This course aims at offering an extensive view of the linear regression model. The class of generalised linear models will be introduced as the first generalisation. Moreover, the issues arising when many covariates are available will be tackled via the penalised approach (LASSO and RIDGE regression). Finally, the Principal component analysis will be introduced as a tool for data reduction, and the Principal component regression will be discussed as a method to handle high-dimensional problems.
At the end of the course, the student will gain the ability to: a) choose, apply and test appropriate regression models for the analysis of different types of data; b) use the free, open-source statistical software R (http://www.r-project.org) for the statistical analysis; c) interpret the results from a decision-making perspective.
Prerequisiti
Good knowledge of the fundamentals of Statistics (i.e. descriptive statistics, probability, inferential statistics, simple linear regression model).
Metodi didattici
The course consists of class lectures and R lab sessions. The lectures & labs calendar will be published at the beginning of the course on the Moodle e-learning platform. Labs will take place within the hours scheduled for the course.
Verifica Apprendimento
The exam consists in: - a test including open-ended and T/F questions (concerning theoretical topics or short applications of the studied methods); - exercises to be solved using the R software (to evaluate the student's ability to analyse different kinds of data and interpret statistical outputs). The two parts of the exam (theoretical and practical) are each worth 50% of the total score, approximately. A positive evaluation of the theoretical part is required to pass the exam.
Contenuti
The Bayesian Approach to Statistics • Multiple regression • Penalized regression (Lasso and Ridge regression) • Generalized Linear models • Principal component analysis • Principal component regression
- Attending class lectures and R labs is strongly recommended. - Documentation about R software is available at the following link: https://www.r-project.org/other-docs.html.
