TMA4267 Linear Statistical Models

Course teacher: Øyvind Bakke (e-mail), Sentralbygg 2, room 1234. Telephone (735)98126.
Teaching assistant: Jacob Skauvold (e-mail)
Refence group: Ingeborg Gullikstad Hem (MTFYMA-IM, e-mail), Andreas Malmgård (MTFYMA-IM, e-mail), Paul Trygsland (MTFYMA-IM, e-mail)


English bokmål nynorsk solutions


Project assignment results

Enter your TMA4267 candidate number: ">


Questions before the exam

You may have questions from the reading list. I will be in my office (Sentralbygg 2, 12th floor, room 1234) most of next week (week 21). Send me an e-mail first if you want to be sure that I am there. Note: Unfortunately I will not be present on Thursday 21 May after 12:00. (13.5.2015)

Last lecture

On Monday 27 April we will go through the exam of May 2014 (2014 V). The room will be EL6. (23.4.2015)

Lecture cancelled

Due to unexpected events, the lecture on Monday 20 April had to be cancelled. I hope that you found the note on the door of G1. The plan is now to go through principal component analysis on Tuesday 21 April, and to look at one of the exam sets of last year on Monday 27. (20.4.2015)

The project assignment

If you wish to work in a group of two students but have not found a partner, e-mail Jacob Skauvold. If he gets response from more than one student, you will be contacted.

The project report should be placed in Skauvold's post shelf (post room to the left when you leave the lift in the 7th floor of Sentralbygg 2). (14.4.2015)

The project assignment

See the bottom of this page and especially the details given at the TMA4267 2014 project web page.

The deadline is Monday 4 May (morning).

In weeks 16–18 (13–30 April) the problem sessions will be extended. Jacob Skauvold will be present Mondays 14:15–15:00 in room 822 (8th floor, Sentralbygg 2) and Thursdays 12:15–14:00 in room 922 (9th floor, Sentralbygg 2 – note new room) to answer questions about the project (as well as about the exercises) .

It is a good idea to consult with Jacob Skauvold or Øyvind Bakke before you start doing experiments. (18.3.2015)

No lectures in week 13

Since a majority of the students are away on an excursion, there will be no lectures this week. The next lecture will be on Monday 13 April. (18.3.2015)

Meeting with reference group

The course teacher will have a meeting with the reference group on Tuesday 17 February at 11:00. Please contact a member if there is something you want to be discussed. (16.2.2015)

Change in exercise set 3

A change has been made to Problem 5 (marked in blue). (12.2.2015)

Reference group

Now the reference group has three members, so NTNU's requirements are met – thanks Paul! (3.2.2015)

Reference group

We have two members of the reference group – thanks to Ingeborg and Andreas! We need at least three members, and preferably all major programmes of study attending the course should be represented. Therefore, it would be nice to have a member from Bachelor's Degree 3-Year Mathematical Sciences programme of study (BMAT) and a member from The International Master of Mathematical Sciences programme of study (MSMNFMA).

See further information about reference groups at NTNU (Norwegian, English). (27.1.2015)

Change of time for lectures and problem sessions

Due to a mistake, lectures for both TMA4267 and TMA4175 were planned on Fridays 10–12. There are five students following both courses. The matter is resolved by moving our Friday lectures to Monday 12:15–14:00 in G1. The problem session, which was planned on Monday 12–14, is moved to Thursday 13:15–14:00 in B1 (only one hour, which will be sufficient). There will be no lecture on Friday 9 January. The first lecture will be on Monday 12 January at 12:15–14:00 in G1. (8.1.2015)

First lecture

The first lecture will be on Friday 9 January at 10:15–12:00 in R9. (6.1.2015)

About the course

General information


Exam and grading

The exam will be on Friday 22 May 2015 at 9:00. It is a 4 hour written exam. Permitted aids are Tabeller og formler i statistikk (Tapir forlag), Matematisk formelsamling by K. Rottmann, one calculator (Casio FX-82ES Plus, Citizen SR-270X, Citizen SR-270X College or HP 30S) and one yellow stamped A5 sheet with your own handwritten notes.

