Aggiornato A.A. 2017-2018
Finalità del corso (quali conoscenze lo studente acquisisce tramite l’insegnamento secondo i 5 descrittori di Dublino)
Descrittori di Dublino
Conoscenza e capacità di comprensione
(Knowledge And Understanding)
Il corso fornisce i fondamenti teorici delle analisi statistiche di base. In particolare, si illustreranno i vari tipi di rappresentazioni grafiche in funzione alle diverse tipologie di dati, nonché i possibili indicatori di sintesi, quali quelli di posizione e di variabilità, con le relative proprietà ed i possibili limiti (Statistica Descrittiva). Successivamente si forniranno le nozioni di base di Probabilità e si illustreranno le principali variabili aleatorie e le relative distribuzioni. Nella seconda parte del corso si forniranno gli strumenti per la verifica delle ipotesi sulla base di campioni (Inferenza Statistica) e per un’analisi di regressione di base, tramite il modello di regressione lineare semplice e con più regressori, di cui saranno indicate le principali assunzioni e proprietà (Modelli di Regressione).
Capacità di applicare conoscenza e capacità di comprensione
(Applying Knowledge And Understanding)
Il corso fornisce gli strumenti necessari per condurre l’analisi statistica di base di qualsiasi tipo di dato, interpretandone correttamente i risultati.
L’utilizzo di dati reali (fonte Eurostati, Istat, NBER, ect…) e di software statistici è parte integrante del corso ed oggetto di tutte le esercitazioni. Tra le finalità del corso rientrano quindi la capacità di reperire e riconoscere dataset di natura diversa (dati sezionali, serie storiche e dati panel) e di gestirlo correttamente, producendone statistiche descrittive e rappresentazioni grafiche adeguate, nonché di produrre stime di modelli di regressione lineari semplici e multipli.
Autonomia di giudizio
(Making Judgements)
Al termine del corso gli studenti imparano a capire quali sono le metodologie statistiche più adeguate per l’analisi di base di diverse tipologie di dati. Saranno in grado di formulare ipotesi e di testarle con l’ausilio dei dati più appropriati, reperendoli dalle giuste fonti disponibili. Infine, saranno in grado di condurre un’analisi di regressione di base, modellando la variabile dipendente come funzione lineare di una o più variabili esplicative.
Abilità comunicative
(Communication Skills)
Tramite gli strumenti forniti dal corso, gli studenti saranno in grado di utilizzare i dati per estrarre indicazioni su un fenomeno (di natura prevalentemente economica) e comunicarle efficacemente. In particolare, gli studenti saranno in grado di saper descrivere le ipotesi in analisi, il dataset utilizzato, sottolineandone eventuali peculiarità (es. osservazioni anomale, particolare natura dei dati, etc.), e le tecniche più adeguate per condurre l’analisi. Al termine del corso gli studenti saranno inoltre in grado di produrre (nonché di leggere ed interpretare) tavole di statistiche descrittive e rappresentazioni grafiche utili alla dimostrazione della tesi. Infine, rientra tra gli obiettivi del corso la capacità di produrre in formato tabulare stime di vari modelli di regressione, al fine di consentirne un rapido e chiaro confronto.
Capacità di apprendere
(Learning Skills)
Il corso consente allo studente di acquisire una maggiore capacità operativa in termini di reperimento ed analisi dei dati, funzionale alle fasi di studio e lavorative che succederanno, nonché di valutare in più autonomia le statistiche che vengono fornite quotidianamente dalle varie fonti di informazione.
Aggiornato A.A. 2017-2018
Course Program
The course is structured into four sub-parts, described in what follows.
Part I: Descriptive Analysis
Introduction to Statistics
Types of data and variables
Summarizing and graphic data
Part II: Probability and main distributions
Experiments, outcomes, sample spaces and probability axioms
Marginal and conditional probability
Independent events
Bayes theorem
Discrete random variables: Bernoulli, Binomial
Continuous random variables: Normal, Chi-Square, t-statistics, F
Part III: Inference
Estimators
Hypothesis testing
Part IV: Regression analysis
Simple linear regression model: Assumptions and properties
Multiple linear regression model: Assumptions and properties
This module (Module I) will cover Part I and Part II.
