripts, Outputs, and Slides:

admissions.R

admission.pdf

admission_fit.pdf

admission_output.pdf

brainsize.R

brainsize.txt

father.R

father.pdf

qqexamples.R

qqexamples.pdf

qqplots.R

qqplots.pdf

qqplot_examples_smallsample.pdf

qqplots_FALSE.pdf

qqplots_TRUE.pdf

tukeyplots.R

tuk1.pdf

tuk2.pdf

tuk3.pdf

xplots.pdf

xplots_FALSE.pdf

xplots_TRUE.pdf

Slides from April 11 (Summary of Linear Regression)

appliedExample.R

applications.pdf

Exam

Here you can find a copy of the lecture notes with everything that was covered during the course marked in blue (but without the additional material covered during the lectures).

Alternative texts:

• John Fox (1997), "Applied Regression Analysis, Linear Models, and Related Methods", Sage Publications. (Intuitive examples, not very mathematical.)
• Sanford Weisberg (2005), "Applied Linear Regression", 3rd edition, Wiley. (Similar as the one by Fox but shorter.)
• Paul D. Allison (1999), "Multiple linear regression, a primer", Thousand Oaks. (Brief, good for interpretations, not very mathematical.)
• Peter Dalgaard (2002), "Introductory Statistics with R", Springer. (Introduction based on the software R.)
• T. Hastie, R. Tibshirani, and J. Friedman (2009), "The Elements of Statistical Learning", 2nd edition, Springer.