## Messages

Here is a list of
4. class courses in statistics.

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

Tuesday January 15 from 14:15 - 16:00 in S4.

Thursday January 17: Simple linear regression

Tuesday January 22: Multiple linear regression

Thursday January 24: Multiple linear regression and idempotent matrices

Tuesday January 29: Applications of projection matrices to linear regression models

Thursday January 31: Inference in multiple linear regression models

Tuesday February 5: Inference in multiple regression models and partial F-test

Thursday February 7: Partial F-test and variable selection

Tuesday February 12: Variable selection and study of residuals

Thursday february 14: Study of residuals and categorical variables

Tuesday February 19: Regression models with orthogonal columns and two-level experiments

Thursday February 21: Two-level experiment, significance of effects and blocking

Tuesday February 26: Blocking of two-level experiments and the analysis of variance table.

Thursday February 28: Analysis of variance table and fractional factorial designs

Tuesday March 5: Fractional Factorial designs

NB! På grunn av Abelkonkurransen har ikkje Geir Arne høve til å vere tilstades på øvingstimane denne veka (torsdag 7. mars 16-18). Istaden kan de få kommme på kontoret hans og stille spørsmaål tysdag og onsdag 12-14 og elles etter avtale.

Thursday March 7: Orientation about the compulsory project. One way analysis of variance.

Tuesday March 12: One-way anova

Thursday March 14: Multiple comparison and randomized block design

Tuesday March 19: Randomized block design and Two-way anova

Thursday March 21: Two-way anova and random effects model

Thursday April 4: Multivariate normal distribution

Tuesday April 9: Properties of the multivariate normal

Thursday April 11: Properties of Multivariate normal and MLE estimation

Tuesday April 16: Applications of the multivariate normal.

Thursday April 18: Principalcomponent analysis

Tuesday April 23: Principal components analysis and contingency tables

**NB! On Thursday April 25. teachers for fourth class courses in statistics will meet in the classroom from 9:30 and be available for questions.**

Thursday April 25: Contingency tables

Tuesday April 30: Repetition. Slides from the repetition is
here.

Scores on the compulsory exercise are here.

## Lectures

Tuesday 14:15 - 16:00 in S4

Thursday 8.15 - 10:00 in S6

## Teacher

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

## Teaching assistant

Geir-Arne Fuglstad, rom 1238 SII. Epost: Geir [dash] Arne [dot] Fuglstad [at] math [dot] ntnu [dot] no

## Reference group

Eirik Myrvoll-Nilsen myrvolln [at] stud [dot] ntnu [dot] no

Thomas Øvestad thomaove [at] stud [dot] ntnu [dot] no

## Weekly Exercises

Thursday 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 4. 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.
matlab 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

NB! På grunn av Abelkonkurransen har ikkje Geir Arne høve til å vere tilstades på øvingstimane denne veka (torsdag 7. mars 16-18). Istaden kan de få kommme på kontoret hans og stille spørsmaål tysdag og onsdag 12-14 og elles etter avtale.

Exercise 7.
Solution Exercise 7.

Exercise 8.
Solution Exercise 8

Exercise 9.
Solution Exercise 9.

Exercise 10. data exercise 10.
Solution Exercise 10.

Geir Arne is away in week 14 so there will be no assistance on Thursday 16.15 - 18:00. If you have problems with the exercise you can contact me (John).

Exercise 11. data exercise 11.
Solution Exercise 11.

Exercise 12.
Solution exercise 12.
Solution problem 1

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, 9. edition by
R. E. Walpole, R. H. Myers, S. L. Myers, K. Ye.
+ additional written notes.

Temporary notes about regression, including transformations and approximation of variance and expectation for functions of random variables is given here.
Regression

Temporary notes about design of experiments and analysis of variance is given here
DOE

Temporary notes about the Multivariate analysis including principal components is given here
Multivariate

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 Contingency tables are given
here

## Curriculum

Walpole, Myers, Myers and Ye:

- Chapter 8.7, 9.13
- Chapter 10: 10.10 - 10.13
- Chapter 11: 11.10 - 11.11
- Chapter 12: 12.1 - 12.11
- Chapter 13: 13.1-13.3, 13.6, 13.9-13.12
- Chapter 14: 14.1- 14.3
- Chapter 15
- Written notes

## Forelesningsplan - oversiktsnivå

Uke | Kapittel | |
---|---|---|

34 | 1 | Innleiing og dataanalyse. Sannsyn |

35 | 2 | Sannsynsrekning. |

36 | 3 | Stokastiske variablr og fordelingar. |

37 | 4 | Forventning, varians og kovarians. |

38 | 5 | Diskrete sannsynsfordelingar. |

39 | 6 | Kontinuerlige sannsynsfordelingar. |

40 | 7+ notat | Funksjoner av stokastiske variabler. Ordningsvariabler. (notat: www.math.ntnu.no/~joeid/TMA4240H11/ordningekstrem.pdf) |

41+42 | 8+9 | Utvalsfordelingar. Estimering og konfidensintervall. |

43-44 | 10 | Hypotesetesting. |

45-46 | 11 | Lineær regresjon. |

47 | Oppsummering og avslutning. |

## Exam

Meeting hours before the exam:

Tuesday May 21: 13-15

Thursday May 23: 12-14, pga føredrag av Abel prisvinnar klokka 14.15

Friday May 24: 13-15

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: 25. mai 2013 , 09:00 - 13:00.

## Earlier exams in TMA4267 and similar courses

Exam TMA4267 August 2013.
Solution Exam TMA4267 August 2013.

Exam TMA4267 May 2013.
Solution Exam TMA4267 May 2013.

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.