## Messages

Welcome to the course TMA4267 Linear statistical models. The first lecture will be given on

Monday January 9 from 10:15 - 12:00 in S4.

Thursday January 12: Simple linear regression

Monday January 16: Multiple linear regression

Thursday January 19: Idempotent matrices and quadratic forms

Monday January 23 Applications of projection matrices to linear regression models

Thursday January 26: Inference in multiple linear regression

Monday January 30: Inference and variabel selection in multiple linear regression

Thursday February 2: Partial F-test, Variable selection and study of residuals

Monday February 6: Study of residuals and some special regression situations

Thursday February 9: Categorical variables in regression models. Orthogonal colums and two-level designs.

Monday February 13: Two-level designs and evaluation of significant effects

NB. There will be a meeting with the reference group on Tuesday 21. Contact the members if there is something you want to bring forward.

Thursday February 16: Normal and Lenth's plot. Variance estimation, interpretation of effects and blocking.

Monday February 20. Blocking and analysis of variance table.

Thursday February 23. Blocking and fractional factorials.

Monday February 27. Fractional factorials

Thursday March 1: Rest of fractional factorials. Example of a compulsory experiment. One-way analysis of variance.

Monday March 5: Theory for One-way Anova.

Thursday March 8: Example One way Anova. Randomized complete block design

Monday March 12: Randomized complete block design

Thursday March 15. Two-way anova

Monday March 19: Random effects model and multivariate normal.

Thursday March 22: The Multivariate normal distribution

Monday March 26: We continue with results about the multivariate normal distribution.

Thursday March 29: Applications of the multivariate normal

Thursday April 12: Applications of the multivariate normal and principal component analysis

Monday April 16: Principal components analysis

Thursday Spril 19: Contingency tables

Monday April 23: Repetition. Slides from the repetition is
here.

Information about 4.th class courses in statistics is here.

You can find the scores from the compulsory exercise here.

## Lectures

Monday 10:15 - 12:00 in S4

Thursday 10.15 - 12:00 in R9

## Teacher

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

## Teaching assistant

Xiangping Hu Xiangping [dot] Hu [at] math [dot] ntnu [dot] no Room 1246, SII.

## Reference group

Stian V. Eriksen-Deinoff deinoff [at] stud [dot] ntnu [dot] no

André Flakke flakke [at] stud [dot] ntnu [dot] no

Guro Seternes guroseter [at] gmail [dot] com

## Weekly Exercises

Tuesday 16:15 - 18.00 in A380, 3. floor north building SII. Those who do not belong to the study program Industrial Mathematics must contact the Department office, 7th floor SII, in order to have entrance to the 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. These exercises will start in week 3. As computer software we will use R. A lot of useful information about R can be found on the
web-site: http://cran.r-project.org/

Exercise 1.
Solution Exercise 1

Exercise 2.
Solution Exercise 2

Exercise 3.
data exercise 3.
Solution Exercise 3

Exercise 4.data exercise 4.
Solution Exercise 4

Exercise 5.
Solution Exercise 5

Exercise 6.
Solution Exercise 6

Exercise 7.
Solution Exercise 7.

Exercise 8.
Solution Exercise 8

Exercise 9.
Solution Exercise 9.

Exercise 10. data exercise 10.
Solution Exercise 10.

Exercise 11. data exercise 11.
Solution Exercise 11.

Exercise 12.
Solution exercise 12.

Exercise 13.Solution exercise 13.

## Compulsory exercise

Information about the compulsory 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 simple regression, transformations and approximation of variance and expectation for functions of random variables.
here

Temporary notes about multiple linear regression and least square estimators are given
here

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

Temporary notes about regression analysis in practise is given
here

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 Analysis of variance is given
here

Temporary notes about the Multivariate Normal distribution is given
here

Those of you who are interested in one way to derive the ML-estimator for the covariance matrix in the multivariate normal case can have a look at this note. There are some useful results about the derivative of determinants and the trace.

Temporary notes about Principal components are given
here

Temporary notes about Contingency tables 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 |

13, 15 | notes | Principal components |

16-17 | 10.14,10.15,10.16 | Contingency tables, Repetition |

## Exam

Meeting hours before the exam:

Wednesday May 16: 10-12

Monday May 21: 10-12

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.

Exam: May 22, 09:00 - 13:00.

## Earlier exams in TMA4267 and similar courses

Exam TMA4267 August 2012.
Solution Exam TMA4267 August 2012.

Exam TMA4267 May 2012.
Solution Exam TMA4267 May 2012.

Exam TMA4267 August 2011

Exam TMA4267 May 2011
Solution Exam TMA4267 May 2011.

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.