Statistical Modelling course
Third-year course of the B.Sc. in Artificial Intelligence (Universities of Milano-Bicocca, Milano and Pavia).
A.A. 2025/2026, 1st semester.
Communications
- Please sign up for the course on the Kiro platform to receive communications via email.
Contacts
Calendar
(may be subject to change)
Course material
Lecture notes
The course material is largely based on the book “Modello lineare - Teoria e Applicazioni con R” (Grigoletto M., Pauli F., Ventura L., 2017), and on the course material kindly provided by Prof. Nicola Sartori and Prof. Bernardo Nipoti.
30 Sep - Class 1
Review of probability and statistics.
Probability review (1) -
Probability review (2)
Statistics review (1) -
Statistics review (2)
02 Oct - Class 2
Introduction: role of the variables; phases of the analysis; types of models.
Simple linear model via ordinary least squares: definition, estimate, interpretation of the parameters, descriptive and inferential properties.
Introduction
Simple linear model via OLS -
Properties
07 Oct - Class 3
Simple Gaussian linear model: definition, estimation via likelihood.
Exact distribution of the maximum likelihood estimators.
Inference about the regression coefficients (confidence intervals, tests). Inference about the mean (prediction).
Simple Gaussian LM -
Inference about beta -
Prediction
09 Oct - Class 4
Partition of the sum of squares. Coefficient of determination R2.
Test about the overall model; equivalence with the test about the significance of β2.
Decomposition of the sum of squares -
Coefficient R2
Test about the overall model -
Equivalence with the test about β2
14 Oct - Class 5 *
Exercises on the simple Gaussian linear model.
Exercises simple LM
Solutions exercise 1
16 Oct - Class 6
Analysis of the residuals (descriptive properties, distribution, types of residuals).
Diagnostics (residuals vs. fitted, ECDF, normal Q-Q plot).
Analysis of the residuals -
Diagnostics
21 Oct - Class 7 *
Exercises on the simple Gaussian linear model (continuation of Class 5).
Solutions exercise 2 -
Example on R
Solutions exercises 3 and 4
23 Oct - Class 8
Multiple Gaussian linear model: specification, assumptions, estimation.
Model specification and assumptions -
Estimation
Past Exams
Exam practice. - Exam 00
Solutions Ex. 1 -
Solutions Ex. 2
25 Jan 2024 - Exam 01
22 Feb 2024 - Exam 02
27 Jun 2024 - Exam 03
23 Jul 2024 - Exam 04
03 Sep 2024 - Exam 05
24 Sep 2024 - Exam 06
Suggested book
Fox, J., 2015. Applied regression analysis and generalized linear models. Sage Publications.
Abraham and Ledolter, Introduction to Regression Modeling, Duxbury Press, 2006 –> pdf
Recordings
(the ones I don’t forget to do)
Folder