Linear models play a central part in modern statistics. Linear models include, as special cases, simple and multiple linear regression, analysis of variance (factorial) models and linear mixedeffects models. These models share a number of properties, such as linearity, that can be exploited to good effect. These common properties enable us to study linear models as a single class, rather than as an unrelated collection of special topics. This course provides an intense, rigorous introduction into the broad spectrum of statistical linear models that is useful in the analysis of data as well as into the mathematical foundations underpinning such models. Students will need a solid background in calculus and matrix algebra. Statistical prerequisites include some exposure to statistical theory and to estimation and testing hypotheses. The following topics are covered by the course:
This course comprises 6 contact hours per week (4 hours of lectures, 2 hour class) and is compulsory for students enrolled in the Master of Applied Statistics programme at the Georg August University Göttingen.
Class  Wednesday  12:15  13:45  Seminar room VG 3.103, Verfügungsgebäude 
Lecture  Wednesday  14:15  15:45  Lecture hall ZHG104, Zentrales Hörsaalgebäude 
Lecture  Thursday  12:15  13:45  Lecture hall MED 23, Humboldtallee 32 
Date  Lecture/Class  Topic  Material  Recommended reading 

October 24th (Wednesday)  Lecture  Setting the scene  Lecture slides Initial data analysis, Rmd file History of regression, Rmd file 

October 25th (Thursday)  Lecture  Preliminaries  Lecture slides, R code  Rencher and Schaalje (2008), Chapters 4 and 5 
November 1st (Thursday)  Lecture  Preliminaries (continuation)  
November 7th (Wednesday)  Class  Study sheet 1  Study sheet 1  
November 7th (Wednesday)  Lecture  Simple linear regression  Lecture slides SLR Lecture slides MLE, R code scores.txt, HTML file, Rmd file 
Rencher and Schaalje (2008), Chapter 6, Section 10.1 and Section 10.2 Casella and Berger (2002), Section 11.3 and Section 12.2 
November 8th (Thursday)  Lecture  Simple linear regression (continuation)  
November 14th (Wednesday)  Class  Study sheet 2  Study sheet 2  
November 14th (Wednesday)  Lecture  Multiple regression: Estimation  Lecture slides table71.txt, HTML file, Rmd file 
Rencher and Schaalje (2008), Chapter 7 
November 15th (Thursday)  Lecture  Multiple regression: Estimation (continuation)  
November 21st (Wednesday)  Class  Study sheet 3  Study sheet 3  
November 21st (Wednesday)  Lecture  Multiple regression: Tests of hypotheses and confidence intervals  Lecture slides Hypothesis testing: HTML file, Rmd file, table74.txt Confidence intervals: HTML file, Rmd file LR tests: HTML file, Rmd file 
Rencher and Schaalje (2008), Chapter 8 
November 22nd (Thursday)  Lecture  Multiple regression: Tests of hypotheses and confidence intervals (continuation)  
November 28th (Wednesday)  Class  Study sheet 4  Study sheet 4, R code for exercise 2  
November 28th (Wednesday)  Lecture  Multiple regression: Diagnostics  Lecture slides HTML file, Rmd file 
Rencher and Schaalje (2008), Chapter 9 
November 29th (Thursday)  Lecture  Multiple regression: Diagnostics (continuation)  
December 5th (Wednesday)  Class  Study sheet 5  Study sheet 5, data1.txt, table75.txt R code for exercise 4, R code for exercise 5, R code for exercise 6, R code for exercise 7 

December 5th (Wednesday)  Lecture  Multiple regression: Bayesian inference  Lecture slides table111.txt, HTML file, Rmd file 
Rencher and Schaalje (2008), Chapter 11 Fahrmeir et al. (2013): Section 4.4.1 
December 6th (Thursday)  Computer Lab  Linear Regression with R  Exercises, dbp.txt, R code  
December 12th (Wednesday)  Class  Study sheet 6  Study sheet 6 R code for exercise 1, R code for exercise 5 

December 13th (Thursday)  Lecture  Shrinkage regression  Lecture slides PCA Lecture slides Shrinkage regression, HTML file, Rmd file 
Jolliffe (2002), Chapter 8 Faraway (2015): Section 11.1, 11.3 and 11.4 
December 19th (Wednesday)  Class  Study sheet 7  Study sheet 7, lesen.txt R code for exercise 1, R code for exercise 2, R code for exercise 4 

December 19th (Wednesday)  Lecture  Shrinkage regression (continuation)  
December 20th (Thursday)  Computer Lab  Crossvalidation and shrinkage methods with R  Exercises, R code  
January 9th (Wednesday)  Class  Study Sheet 8  Study sheet 8, R code for exercise 4  
January 9th (Wednesday)  Lecture  Factorial models  Lecture slides One way ANOVA: table132.txt, HTML file, Rmd file Twoway ANOVA:table142.txt, HTML file, Rmd file 
Rencher and Schaalje (2008), Chapter 12 
January 10th (Thursday)  Lecture  Factorial models (continuation)  
January 16th (Wednesday)  Class  Study Sheet 9  Study sheet 9, table136.txt R code for exercise 1, R code for exercise 2, R code for exercise 4 

January 16th (Wednesday)  Lecture  Linear mixedeffects models  Lecture slides, HTML file, Rmd file  Fahrmeir et al. (2013), Section 7.1, 7.2, 7.3 and 7.7 (or Rencher and Schaalje (2008), Chapter 17) 
January 17th (Thursday)  Lecture  Linear mixedeffects models (continuation)  
January 23rd (Wednesday)  Class  Study Sheet 10  Study sheet 10, R code for exercise 4  
January 23rd (Wednesday)  Computer Lab  ANOVA and Linear mixedeffects models with R  Exercises, R code 
Topic  Material 

Matrix Algebra  Lecture slides and exercises from the course Mathematical Foundations of Applied Statistics 
R package HistData  Data Sets from the History of Statistics and Data Visualization, R package version 0.78. URL: https://cran.rproject.org/web/packages/HistData/ 
Written exam (duration: 90 minutes). The exam will take place on Thursday, January 31^{st} 2019, between 12:15 p.m. and 13:45 p.m. in the lecture hall MED 23, Humboldtallee 32. The permitted examination aids are: