TMA4267 Linear Statistical Models
TMA4267 Linear Statistical Models
(Spring 2024)
Messages:
The last lecture 22.04.24
08.04.24: There will be no lectures in week 16 (15.04 and 18.04). Work with the obligatory project.
29.02.24: On Monday (4.03) there is no lecture in the classroom. Instead watch the record of Lecture 18 in
section "Lecture records" below.
27.02.24: There will be no lectures in week 12 (18.03 and 21.03). Work with the obligatory assignments.
21.01.24: There is only one volunteer for the reference group. Please be more active.
15.01.24: We have to establish a reference group. Request for volunteers to send a message
to the lecturer.
07.12.23: First lecture is 08.01.2024.
07.12.23: Exercises start in week 3.
07.12.23: Lecture records from the previous year are posted below.
07.12.23: Welcome to the home page of TMA4267 Linear Statistical Models.
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Teaching material
From the book
Applied multivariate statistical analysis, 4th edition (2015) by Härdle and Simar (HS)
From the book
Regression: models, methods and applications (2013) by Fahrmeir, Kneib, Lang and Marx (FKLM)
Note: Design of experiments by Tyssedal (T)
Note: Multiple hypothesis testing by Halle, Bakke and Langaas (HBL)
Statistical software: R
Here are some links concerning R
https://www.r-project.org/about.html
https://www.r-project.org
https://rstudio.com
https://link.springer.com/book/10.1007/978-0-387-79054-1
Lecturer
Nikolai Ushakov
http://www.math.ntnu.no/~ushakov
Teaching assistant
Philip Stanley Mostert (philip.s.mostert@ntnu.no)
Reference group
Gonchigsuren Bor (gonchigsuren.bor@ntnu.no)
Rasmus Grødeland (rasmug@stud.ntnu.no)
Name (address)
Lectures:
Monday 08:15-10:00 GL-GE G1
Thursday 10:15-12:00 GL-GE G1
Exercises:
Friday 08:15-10:00 GL-SB1 S1
Week 3: Recommended exercise 1.
Solutions.
Week 4: Recommended exercise 2.
Solutions.
Week 5: Recommended exercise 3.
Solutions.
Week 6: Recommended exercise 4.
Solutions.
Week 7: Compulsory assignment 1.
Week 8: Recommended exercise 5.
Solutions.
Week 9: Recommended exercise 6.
Solutions.
Week 11: Compulsory assignment 2.
Week 12: Recommended exercise 7.
Solutions.
Week 14: Recommended exercise 8.
Solutions.
Week 15: Recommended exercise 9-10.
Solutions.
Compulsory assignment 3.
Progress:
Lecture 1 (08.01.2024): Multivariate distributions and expectations (HS 4.1-4.2).
Lecture 2 (11.01.2024): Multivariate moments (HS 4.2 using HS 2.1-2.4).
Lecture 3 (15.01.2024): Transformations (HS 4.3, 4.4), PCA (HS 11.1-11.3).
Lecture 4 (18.01.2024): Charactestic functions (HS 4.2). Multivariate normal distribution
(HS 4.4, 5.1).
Lecture 5 (22.01.2024): Multivariate normal distribution (HS 4.4, 5.1).
Lecture 6 (25.01.2024): Multivariate normal distribution (HS 4.4, 5.1).
Lecture 7 (29.01.2024): Multivariate normal distribution (HS 4.4, 5.1).
Estimation in the multivariate normal distribution (HS 3.3, 4.5).
Lecture 8 (01.02.2024): Estimation in the multivariate normal distribution (HS 3.3, 4.5).
Quadratic forms and idempotent matrices (FKLM Appendix B, Th. B2, B8).
Lecture 9 (05.02.2024): Quadratic forms and idempotent matrices (FKLM Appendix B, Th. B2, B8).
Multiple linear regression: model, parameter estimation (FKLM 3.1, 3.2).
Lecture 10 (08.02.2024) Multiple linear regression: model, parameter estimation
(FKLM 3.1, 3.2).
