Linear & Generalized Linear Models

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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

Exercises

Annals