# Coursebooks

## Linear models

Panaretos Victor

English

#### Summary

Regression modelling is a basic tool of statistics, because it describes how one variable may depend on another. The aim of this course is to familiarize students with the basis of regression modelling, and of some related topics.

#### Content

• Properties of the multivariate Gaussian distribution and related quadratic forms.
• Gaussian linear regression: likelihood, least squares, geometrical interpretation.
• Distribution theory, confidence and prediction intervals.
• Gauss-Markov theorem.
• Model checking and validation: residual diagnostics, outliers and leverage points.
• Analysis of variance.
• Model selection: bias/variance tradeoff, stepwise procedures, information-based criteria.
• Multicollinearity and penalised estimation: ridge regression, LASSO.
• Robust regression and M-estimation.
• Other topics as time permits: logistic and Poisson regression, nonparametric regression.

#### Learning Prerequisites

##### Recommended courses

Analysis, Linear Algebra, Probability, Statistics

#### Learning Outcomes

By the end of the course, the student must be able to:
• Recognize when a linear model is appropriate to model dependence
• Interpret model parameters both geometrically and in applied contexts
• Estimate the parameters determining a linear model from empirical observations
• Test hypotheses related to the structural characteristics of a linear model
• Construct confidence bounds for model parameters and model predictions
• Analyze variation into model components and error components
• Contrast competing linear models in terms of fit and parsimony
• Construct linear models to balance bias, variance and interpretability
• Assess / Evaluate the fit of a linear model to data and the validity of its assumptions.
• Prove basic results related to the statistical theory of linear models

#### Teaching methods

Lectures ex cathedra, exercises in class, take-home projects

#### Assessment methods

Continuous control, final exam.

Seconde tentative : Dans le cas de l'art. 3 al. 5 du Règlement de section, l'enseignant décide de la forme de l'examen qu'il communique aux étudiants concernés.

#### Supervision

 Office hours No Assistants Yes Forum Yes

No

### Reference week

MoTuWeThFr
8-9    MAA330
9-10
10-11
11-12
12-13
13-14
14-15
15-16
16-17  MAB111
17-18
18-19
19-20
20-21
21-22

Lecture
Exercise, TP
Project, other

### legend

• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German