Linear model

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.

 - 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.

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, ...)

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

Hourly volumes :
CM : 21h
TD : 21h
TP :
Field :