Linear Models

Objectifs

Understand the construction of a linear regression model
Carry out a complete linear regression study
Perform a constructive residual analysis
Select relevant variables
Use R software packages and the statsmodel library under Python

Plan

Reminders: orthogonal projections, Gaussian vectors and conditional expectation
The multiple linear regression model
The multiple linear regression model under Gaussian assumption
Model validation, variable selection, diagnostic measures

Prérequis

Standard probability laws, Gaussian vectors, confidence regions, statistical tests, matrix algebra, orthogonal projection