Statistical Modelling course

Third year course of the B.Sc. course in Artificial Intelligence (Universities of Milano-Bicocca, Milano Statale and Pavia).
A.A. 2023/2024, 1st semester.
6 CFU (32 hours lectures, 24 hours exercise classes).


Communications
  • 10/01/2024: The exam will include 2 or 3 exercises (in line with the exercises seen during the course).
    Please bring:
    ✓ a calculator,
    ✓ ID or student card,
    ✓ a pen.
    Course notes, books, and other materials are NOT allowed (including mobile phones, smart watches, etc). You will be given the quantiles needed for the exercises (you do not need to bring the tables).
  • 20/12/2023: the class of Thursday 21/12/2023 will be both online and in-person. Link and password for following remotely.
  • 18/12/2023: corrected typo in “Notes part 18". There was a missing “/N” in the expressions of σ̂2 and σ̃2 (end of the notes, before the definition of the F test).

Contacts

Lectures
Laura D’Angelo: laura.dangelo@unimib.it
Zoom link: https://unipd.zoom.us/my/laura.dangelo

Exercises
Valentina Zangirolami: valentina.zangirolami@unimib.it


Calendar

(may be subject to change)



Course material
Lecture notes

17 Oct - Lecture 1
Introduction to statistical models; types of regression models (number of variables, parametric/nonparametric).
Simple linear model via OLS: introduction, assumptions, estimation, interpretation.
Notes part 1 - Notes part 2

19 Oct - Lecture 2
Descriptive properties of OLS regression line; inferential properties of the estimators.
Gaussian simple linear model: assumptions, estimation via likelihood.
Notes part 3 - Notes part 4

24 Oct - Lecture 3
Exact distribution of the ML estimators; inference about the regression coefficients, inference about the mean (prediction).
Decomposition of the total sum of squares, coefficient of determination R^2.
Notes part 5 - Notes part 6

31 Oct - Lecture 4
Test F for the simple Gaussian linear model.
Diagnostics: analysis of the residuals.
Notes part 7 - Notes part 8

02 Nov - Lecture 5
Multiple Gaussian linear model: specification, interpretation of the parameters, estimation.
Geometric interpretation.
Notes part 9 - Notes part 10 - Notes part 11

07 Nov - Lecture 6
Exercise on the cuckoo dataset (equivalence of two-sample t-test and test on the coefficient of a simple linear model).
Multiple Gaussian linear model: properties of the estimators.
The Gauss-Markov theorem.
Notes part 12 - Notes part 13 - Notes part 14

09 Nov - Lecture 7
Inference in the multiple linear model: test about an individual coefficient (t-test); test about the significance of the overall model; test about a subset of the regression parameters.
Notes part 15 - Notes part 16

14 Nov - Lecture 8
Model comparison and the R^2 coefficient.
Notable examples of the linear model: ANOVA and ANCOVA.
Introduction to generalized linear models.
Notes part 17 - Notes part 18 - Notes part 19 - Notes part 20 corrected typo in “Notes part 18” on 18/12/2023

16 Nov - Lecture 9
Poisson regression: assumptions, interpretation, estimation, inference.
Notes part 21

21 Nov - Lecture 10
Regression for binary data: grouped and ungrouped data, general assumptions.
Logistic regression (ungrouped data): assumptions, interpretation, estimation, inference.
Probit regression: interpretation as a threshold model.
Notes part 22 - Notes part 23 - Notes part 24

28 Nov - Lecture 11
Logistic regression (general formulation with grouped data): assumptions, estimation, inference.
Exercise on the multiple linear model.
Notes part 25 - Notes part 26


Exercise

23 Nov - Exercise 1
Simple linear model (OLS), simple Gaussian linear model.
Ex. 1 - Ex. 2 - Ex. 3 - Solutions

30 Nov - Exercise 2
Simple Gaussian linear model.
Ex. 4 - Solutions

5 Dec - Exercise 3
Simple Gaussian linear model: interpretation, validation, analysis of residuals.
Ex. 5

14 Dec - Exercise 4
Multiple Gaussian linear model
Ex. 6 - Solutions
Ex. 7 - Solutions

19 Dec - Exercise 5
Multiple Gaussian linear model.
Ex. 8

21 Dec - Exercise 6
Generalized linear models.
Ex. 9 - Solutions

9 Jan - Exercise 7
Generalized linear models.
Ex. 10

11 Jan - Exercise 8
Exam practice.
Exam 00
Solutions Ex. 1 - Solutions Ex. 2


Past Exams

25 Jan - Exam 01
22 Feb - Exam 02
27 Jun - Exam 03
23 Jul - Exam 04
03 Sep - Exam 05
24 Sep - Exam 06

Suggested book

Abraham and Ledolter, Introduction to Regression Modeling, Duxbury Press, 2006 –> pdf

Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications.