# TMA4267 Linear statistical models

Course description is given here

## Messages

Welcome to the course TMA4267 Linear statistical models. The first lecture will be given on Monday January 11 from 15:15 - 17:00 in R9.

January 25. We will continue to give the theoretical background for the results in Chapter 12.4 and 12.5. Also Chapter 8.8.

January 28. Chapter 12.5 and 12.6.

February 1. Chapter 12.6, 12.7 and 12.8

February 4. Chapter 12.8, 12.9 and 12.10

February 8. Chapter 12.10 and 12.11

February 11. Chapter 12.11 + notes on Two-level designs and blocking

February 15. Two-level designs. From notes.

February 18. We continue with two-level designs from notes

February 22. Blocking of two-level designs from notes

February 25. Blocking and fractions of two-level designs from notes

March 1. Fraction of two-level designs from notes

March 4. Finish fractions of two-level design. Show an example of a project.
Start on analysis of variance.

March 8. Analysis of variance. Chapter 13.3,13.6 +notes. There will also be a meeting in the reference group at 14.00 in room 1132, SII.

March 11. One-way anova,13,6 and randomized complete block design 13.9, +notes.

March 15. Randomized complete block desigm and Two-way Anova. Chapter 13.9 and 14.1-14.3

March 18. Two-way anova 14.1-14.3. Random effects model 13.13.

March 22. Random effects model,13,13, GOF-tests,10.14.

March 25. Contingency tables 10.15,10.16.

April 8. The Multivariate Normal distribution from notes

April 12, We continue with the multivariate normal from notes

April 15. More about Multivariate normal and it's applications from notes

April 19. Applications of the Multivariate normal and Principal components

April 22. Principalcomponents

April 26. Repetition.
Slides from the last lecture can be found
here

The results for the compulsory exercise as a score from 1-20 are now available
here

## Lectures

Monday 15:15 - 17:00 in R9

Thursday 14.15 - 16:00 in R9

## Teacher

John Tyssedal tyssedal [at] stat [dot] ntnu [dot] no Room 1132, SII.

## Teaching assistants

- Javad Rezaie Javad [dot] Rezaie [at] math [dot] ntnu [dot] no Room 1038, SII.
- Xiangping Hu Xiangping [dot] Hu [at] math [dot] ntnu [dot] no Room 1024, SII.

## Reference group

Kristin Hornæs. krishorn [at] stud [dot] ntnu [dot] no

Christine Haugland. chh [at] stud [dot] ntnu [dot] no

Christian Page. christpa [at] stud [dot] ntnu [dot] no

## Weekly Exercises

Tuesday 16:15 - 18.00 in A380, 3. floor north building SII.

There is one compulsory exercise in this course which will count 20 percent on the exam.
In addition there will be given ordinary exercises each week. As computer software we will use R.

Exercise 1

Exercise 2
Solution exercise2.
Solution computer exercise2

Exercise 3. Data for exercise 3 can be found here data exercise 3.
Solution Exercise 3.
Solution computer exercise 3.

Exercise 4. Data for exercise 4 can be found here data exercise 4.
Solution Exercise 4.
Solution computer exercise 4.

Exercise 5.Solution Exercise 5.
Solution computer exercise 5.

Exercise 6.
Solution Exercise 6.
Solution computer exercise 6.

Exercise 7
Solution Exercise 7.

Exercise 8.
Solution Exercise 8.
Solution computer exercise 8.

Exercise 9. Data for exercise 9 can be found here data exercise 9.
Solution Exercise 9.

Exercise 10. Data for exercise 10 can be found here data exercise 10.
Solution Exercise 10.

Exercise 11. Data for exercise 11
data exercise 11.
Solution Exercise 11.

Exercise 12.
Solution Exercise 12.
Solution Computer Exercise 12.

Exercise 13.
Solution Exercise 13.

## Compulsary exercise

Information about the compulsary exercise can be found here. To get some more ideas of what to do you may like to have a look at some experiments performed in a similar course in Madison, Wisconsin. experimental ideas.

## Teaching material

Probability & statistics for Engineers & Scientists, 8. edition by
R. E. Walpole, R. H. Myers, S. L. Myers, K. Ye.
+ additional written notes.

Temporary notes about Idempotent matrices and quadratic forms and their application to Multippel linear regression is given
here

Notes on influential observations

Temporary notes about two-level designs and their blocking is given
here

Temporary notes about fractionated two-level designs is given
here

Temporary notes about quadratic forms in Analysis of variance is given
here

Temporary notes about the Multivariate Normal distribution is given
here

Temporary notes about Principal components are given
here

## Curriculum

Walpole, Myers, Myers and Ye:

- Chapter 8.8, 9.13
- Chapter 10.13 - 10.16
- Chapter 11: 11.10, 11.11
- Chapter 12
- Chapter 13: 13.1-13.3, 13.6, 13.9-13.10. 13.13
- Chapter 14: 14.1- 14.3
- Chapter 15
- Written notes

## Tentative lecture plan

Week | Chapter | Topic |
---|---|---|

2 | 11.10, 11.11 | Simple linear regresion |

3,4,5 | 8.8, 10.13, 12 + notes | Multippel linear regression |

6,7,8 | 15 /notes | Two-level experiments |

9, 10 | 13, 14 | Analysis of variance |

11, 12 | notes | Multivariate normal distribution |

14, 15 | notes | Principal components |

16 | 10.14,10.15,10.16 | Contingency tables |

17 | Repetition |

## Exam

You are allowed to bring with you a stamped yellow A5 sheet of paper with your own notes for the exam. You can fill it out on both sides. The stamped sheet of paper can be picked up outside the Department office. Also be sure to bring with you "Tabeller og formler i statistikk" . You are also allowed to use K. Rottman: Matematisk formelsamling.

Meeting hours before the exam in my office

Wednesday June 2: 13-15

Thursday June 3: 12-14

Friday June 4 : 12-14

Exam: June 5, 9:00 - 13:00.

## Earlier exams in TMA4267 and similar courses

Exam TMA4267Jun10.
Solution Exam TMA4267Jun10.

Exam TMA4267Jun09.
Solution Exam TMA4267Jun09.

Exam TMA4255Dec08.

Exam TMA4255Aug07.

Exam TMA4255May07.

Exam TMA4255May06.

Exam TMA4255Aug04.

Exam TMA4260Dec03.

Solution to most of these exams together with a lot more exams can be found on the homepages of the courses TMA4255 and TMA4260. Be aware that most of the solutions will be in Norwegian.