Linear model

The linear model is a tool that is both simple and very powerful, forming the basis of many statistical methods. Mastering and thoroughly understanding it is very useful both from a practical standpoint—for conducting detailed analyses of certain datasets—and from a conceptual standpoint—for understanding the theoretical foundations of more advanced machine learning methods, including those currently in use.
 
This course offers an introduction to simple and multiple linear regression models, using both quantitative and qualitative variables. It presents the formal derivation and theoretical analysis of least squares and maximum likelihood estimators in the Gaussian case. It also provides tools for validating and selecting variables to explore the model’s limitations. Finally, it introduces the practical application of this tool to simple datasets 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 based on data using the R software.
- Be able to interpret the results and limitations of the model.

Level L Probability and Descriptive Statistics
HAX710X Inferential Statistics
Level L Linear Algebra
 

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

1 - Simple Linear Regression

  1.1 - Least Squares

Properties of Least-Squares Estimators, Predictions, and Geometric Interpretation

  1.2 - Gaussian Model

The Law of Maximum Likelihood Estimators, Confidence Intervals, and Confidence Regions

2 - Multiple Linear Regression

  2.1 - Least Squares

Properties of Least-Squares Estimators, Predictions, and Geometric Interpretation

  2.2 - Gaussian Model

The Law of Maximum Likelihood Estimators, Confidence Intervals, and Confidence Regions

  2.3 - Variable Selection

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

3 - Model Validation

  3.1 - Residue Analysis

Structure, Normality, Homoscedasticity

  3.2 - Key Factors and Outliers

Projection matrix, Cook's distance

4 - Linear Regression with Categorical Variables

  4.1 - One-Way ANOVA

Model, Hypothesis Testing

  4.2 - Two-Factor ANOVA 

Model, Hypothesis Testing

Class Schedule:
Lecture: 9:00 p.m.
Tutorial: 9:00 p.m.
Lab:
Fieldwork: