Linear models

Summary

Regression models are fundamental in statistics, because they describe how the law of a random variable of interest may depend on other variables. This course introduces students to the core theory and methods of linear statistical models.

Content

Learning Prerequisites

Recommended courses

Analysis, Linear Algebra, Probability, Statistics

Learning Outcomes

By the end of the course, the student must be able to:

• Recognize when a linear model is appropriate to model dependence
• Interpret model parameters both geometrically and in applied contexts
• Estimate the parameters determining a linear model from empirical observations
• Test hypotheses related to the structural characteristics of a linear model
• Construct confidence bounds for model parameters and model predictions
• Analyze variation into model components and error components
• Contrast competing linear models in terms of fit and parsimony
• Construct linear models to balance bias, variance and interpretability
• Assess / Evaluate the fit of a linear model to data and the validity of its assumptions.
• Prove basic results related to the statistical theory of linear models

Teaching methods

Lectures ex cathedra, exercises in class

Assessment methods

Final exam.

Supervision

Resources

Virtual desktop infrastructure (VDI)

No

Moodle Link

• https://go.epfl.ch/MATH-341