Regression

First Lecture: 22. Februar 2012.

Exercises: Have a look here.

Exam: Have a look here. (This is not a complete list of questions, but should give you a better idea of what type of questions you can expect).

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.

Text:

• Text by Prof. Kunsch: German/English
  
• Practical regression with R by Julian R. Faraway (2002) with R-code

Slides:

Week 1:
Role of statistical models

(Nonparametric) Regression

Examining Data

Weeks 2-4:

Transformations

Linear Regression

Weeks 5-8:

Dummy variable Regression

Weeks 9-13:

Model diagnostics and unusual and influential data

Model building

Robust regression

Logistic regression

R Code:

Week 1:
Introduction

(Nonparametric) Regression

Examining Data

Weeks 2-4:

Transformations

Linear Regression

Ozone Data Set

Weeks 5-8:

Testing and p-values

Categorical predictors

Confidence intervals and bands
fruitfly code

Weeks 9-13:

Diagnostics

Model building

Chicago insurance_redlining

Logistic regression

Coxph

Additional material:

R reference card by Tom Short: http://cran.r-project.org/doc/contrib/Short-refcard.pdf

Cox Proportional-Hazards Regression for Survival Data by John Fox: http://cran.r-project.org/doc/contrib/Fox-Companion/appendix-cox-regression.pdf

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.)