Quantitative Methods
A.Y. 2023/2024
Learning objectives
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.
Expected learning outcomes
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.
Lesson period: Second trimester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course can be attended as a single course.
Course syllabus and organization
Single session
Responsible
Lesson period
Second trimester
Lectures will be in presence only.
Eventual variations of the teaching method, due to the health situation will be promptly communicated.
Syllabus and Materials
The contents and materials will not be changed. In the remote case of changes, they will be promptly notified on Ariel website.
Assessment methods and Criteria
The final written test, if allowed, will be in person as a written exam. Otherwise, it will be online through the platform exam.net or Moodle.
The second part of the exam will remain unchanged. In the remote case some aspects of the report need be discussed, this will be organised online through Microsoft Teams.
Eventual variations of the teaching method, due to the health situation will be promptly communicated.
Syllabus and Materials
The contents and materials will not be changed. In the remote case of changes, they will be promptly notified on Ariel website.
Assessment methods and Criteria
The final written test, if allowed, will be in person as a written exam. Otherwise, it will be online through the platform exam.net or Moodle.
The second part of the exam will remain unchanged. In the remote case some aspects of the report need be discussed, this will be organised online through Microsoft Teams.
Course syllabus
Theory:
- Course introduction
- Essentials of linear algebra
- Linear regression model
- Principal component analysis
- Models for categorical dependent variables and classification
- Cluster analysis
- Models for panel data
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
- Models for panel data in R
- Course introduction
- Essentials of linear algebra
- Linear regression model
- Principal component analysis
- Models for categorical dependent variables and classification
- Cluster analysis
- Models for panel data
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
- Models for panel data in R
Prerequisites for admission
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 od sequences and of functions
- 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 at least)
- Hypothesis testing (for the mean) in the case of known and unknown variance, p-value.
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 od sequences and of functions
- 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 at least)
- Hypothesis testing (for the mean) in the case of known and unknown variance, p-value.
Some knowledge of linear algebra is also advised.
Teaching methods
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 invited to bring their laptop during laboratory sessions.
Teaching Resources
An Introduction to Statistical Learning, with Applications in R, di
Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, Springer (2017).
Notes of the course made available in the course site (in Ariel)
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).
Notes of the course made available in the course site (in Ariel)
Additional references:
Introduction to Econometrics, 4th Edition
James H. Stock, Mark W. Watson (2019).
Principal Component
Analysis, I.T. Jolliffe, ed. Springer.
Assessment methods and Criteria
The exam consists in two parts each weighting one half of the final grade.
The first part is a written test, consisting of multiple choice and/or open questions on the theory.
The second part is the analysis of a dataset (chosen by the student(s)), to be presented in the form of a written report.
Details on the praparation of the report will be given in class and in the course webpage in Ariel.
The first part is a written test, consisting of multiple choice and/or open questions on the theory.
The second part is the analysis of a dataset (chosen by the student(s)), to be presented in the form of a written report.
Details on the praparation of the report will be given in class and in the course webpage in Ariel.
SECS-S/01 - STATISTICS - University credits: 6
SECS-S/03 - ECONOMIC STATISTICS - University credits: 6
SECS-S/03 - ECONOMIC STATISTICS - University credits: 6
Lessons: 80 hours
Professor:
Leorato Samantha
Educational website(s)
Professor(s)
Reception:
Next office hours: Thursday May the 2nd 10:30-13:30.
Room 32 third floor