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Second Semester 
Teaching style
Lingua Insegnamento

Informazioni aggiuntive

Course Curriculum CFU Length(h)


The course aims to provide an introduction to basic and advanced statistical methods for the study of relationships between more than two variables. Will be presented the model of Multiple regression and correlation, the Analysis of Variance and Covariance, the methods for the selection of models and will be introduced logistic regression models.

At the end of the course the student will be able to choose and apply suitably appropriate methodologies for studying the association / dependency between more than two variables (using response variables both qualitative and quantitative). The students shall be able to read and interpret the resulting output of the application of multiple regression models, models of variance analysis (ANOVA), to couple the regression and ANOVA, to understand the most basic procedures for the selection of statistical models


Basic concepts of probability theory (random variables and probability distributions); characteristics of probability distributions (expected value, mean, variance, covariance) and main sampling distributions; point estimates; confidence intervals, hypothesis testing, simple linear regression model. The pre-requisites indicated are earned by students who have passed the examination (at list a semester course) in Statistics or Social Statistics in the three-year degree program (Bachelor)


- Recall on the basic concepts of inference (distributions, confidence intervals, test)
- Recall the study of the relationship between two variables (categorical or quantitative)
- Introduction to multivariate relations
- Multiple Regression and Correlation
- Multicollinearity, multiple correlation and R-squared
- Inference for multiple regression
- Partial correlation
- Analysis of Variance. Variability within groups and between groups
- Multiple comparisons of means. Bonferroni confidence intervals
- ANOVA and regression models
- Two-way ANOVA
- Analysis of Covariance
- Adjusted means
- Choice of models for the multiple regression (outline)
- Limits of procedures for the automatic choice of the models (outline)
- Regression Diagnostic (outline)
- Generalized Linear Models (outline)
- Logistic Regression

Teaching Methods

Lectures (min 54 hours)

If the emergency regime due to the COVID-19 epidemic remains, the teaching will be provided simultaneously both in presence and online. At the beginning of the semester, the student will opt for face-to-face or distance teaching, the choice will be binding for the entire semester. If the number of students exceeds the capacity of the classrooms, determined on the basis of government provisions on health matters for the purpose of combating the pandemic, access to teaching facilities will be regulated through a shift system that will be communicated in due time to interested students

Verification of learning

Written test and discussion of the assignment.

To determine the final grade, the following criteria will be considered:
1. the method followed by the student to solve the exercises;
2. the accuracy of the procedure identified to answer the questions;
3. the accuracy, from a statistical point of view, of the proposed solution (related to the statistical skills acquired by the student at the end of course);
4. the use of an appropriate statistical language;
5. the use of a correct statistical-mathematical notation.

The fulfillment of the facets 1 and 2 is necessary to achieve a positive evaluation. The completion of the third point is also necessary to better reach the final grade. A grade above 28/30 will be awarded to students, whose final tests fully include the above listed points.

Statistics on the test results of June-July 2019 (data updated to July 2019):
- Mean = 25.10
- Dev.Std = 3.14
- Number of tests on which the mean was calculated = 40
- Percentage of successful tests = 93%


Suggested: Agresti - Finlay, Statistical Methods for the Social Sciences, Pearson, Last ed.

Further readings: Tabachnick - Fidell, Using Multivariate Statistics, Pearson, Last ed.

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