TMA4267 Linear Statistical Models

TMA4267 Linear Statistical Models

(Spring 2020)

Messages:

23.07.20: The continuation exam in TMA4267 is in the same form as the exam Spring 2020 i.e. the exam consists of 4 obligatory assignments (see description on this web page of the course), giving 10%, 10%, 60%, 20% of the final result. Pass/fail are used as grades (40% for pass). Send all assignments to the lecturer (Nikolai Ushakov, nikolai.ushakov@ntnu.no). Deadline for delivering is 23.08.2020.
02.05.20: New deadline for delivering Assignment 3 is 12.05.2020.
19.04.20: New deadline for delivering Assignment 4 is 27.04.2020.
19.04.20: Example of DOE in R (by Mette Langaas) is here.
15.04.20: In Problem 3 (Assignment 4) the table with x-s and y-s is given only for illustration. Nothing is based on this table (everything is based on the R output). Values of y-s in the table are given (naturally) in a rounded form. Therefore, if you use lm(y ~ x1 + x2) with x-s and y-s from the table, you do not obtain the same R output as given in the problem (there y-s are obtained by simulation, using
>eps<-rnorm(15,0,0.5)
>y<-b0+b1*x1+b2*x2+eps
not from the table).
10.04.20: There was a misprint in the table of Problem 3 of Assignment 4. It is corrected now.
02.04.20: Compulsory assignment 3 is now ready, see below.
02.04.20: It is allowed to work in groups for assignment 4.
30.03.20: Compulsory assignment 4 is ready, see below.
26.03.20: Information about the exam is below, see Exam.
15.03.20: Since we need to change the form of education and use internet, let us try (as the first step) a self-study using the web page of the course (see below).
24.02.20: There will be no lecture on Tuesday, February 25.
17.01.20: Attention! Change in the schedule. See Lectures.
13.01.20: Some information about R is below.
06.01.20: The first lecture (07.01.20) is 16:15-18:00, room F2.
06.01.20: Attention! The first lecture (07.01.20) is not 14:15, F2. I inform later when and where.
23.12.19: Exercises start in week 3.
23.12.19: First lecture is 07.01.2020.
17.12.19: In this course we will use also the system Blackboard.

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   
Haris Fawad (haris.fawad@ntnu.no)

Reference group   
Emma Skarnes (emmaska@stud.ntnu.no) MTFYMA
Simen Knutsen Furset (simenkfu@stud.ntnu.no)
Tinius Petter Mellbye (tiniuspm@stud.ntnu.no)

Lectures:
Tuesday 14:15-16:00 KJL1
Friday 10:15-12:00 S4

Exercises:
Thursday 12:15-14:00 F3

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 13: Recommended exercise 8. Solutions.
Week 14: Recommended exercise 9-10. Solutions.
Compulsory assignment 3.
Compulsory assignment 4.

Progress:

  • Lecture 1 (07.01.2020): Introduction to multivariate distributions (HS 4.1).
  • Lecture 2 (10.01.2020): Multivariate expectations and moments (HS 4.2 using HS 2.1-2.3)
  • Lecture 3 (14.01.2020) Multivariate moments (HS 4.2). Transformations: Mahalanobis (HS 3.3), PCA (HS 11.1-11.3).
  • Lecture 4 (17.01.2020) Transformations (HS 11.1-11.3, 4.3). Charactestic functions (HS 4.2). Multivariate normal distribution (HS 4.4, 5.1).
  • Lecture 5 (21.01.2020) Multivariate normal distribution (HS 4.4, 5.1).
  • Lecture 6 (24.01.2020) Multivariate normal distribution (HS 4.4, 5.1).
  • Lecture 7 (28.01.2020) Multivariate normal distribution (HS 4.4, 5.1). Estimation in the multivariate normal distribution (HS 3.3, 4.5).
  • Lecture 8 (31.01.2020) Quadratic forms and idempotent matrices (FKLM Appendix B, Th. B2, B8).
  • Lecture 9 (04.02.2020) Multiple linear regression: model, parameter estimation (FKLM 3.1, 3.2).
  • Lecture 10 (07.02.2020) Properties of estimators, fitted values, residuals (FKLM 3.2).
  • Lecture 11 (11.02.2020) Multiple linear regression: properties of estimators, inference about coefficients.
  • Lecture 12 (14.02.2020) ANOVA decomposition and coefficient of determination (FKLM 3.2, 3.3). F-test for regression coefficients (a special case).
  • Lecture 13 (18.02.2020) General F-test for regression coefficients (FKLM 3.3, 3.5).
  • Lecture 14 (21.02.2020) General F-test for regression coefficients.
  • Lecture 15 (28.02.2020) Transformation of data. Model analysis and model selection.
  • Lecture 16 (03.03.2020) Model analysis and model selection (FKLM 3.4).
  • Lecture 17 (06.03.2020) Model selection (FKLM 3.4). Multiple hypothesis testing (HBL).
  • Lecture 18 (10.03.2020) Multiple hypothesis testing (HBL). ANOVA (HS 8.1.1).

    Distance teaching

  • Self-study (Week 12) ANOVA (HS 8.1.1). Design of experiment (DOE): two-level factorial design (T).
    Recommendations
    Notes for the rest of the course
    Example (2019, Pr. 4)

  • Self-study (Week 13) Design of experiment (DOE): two-level factorial design (T).
    Recommendations
    Notes for the rest of the course
    Slide for Fractional factorial design
    Slide 1 for Blocks
    Slide 2 for Blocks
    Slide 3 for Blocks

  • Self-study (Week 14) This week, work with the obligatory project (Assignment 3) and obligatory exercises (Assignment 4, it will be ready very soon).

  • Self-study (The rest of the semester) Repetition.
    Notes for the repetition
    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.
    Lecture notes: completely i.e. pp. 1-86.
    Exam

    The exam consists of the following parts.
    1. Two obligatory assignments (Assignment 1 and Assignment 2), which have already fulfiled. Count 20% of the final result.
    2. New additional assignment (Assignment 4) covering the core curriculum. Problems will be ready in a few days and will be on the Wiki page of the course. Deadline for delivering is 20.04.2020 (can be changed, let me know if you need more time). Counts 20% of the final result
    3. The experimental design project (called also Assignment 3). Deadline for delivering is 07.05.2020 (can be changed, let me know if you need more time). Counts 60% of the final result. The project is individual.
    Pass/fail are used as grades (40% for pass).
    Please send Assignment 3 and Assignment 4 to the Lecturer.
    Table of previous exams:
     
    Exam Problems Solutions
    June 2019 pdf pdf
    May 2018 pdf pdf
    May 2017 pdf pdf
    June 2016 pdf pdf
    May 2015 pdf pdf
    May 2014 pdf pdf
    August 2014 pdf pdf