I am looking for exercises (more theoretical than applied) about linear regression models. Maybe you can advice me where I can find such exercises. Here is what my linear models course deals with if you want an idea :
- Properties of the multivariate Gaussian distribution and related quadratic forms.
- Gaussian linear regression: likelihood, least squares, geometrical interpretation.
- Distribution theory, confidence and prediction intervals.
- Gauss-Markov theorem.
- Model checking and validation: residual diagnostics, outliers and leverage points.
- Analysis of variance.
- Model selection: bias/variance tradeoff, stepwise procedures, information-based criteria.
- Multicollinearity and penalised estimation: ridge regression, LASSO.
- Robust regression and M-estimation.
- Nonparametric regression and smoothing splines.