Linear model

The linear model is a simple yet powerful tool that forms the basis of many statistical methods. Mastering and understanding it is very useful both from a practical standpoint, for analyzing certain data sets in detail, and from a conceptual standpoint, for understanding the theoretical foundations of more advanced learning methods, including current ones.
 
This course offers an introduction to simple and multiple linear regression models, 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 provides tools for validating and selecting variables in order to study the model's limitations. Finally, it introduces the practical use of this tool on simple data sets using the R software.

 - Understand the theoretical properties of linear models, with quantitative or qualitative variables.
- Know how to construct and estimate a linear model on data using R software.
- Be able to interpret the results and limitations of the model.

Probability and descriptive statistics at L level
HAX710X Inferential statistics
Linear algebra at L level
 

Recommended prerequisites: Knowledge of R software would be an asset.

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 confidence 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 confidence regions

  2.3 - Variable Selection

Hypothesis testing, model selection criteria (AIC, BIC, etc.)

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

Hours per week:
CM: 21 hours
TD: 21 hours
TP:
Fieldwork: