Statistics, Finance and Actuarial sciences

MARIA BRIGIDA FERRARO

Learning goals.
The primary objective is to provide students with basic concepts and procedures of descriptive statistics.
At the end of the course the student must be able to design a small census survey and to conduct descriptive analyses of the data through the use of a statistical software.
Knowledge and understanding.
Upon completion of the course, students know and understand the main procedures of descriptive statistics.
They are able to organize data in simple and contingency tables and to synthesize them through graphical representations.
They know and are able to calculate the most important statistical indicators that measure
(a) position, variability and form of simple distributions and
(b) important aspects of the joint distribution of two variables.
Furthermore, they have acquired the notion of statistical model and are able to implement a simple regression model.
Applying knowledge and understanding.
Upon completion of the course, students are able to apply the knowledge acquired, in order to interpret and critically evaluate the results of descriptive analysis.
Making judgements.
Through a large number of exercises on all the topics covered, students develop autonomous judgment skills that allow to identify the most appropriate methods to solve problems of descriptive statistics and to critically interpret the results of the elaborations provided by the software.
Communication skills Students, through the study and the performance of practical exercises, acquire the technical-scientific language of the discipline, that must be properly used both in the written and in the oral examinations.
Learning skills Students who pass the exam will have knowledge of the fundamental notions for the descriptive analysis of data.
They will also be able to implement simple codes to organize data in tables and synthesize them through graphics and/or calculation of important indicators.
Therefore, they have acquired the basics to learn what will be proposed in the subsequent statistical courses.

The primary objective is to provide students with basic concepts and procedures of descriptive statistics.
At the end of the course the student must be able to design a small census survey and to conduct descriptive analyses of the data through the use of a statistical software.
Knowledge and understanding.
Upon completion of the course, students know and understand the main procedures of descriptive statistics.
They are able to organize data in simple and contingency tables and to synthesize them through graphical representations.
They know and are able to calculate the most important statistical indicators that measure
(a) position, variability and form of simple distributions and
(b) important aspects of the joint distribution of two variables.
Furthermore, they have acquired the notion of statistical model and are able to implement a simple regression model.
Applying knowledge and understanding.
Upon completion of the course, students are able to apply the knowledge acquired, in order to interpret and critically evaluate the results of descriptive analysis.
Making judgements.
Through a large number of exercises on all the topics covered, students develop autonomous judgment skills that allow to identify the most appropriate methods to solve problems of descriptive statistics and to critically interpret the results of the elaborations provided by the software.
Communication skills Students, through the study and the performance of practical exercises, acquire the technical-scientific language of the discipline, that must be properly used both in the written and in the oral examinations.
Learning skills Students who pass the exam will have knowledge of the fundamental notions for the descriptive analysis of data.
They will also be able to implement simple codes to organize data in tables and synthesize them through graphics and/or calculation of important indicators.
Therefore, they have acquired the basics to learn what will be proposed in the subsequent statistical courses.

Conoscenze di matematica di base.

Parte a (18 ore circa):
- Nozioni introduttive: collettivo statistico, unità statistica e caratteri
- Distribuzioni statistiche
- Rappresentazioni grafiche

Parte b (34 ore circa):
- Indici di posizione: definizioni, proprietà, calcolo e utilizzo
- Indici di variabilità: definizioni, proprietà, calcolo e utilizzo
- Indici di forma: definizioni, proprietà, calcolo e utilizzo

Parte c (20 ore circa):
- Distribuzioni doppie
- Dipendenza
- Dipendenza in media
- Correlazione lineare
- Regressione lineare semplice

G. Cicchitelli, P. D’Urso, M. Minozzo
STATISTICA: PRINCIPI E METODI, Terza Edizione.

G. Cicchitelli, P. D’Urso, M. Minozzo
STATISTICA: PRINCIPI E METODI, Terza Edizione.

- Lectures
- Tutorial sessions in computer laboratory (R/RStudio).

La frequenza è fortemente raccomandata. In caso di impossibilità a frequentare le lezioni, si consiglia di contattare il docente.

(a) Prova scritta [2 ore]
La prova scritta è articolata in due parti, entrambe obbligatorie:

(a1) esercizi tradizionali -- 1/3 voto finale
(a2) prova pratica con R/Rstudio -- 1/6 voto finale

(b) Prova orale* [30 minuti circa] -- 1/2 voto finale

*Per essere ammessi alla prova orale è necessario superare entrambe le parti della prova scritta, ovvero ottenere almeno la sufficienza sia negli esercizi tradizionali (a1), sia nella prova pratica con R/RStudio (a2).

Esempio esercizio:

Nella seguente tabella sono riportati i valori relativi al reddito (in euro) di 96 dipendenti di un'azienda di Verona.

1) Qual è l'unità statistica?

2) Qual è il carattere? Di che tipo di carattere si tratta?

3) Qual è il reddito medio?

4) Come varia il reddito dei 96 dipendenti rispetto al reddito medio?

5) Calcola il rapporto di concentrazione R del reddito.

6) Disegna la curva di concentrazione.

Esempio quesito R:

- Carica nella tua area di lavoro il dataset ‘datiesame.RData'
- Considera in particolare il carattere X.
a. Fornisci una adeguata rappresentazione grafica.
b. Calcola i principali indici di posizione che conosci.
c. Calcola un opportuno indice di asimmetria e commenta.