The grading will be based on the exam and a compulsory project assignment. The exam counts 80% and the project assignment 20%. Both the exam and the project must be passed (at least a 40% score) in order to achieve a passing grade for the course.

Textbooks and notes

The material in the reading list can be found in:

N. H. Bingham, J. M. Fry: Regression – Linear Models in Statistics, 2010 (book)
G. James, D. Witten, T. Hastie, R. Tibshirani: An Introduction to Statistical Learning – with Applications in R, 2013 (book)
J. Tyssedal: Design of Experiments (notes)

Also the following book may be helpful:

P. Dalgaard: Introductory Statistics with R, 2008 (book)

All books can be viewed online by NTNU students if you are connected to NTNU's network. Otherwise, e.g. at home, you could use VPN.

Reading list (may be modified during the course)

From Bingham and Fry

1. Linear regression
2. The analysis of variance (ANOVA)
3. Multiple regression
4. Further multiple regression
7. Model checking and transformation of data

From James et al.

6. Linear model selection and regularization
10.2. Principal component analysis (note: only section 10.2)

Notes by J. Tyssedal

Design of Experiments

Statistical software: R

We will use the R language and environment for statistical computing and graphics. See the TMA4267 2014 statistical software web page for further information.



Lectures are on Mondays at 12:15–14:00 in room G1 and on Tuesdays at 08:15–10:00 in room EL6.

Problem sessions

You will find exercises in the teaching plan below, approximately every second week. There will be seven sets of exercises. You can discuss the exercises with the teaching assistant at the problem sessions on Thursdays at 13:15–14:00 in B1 (room 922 of Sentralbygg 2 starting 16 April).

Provisional teaching plan

The plan will be updated gradually.

Links to R code are shown as R.

BF = Bingham and Fry; T = Tyssedal; JWHT = James et al. (see above)

WeekExercisesDateLecture no.Book/chapter/section
  3 12.1  1BF 1.1–5
Set 1  Solutions13.1  2BF 1.5–8
  4 19.1  3BF 2.1–2
20.1  4BF 2.3–6
  5 26.1  5BF 2.6 R
Set 2  Solutions 27.1  6BF 2.6–8, 3.1 R R
  6   2.2  7BF 3.1–2
  3.2  8BF 3.3–4
  7   9.2  9BF 3.4 R
Set 3  Solutions 10.2 10BF 3.4
  8 16.2 11BF 3.5–6
17.2 12BF 3.6 R
  9 23.2 13BF 4.1–3
Set 4  Solutions 24.2 14BF 4.3–4
10   2.3 15BF 4.5–6
  3.3 16BF 4.7, 7.1 R
11   9.3 17BF 7.1–4, T Two-level factorial designs R
Set 5  Solutions 10.3 18T Two-level factorial designs, Full factorial designs R
12 16.3 19T Full factorial designs R
Set 6  Solutions 17.3 20T Blocking, Fractional factorial designs R
16 13.4 21JWHT 6.1 R
Set 7  Solutions 14.4 22JWHT 6.2 R
17 20.4 Lecture cancelled
21.4 23JWHT 6.3, 10.2 R
18Note: Room EL6 27.4 24Exam problems from May 2014

Project assignment

The semester assignment is compulsory, and it will count 20% of the grade for the course (the final written examination counts 80%).

The task is to carry out a k-factor two-level experiment where the goal is to determine how the various factors influence a response. Alternatively, you may do a different statistical analysis (for example using multiple linear regression), using your own data. In the latter case, you should present a brief sketch to the course teacher before the project starts. A report should be written.

The deadline for submitting the report will be announced later (but it will be in the second half of the course).

The report should not exceed 10 pages (preferably 6–7 pages). You may do the assignment alone or in a group of two students handing in a common report. Handwritten reports are allowed. You may write in Norwegian or in English. The report should be identified by candidate number (not name or student number) so that the result can easily be merged with the result of the written exam.

You should read detailed information, suggestions for projects and hints given at the TMA4267 2014 project web page. All of it (except the submission date) applies also in 2015.

Previous exams