ECTS
5 credits
Component
Faculty of Science
Description
The linear model is both a simple and very rich tool, which is the basis of many statistical methods. Its mastery and good understanding are very useful both from a practical point of view, to analyze finely certain data sets, and from a conceptual point of view, to understand the theoretical basis of more advanced learning methods, including current ones.
This course proposes an introduction to the linear model of simple and multiple regression, with quantitative or qualitative variables. It presents the formal derivation and theoretical study of least squares and maximum likelihood estimators in the Gaussian case. It also gives validation and variable selection tools to study the limits of the model. Finally, it introduces the practical use of this tool on simple data sets using the R software.
Objectives
- Understand the theoretical properties of linear models, with quantitative or qualitative variables.
- Know how to build and estimate a linear model on data with the R software.
- Be able to interpret the results and limitations of the model.
Necessary pre-requisites
L-level probability and descriptive statistics
HAX710X inferential statistics
L-level linear algebra
Recommended Prerequisites: Knowledge of R software would be an asset
Syllabus
1 - Simple Linear Regression
1.1 - Least Squares
Properties of least squares estimators, predictions, geometric interpretation
1.2 - Gaussian model
Law of maximum likelihood estimators, confidence intervals and regions
2 - Multiple Linear Regression
2.1 - Least Squares
Properties of least squares estimators, predictions, geometric interpretation
2.2 - Gaussian model
Law of maximum likelihood estimators, confidence intervals and regions
2.3 - Variable Selection
Hypothesis testing, model selection criteria (AIC, BIC, ...)
3 - Model Validation
3.1 - Residue analysis
Structure, normality, homoscedasticity
3.2 - Leverage points and outliers
Projection matrix, Cook's distance
4 - Linear regression with qualitative variables
4.1 - One-way ANOVA
Model, hypothesis testing
4.2 - Two factor ANOVA
Model, hypothesis testing
Additional information
Hourly volumes :
CM : 21h
TD : 21h
TP :
Field :