Linear & Generalized Linear Models
A second-year 2A ENSAI course, taught in collaboration with Frédéric Lavancier. It covers the linear model — definition, inference, validation, selection and ANOVA/ANCOVA — and then generalizes to logistic, categorical and counting models. Most resources are adapted from Frédéric Lavancier’s teaching materials.
The Linear Model
🧭 Introduction From correlation and covariance to least squares, significance and over-fitting. ▶ Slides
📐 Definition of the Linear Model The model and OLS estimator, the regression plane, and collinearity. ▶ Slides
🎯 Inference Estimators, confidence & prediction intervals, and Student / Fisher tests. ▶ Slides
🔎 Validation Residuals, R² / R²ₐ, VIF, leverage, outliers and Cook’s distance. ▶ Slides
🧮 Model Selection Cₚ, AIC, BIC, adjusted R², and forward / backward stepwise selection. ▶ Slides
📊 ANOVA / ANCOVA Factors, interactions, and mixing factors with continuous covariates. ▶ Slides
The Generalized Linear Model
🔗 Introduction to GLM Exponential families, link functions, and the GLM framework. ▶ Slides
🪙 Logistic Model Binary outcomes: odds, the logit link, and interpretation. ▶ Slides
🗂️ Models for Categorical Data Multinomial and ordinal responses. ▶ Slides
🔢 Counting Models Poisson and over-dispersed models for count data. ▶ Slides