Lecture 11 (12.02.2024) Properties of estimators, fitted values, residuals (FKLM 3.2).
Inference about coefficients (FKLM 3.3).
Lecture 12 (15.02.2024) Multiple linear regression: t-test about coefficients,
ANOVA decomposition, coefficient of determination, F-test (FKLM 3.2, 3.3).
Lecture 13 (19.02.2024) F-test for regression coefficients (FKLM 3.2, 3.3, 3.5).
Lecture 14 (22.02.2024) General F-test for regression coefficients (FKLM 3.2, 3.3, 3.5).
Lecture 15 (26.02.2024) General F-test for regression coefficients, transformation of data (FKLM 3.2, 3.3, 3.4, 3.5).
Lecture 16 (29.02.2024) Model analysis and model selection (FKLM 3.4).
Lecture 17 (04.03.2024) Multiple hypothesis testing (HBL).
Lecture 18 (07.03.2024) Examples.
Lecture 19 (11.03.2024) ANOVA (HS 8.1.1). Design of experiment (DOE): two-level factorial design (T).
Lecture 20 (14.03.2024) Design of experiment (DOE): two-level factorial design (T).
Lecture 21 (04.04.2024) Design of experiment (DOE): two-level factorial design (T).
Lecture 22 (08.04.2024) Design of experiment (DOE): two-level factorial design (T).
Lecture 23 (11.04.2024) Repetition.
Lecture 24 (22.04.2024) Repetition.
Lecture records (2022)
Lecture 1 Part 1
Lecture 1 Part 2
Lecture 2 Part 1
Lecture 2 Part 2
Lecture 3 Part 1
Lecture 3 Part 2
Lecture 4 Part 1
Lecture 4 Part 2
Lecture 5 Part 1
Lecture 5 Part 2
Lecture 6 Part 1
Lecture 6 Part 2
Lecture 7 Part 1
Lecture 7 Part 2
Lecture 8 Part 1
Lecture 8 Part 2
Lecture 9 Part 1
Lecture 9 Part 2
Lecture 10 Part 1
Lecture 10 Part 2
Lecture 11 Part 1
Lecture 11 Part 2
Lecture 12 Part 1
Lecture 12 Part 2
Lecture 13 Part 1
Lecture 13 Part 2
Lecture 14 Part 1
Lecture 14 Part 2
Lecture 15 Part 1
Lecture 15 Part 2
Lecture 16 Part 1
Lecture 16 Part 2
Lecture 17 Part 1
Lecture 17 Part 2
Lecture 18 Part 1
Lecture 18 Part 2
Lecture 19 Part 1
Lecture 19 Part 2
Lecture 20 Part 1
Lecture 20 Part 2
Lecture 21 Part 1
Lecture 21 Part 2
Lecture 22 Part 1
Lecture 22 Part 2
Lecture 23 Part 1
Lecture 23 Part 2
Lecture 24 Part 1
Lecture 24 Part 2
Lecture 25 Part 1
Lecture 25 Part 2
Pensum - Syllabus
HS: 2.1-2.5 (pp. 53-68), 3.3 (pp. 89-93), 4.1-4.5 (pp. 118-143), 5.1 (pp.183-188), 8.1.1 (pp. 255-259), 11.1 (pp. 320-324).
FKLM: 3.1 (pp. 73-86), 3.2 (pp. 104-125), 3.3 (pp. 125-139), 3.4 (pp. 139-150), 3.5 (pp. 169, 171-174), B2 (Theorem B.2(8)),
B3 (Theorem B.8).
HBL: 3 (pp. 3-4), 5 (pp. 4-6).
T: pp. 1-7, 9-13, 15-16, 20-21, 24-25.
Exam
4 hour written exam
Permitted examination support material: C:
– Tabeller og formler i statistikk, Tapir forlag,
– K.Rottman. Matematisk formelsamling,
– Stamped yellow A5 sheet with your own handwritten notes,
– Calculator: HP30S, Citizen SR-270X, Citizen SR-270X College or Casio fx-82ES PLUS.
Table of previous exams: