The student will be introduced to the basic concept, the inferential techniques and the diagnostic tools for linear models. Eventually, he will be able to use appropriately such techniques in real applications.

Mainly linear algebra and statistical inference.

1. Introduction. 2. Simple linear regression: model specification and model assumptions. Estimation of parameters: mean square and maximum likelihood. Hypotheses testing on regression coefficients. Confidence intervals. Goodness of fit. 3. Multiple regression model: matrix specification, generalization of estimates and tests. 4. Model validation and model selection: diagnostics (residuals), methods for variable selection. 5. Use of dummy variables: covariance analysis. 6. Analysis of variance. 7. Limitations of linear model and reasons for its generalizations.

Grigoletto M., Pauli F., Ventura L. “Modello lineare”, G. Giappichelli Editore, 2017

Faraway, J.J. “Practical Regression and Anova using R”, downloadable from http://cran.at.r-project.org/doc/contrib/Faraway-PRA.pdf (ch. 1, 2, 3, 5, 7, 10, 15, 16), 2002.

Weisberg, S. "Applied Linear Regression", Wiley, 2005

Additional materials (lessons slides, R scripts) will be available on Moodle.

Traditional lectures and practical session in computer lab.

Oral exam involving theoretical questions (proofs of main results included) as well as verification of the capacity to apply the techniques taught in the course by means of exercises and the discussion of a practical homework solved using R.