## Program

### Updated A.Y. 2020-2021

3. Inferenza statistica

(a) Campionamento e distribuzioni campionarie.

(b) Stima puntuale. Stimatori di massima verosimiglianza. Metodo dei momenti.

(c) Stima per intervallo

(d) Verifica di ipotesi

4. Il modello di regressione lineare

### Updated A.Y. 2020-2021

3. Statistical Inference

(a) Sampling and sampling distribution.

(b) Point Estimation. Maximum likelihood estimation. Method of moments.

(c) Interval estimation.

(d) HypothesisTesting

4. The linear regression model.

### Updated A.Y. 2019-2020

*Course Program *

The course is structured into the following sub-parts:

Part I: Descriptive Analysis

Introduction to Statistics

Types of data and variables

Summarizing and graphic data

Part II: Probability

Experiments, outcomes, sample spaces and probability axioms

Marginal and conditional probability

Independent events

Main probability distributions: Bernoulli, Binomial, 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 II) will cover Part III and Part IV.

Course Methodology

The course offers two weekly classes, aimed at illustrating the theoretical foundations of statistical instruments and at implementing via examples and exercises. Besides, one weekly lecture will be specifically devoted to practice with exercises and problems.

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 the course's website.

Exam structure

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 as well as applied notions illustrated during the course.

Exam rules

• There will be no mid-term exam

• Students must book for the exam. Please notice that students not booked will not be allowed to take the exam.

• The exam can be taken only once per session.

• The students are allowed to bring with them in the exam room pens, calculator, and ID document. Textbooks, notes or other material are not allowed and their use by the students will invalid the exam. In such an event, the student will be allowed to re-sit the exam during the following 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.

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.

### Updated A.Y. 2018-2019

*Course Program *

The course is structured into the following sub-parts:

Part I: Descriptive Analysis

Introduction to Statistics

Types of data and variables

Summarizing and graphic data

Part II: Probability

Experiments, outcomes, sample spaces and probability axioms

Marginal and conditional probability

Independent events

Main probability distributions: Bernoulli, Binomial, 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 II) will cover Part III and Part IV.

Course Methodology

The course offers two weekly classes, aimed at illustrating the theoretical foundations of statistical instruments and at implementing via examples and exercises. Besides, one weekly lecture will be specifically devoted to practice with exercises and problems.

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 the course's website.

Exam structure

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 as well as applied notions illustrated during the course.

Exam rules

• There will be no mid-term exam

• Students must book for the exam. Please notice that students not booked will not be allowed to take the exam.

• The exam can be taken only once per session.

• The students are allowed to bring with them in the exam room pens, calculator, and ID document. Textbooks, notes or other material are not allowed and their use by the students will invalid the exam. In such an event, the student will be allowed to re-sit the exam during the following 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.

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.

### Updated A.Y. 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 II) will cover Part III and Part IV.

**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 in 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 labour market. Moreover, it will allow students to evaluate and interpret more independently and effectively the numerous statistics daily provided by all types of media.

### Updated A.Y. 2016-2017

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

Simple linear regression model: Assumptions and properties

Multiple linear regression model: Assumptions and properties

This module (Module II) will cover Part III and Part IV.

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 in 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.

• A midterm written exam will be held during the week scheduled for the intermediate tests. If the midterm exam is passed and the candidate accepts the mark, the exam taken during the winter session 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 weigths equal to 50% and 50% respectively.

• Students who are not satisfied with the mark of the midterm exam can resit and take the full exam in the regular exam sessions.

• Please notice that the first part of the program will not be waived if the final exam is taken in any other exam session but the first one, even if the midterm exam is passed. This means that if you take your final exam in June/July or September you will have to take the full exam, even if you got a sufficient mark in the midterm exam.

Course objectives (according to the 5 Dublin Descriptors)

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.

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.

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, ect) 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 an substantial operative ability in terms of data retrieval and analysis of data, which is functional to the following courses and appreciated by the labour market. Moreover, it will allow students to evaluate and interpret more independently and effectively the numerous statistics daily provided by all types of media.