Quantitative methods
A.A. 2026/2027
Obiettivi formativi
The aim of this course is to provide students with practical and theoretical understanding of some of the most used multivariate statistical methods, with a particular attention to techniques useful for business and marketing applications. More specifically, the scope of the course is to give the students the necessary tools to be able to deal with simple and complex problems that a company may be facing, by using information and statistical methods suitable for the purpose, such as regression analysis, cluster analysis or principal component analysis, among the others.
Risultati apprendimento attesi
At the end of the course, students will be able to represent a dataset through tables and graphs, to summarise the relevant information using descriptive statistics, by appropriately considering eventual outliers.
Students will be acquainted with statistical models, their theoretical foundations and their correct use and interpretation.
Specifically, they will be able to choose the statistical tool suitable to a specific problem, they will learn to select a regression model for a response (dependent) variable, given a set of covariates, to estimate the parameters of the model and to use tests of hypotheses in order to answer a research question or to take decisions. They will put in practice the use of advanced descriptive tools, such as cluster analysis or principal component analysis, aimed at detecting the existence of homogeneous groups of observations or to synthesise the total information in a small number of "factors"." Through the introduction of the statistical software R, students will learn to apply the appropriate quantitative tools on various real-data scenarios and an adequate representation of the results. As part of their final exam, they will also be able to design and develop an "empirical exercise" on their own.
Students will be acquainted with statistical models, their theoretical foundations and their correct use and interpretation.
Specifically, they will be able to choose the statistical tool suitable to a specific problem, they will learn to select a regression model for a response (dependent) variable, given a set of covariates, to estimate the parameters of the model and to use tests of hypotheses in order to answer a research question or to take decisions. They will put in practice the use of advanced descriptive tools, such as cluster analysis or principal component analysis, aimed at detecting the existence of homogeneous groups of observations or to synthesise the total information in a small number of "factors"." Through the introduction of the statistical software R, students will learn to apply the appropriate quantitative tools on various real-data scenarios and an adequate representation of the results. As part of their final exam, they will also be able to design and develop an "empirical exercise" on their own.
Periodo: Terzo trimestre
Modalità di valutazione: Esame
Giudizio di valutazione: voto verbalizzato in trentesimi
Corso singolo
Questo insegnamento può essere seguito come corso singolo.
Programma e organizzazione didattica
Edizione unica
Responsabile
Periodo
Terzo trimestre
More detailed directions on the teaching modalities for the academic year 2026/27 will be given in the following months, based on the evolution of the sanitary situation.
Programma
Theory:
- Course introduction
- Linear regression model
- Models for categorical dependent variables and classification
- Principal component analysis
- Cluster analysis
- Additional topic (changing every year: models for longitudinal data, decision trees,...)
Laboratory:
- Introduction to R
- Data manipulation and representation
- linear regression model
- Principal component analysis
- Models for categorical dependent variables in R
- Cluster analysis in R
- Examples in R of the additional topic
- Course introduction
- Linear regression model
- Models for categorical dependent variables and classification
- Principal component analysis
- Cluster analysis
- Additional topic (changing every year: models for longitudinal data, decision trees,...)
Laboratory:
- Introduction to R
- Data manipulation and representation
- linear regression model
- Principal component analysis
- Models for categorical dependent variables in R
- Cluster analysis in R
- Examples in R of the additional topic
Prerequisiti
Students must be acquainted with a basic course in statistics (descriptive and inferential) and mathematics.
The following topics will be assumed as known:
Mathematics:
- functions of one or more variables
- sequences and series
- limits, derivatives of a functions, monotonicity, convexity/concavity of a function
- optimisation (maximisation/minimisation) of a function
Statistics:
- types of data and their representation
- location and scale indices
- dependence measures between qualitative variables (chi-square) and quantitative variables (covariance/correlation)
- random variables, continuous and discrete
- Gaussian and binomial distribution
- law of large numbers and central limit theorems
- simple random sampling
- Point estimation of mean and variance of a population: sample mean and sample variance
- Confidence intervals (for the mean)
- Hypothesis testing (for the mean) in the case of known and unknown variance.
Some knowledge of linear algebra is also advised.
The following topics will be assumed as known:
Mathematics:
- functions of one or more variables
- sequences and series
- limits, derivatives of a functions, monotonicity, convexity/concavity of a function
- optimisation (maximisation/minimisation) of a function
Statistics:
- types of data and their representation
- location and scale indices
- dependence measures between qualitative variables (chi-square) and quantitative variables (covariance/correlation)
- random variables, continuous and discrete
- Gaussian and binomial distribution
- law of large numbers and central limit theorems
- simple random sampling
- Point estimation of mean and variance of a population: sample mean and sample variance
- Confidence intervals (for the mean)
- Hypothesis testing (for the mean) in the case of known and unknown variance.
Some knowledge of linear algebra is also advised.
Metodi didattici
Lectures are divided (approximately 50-50) into traditional classes, where the theory is introduced, and laboratories, where the theory is put in practice through the use of the statistical package R. Students are expected to bring their laptop during laboratory sessions.
Additional tutorial classes are also available
Additional tutorial classes are also available
Materiale di riferimento
An Introduction to Statistical Learning, with Applications in R, di
Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, Springer (2017).
Saranno disponibili dispense scaricabili dal sito myAriel del corso.
Additional references:
Introduction to Econometrics, 4th Edition
James H. Stock, Mark W. Watson (2019).
Principal Component
Analysis, I.T. Jolliffe, ed. Springer.
Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, Springer (2017).
Saranno disponibili dispense scaricabili dal sito myAriel del corso.
Additional references:
Introduction to Econometrics, 4th Edition
James H. Stock, Mark W. Watson (2019).
Principal Component
Analysis, I.T. Jolliffe, ed. Springer.
Modalità di verifica dell’apprendimento e criteri di valutazione
Attending students (minimum attendance required). The final grade will be based on: (i) participation to tests in class; (ii) Hackathon/team challenge(s)
Non-attending students. Written exam, based on closed questions, open questions and exercises.
Non-attending students. Written exam, based on closed questions, open questions and exercises.
STAT-01/A - Statistica - CFU: 6
STAT-02/A - Statistica economica - CFU: 6
STAT-02/A - Statistica economica - CFU: 6
Lezioni: 80 ore
Docente:
Leorato Samantha
Docente/i
Ricevimento:
Monday 14:30-16 or Thursday 9-10:30 (online). Email is required
Stanza 32 terzo piano