Linear model

The linear model is both a simple and a very rich tool, forming the basis of many statistical methods. Its mastery and understanding are very useful both from a practical point of view, for fine-tuning the analysis of certain data sets, and from a conceptual point of view, for understanding the theoretical foundations of more advanced learning methods, including current ones.

This course provides 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 provides validation and variable selection tools to study model limitations. Finally, it introduces the practical use of this tool on simple data sets using R software.

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

L-level probability and descriptive statistics
HAX710X inferential statistics
L-level linear algebra
 

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 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, etc.)

3 - Model validation

  3.1 - Residual analysis

Structure, normality, homoscedasticity

  3.2 - Lever points and outliers

Projection matrix, Cook distance

4 - Linear regression with categorical variables

  4.1 - One-way ANOVA

Model, hypothesis testing

  4.2 - Two-factor ANOVA 

Model, hypothesis testing

Volumes horairestrio :
CM : 21h
TD : 21h
TP :
Field :