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 class courses in statistics is here.
You can find the scores from the compulsory exercise here.


Monday 10:15 - 12:00 in S4
Thursday 10.15 - 12:00 in R9


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

Teaching assistant

Reference group

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:
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 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


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


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

2012-08-20, John Sølve Tyssedal