Course Methodology
The course offers three weekly classes, aimed at illustrating the theoretical foundations of statistical instruments and at implementing them via examples and exercises. Besides, one weekly lecture will guide the students in practicing with paper and pencil exercises as well as with real data statistical analysis.
Material
The main textbook is Introductory Statistics (8th Edition), by P. S. Mann, edited by Wiley.
Slides presented in class and additional material will be also provided on this website.
Exam
The final evaluation is based on a closed-book written exam, covering the entire course’s program.
It includes open questions, multiple choices questions, and exercises aimed at evaluating the knowledge and understanding of the theoretical notions illustrated during the course. Part of the exam focuses on the computation and interpretation of the coefficients and the diagnostics of linear regression models, aimed at evaluating the ability of students of applying the knowledge acquired in the course.
Other rules
• Students must book for the exam.
• The exam can be taken only once per session.
• Final marks are published on the dedicated web page (normally within one week after the exam) and are uploaded on the Delphi system so to be individually received by email by candidates.
• Midterm written exams will be held during the weeks scheduled for the intermediate tests. If the first midterm exam is passed, and the candidate accepts the mark, the candidate can also take the second mid term, that will be held before Christmas break, and will concern the topics covered in the second part of the course only.The final evaluation will be the average of the two marks obtained in the midterm and in the final exam, with weights equal to 50% and 50% respectively.
• Students who are not satisfied with the mark of one or both the midterm exams can resit and take the full exam in the regular exam sessions.
• Please notice that no part of the program will be waived if the final exam is taken during regular exam sessions, even if one or both midterm exams are passed. This means that if you take your final exam in January/February or June/July or September you will have to take the full exam, even if you got a sufficient mark in one or both the midterm exams.
Course objectives (according to the 5 Dublin Descriptors)
Knowledge And Understanding
The course provides the students with the theoretical undergrounds of basic statistical analyses. The course will start with an overview of the descriptive analyses, illustrating for each type of data, the most suitable graphical representations and summary statistics, highlighting points of strength and caveats. Then, the fundamentals of Probability will be given, followed by the presentation of the main features of the mostly used random variables models (Bernoulli, Binomial, Normal, Chi-square, t-Student, F). Then, sampling distributions and hypotheses tests will be illustrated, with specific attention to tests about the mean and variance of the population. Finally, simple linear regression and multiple regression models will be presented, specifying the main assumptions and properties.
Applying Knowledge And Understanding
The students will be able to produce and interpret basic statistical analyses. The use of real data (taken from Eurostat, Istat, NBER, etc…) and of appropriate statistical software is focal all throughout the course classes and lectures. The objectives of the course, thus, include the ability of finding the appropriate dataset, recognizing the different types of data (cross-section, time-series, panel) and their peculiarities, the ability of producing descriptive statistics and suitable graphical representations, as well as of conducting a correct correlation analysis, via the estimation of linear regression models.
Making Judgements
The students will be able to evaluate which, among the different statistical tools acquired, is/are the most appropriate for the problem at hand. They will be able to formulate statistical hypotheses and to test them with suitable data, properly found among the tons of data available to date. Finally, they will be able to set up a linear regression analysis, evaluating the reliability and suitability of the model based on the estimation output.
Communication Skills
The students will be able to use data to get indications about economic phenomena and to effectively communicate them, via e.g. graphical representations and summary statistics. Moreover, they will be able to produce short reports describing the research question, the statistical hypotheses to be tested, the dataset used (highlighting the nature of the dataset, potential outliers, etc) and the statistical tools used for the analysis. They will also be able to produce, interpret, evaluate and compare linear regression models.
Learning Skills
The course endows the students with a substantial operative ability in terms of data retrieval and analysis of data, which is functional to the following courses and appreciated by the labor market. Moreover, it will allow students to evaluate and interpret more independently and effectively the numerous statistics daily provided by all types of media.
Prof.ssa Lucia Leonelli
