Welcome to the course TMA4267 Linear statistical models. The first lecture will be given on Tuesday January 11 from 10:15 - 12:00 in KJL2.
Tuesday January 18: Multiple linear regression
Thursday,January 20: Idempotent matrices and Quadratic forms
Tuesday January 25: Application of projection matrices to multiple linear regression.
Thursday,January 27: Inference in multiple linear regression
Tuesday,February 1: Variable selection and partial F-tests.
Thursday,February 3: Variable selection and study of residuals
Tuesday, February 8: Multicollinearity and some special regression situations
Thursday, February 10: Two-level experiments.
Tuesday, February 15: We continue with two-level experiments
Thursday, February 17: Interpretation of effects and blocking
Tuesday, February 22: Analysis of variance table and fractions of two-level design
Thursday, February 24: Fractional factorial designs
Tuesday March 1: We finish factorial designs
Thursday March 3: One-way analysis of variancen
Tuesday March 8: We continue with one-way analysis of variance and the randomized block design
Thursday March 10: Randomized complete block design
Tuesday March 15: Two-way anova
Thursday March 17: Random effects and the Multivariate normal distribution
Tuesday March 22: The Multivariate normal distribution
Thursday March 24: Conditioning in the Multivariate normal distribution
Tuesday March 29: Maximum likelihood estimation in the multivariate normal distribution
Thursday March 31 Applications in the multivariate normal
Tuesday April 5: Principalcomponents
Thursday April 7: Contingency tables
Tuesday April 12: Contingency tables, repetition
Thursday April 14: Repetition. Slides from the repetition is here.
May 2. The scores on the Compulsory Exercise can be found here.

Meeting hours before the exam:
Wednesday May 18: 10-12 room 1132
Thursday May 19: 14-16 room 1132


Tuesday 10:15 - 12:00 in KJL2
Thursday 10.15 - 12:00 in R9


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

Teaching assistants

Reference group

Weekly Exercises

Thursday 15:15 - 17.00 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.
Exercise 1 Solution Exercise 1
Exercise 2 Solution Exercise 2
Exercise 3. data exercise 3. Solution Exercise 3
Exercise 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 for exercise 10 can be found here data exercise 10. Solution Exercise 10.
Exercise 11. Data for exercise 11 can be found here 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
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 Analysis of variance is given here

Temporary notes about the Multivariate Normal distribution is given here
Temporary notes about Principal components are given here
Temporary notes about Contingency tables are given here


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, 14 notes Principal components
15 10.14,10.15,10.16 Contingency tables, Repetition


Meeting hours before the exam:
Wednesday May 18: 10-12 room 1132
Thursday May 19: 14-16 room 1132

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 20, 15:00 - 19:00.

Earlier exams in TMA4267 and similar courses

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.

2011-05-25, John Sølve Tyssedal