## Syllabus

EN
IT

### Learning Objectives

LEARNING OUTCOMES: The course provides the fundamental theoretical notions of the statistical analysis and illustrates the basic techniques for organizing, summarizing and graphically representing ungrouped data. Basics of statistical inference and correlation analysis (ANOVA, linear and multiple regression model) will also be illustrated.

KNOWLEDGE AND UNDERSTANDING: The students remember and understand thefundamental theoretical notions of the analysis of any type of statistical data, including summarizing, organizing and graphically representing the data with the most suitable measures and graphs. They will also be able to formulate and conduct simple hypothesis testing and to set basic regression analysis on small datasets.

APPLYING KNOWLEDGE AND UNDERSTANDING: The students will be able to produce and interpret basic statistical analyses. The use of examples based on real data (taken from Bank of Italy, Eurostat, Istat, NBER, etc… ) is focal throughout the entire course. The objectives of the course, thus, include the ability of recognizing the different types of data (cross-section, time-series, panel) and their peculiarities, the ability of producing descriptive

statistics and suitable graphical representations, the ability of remembering and understanding the basics of statistical inference as well as of conducting a correct correlation analysis, via the estimation of linear regression models.

MAKING JUDGEMENTS: The students will be able to autonomously evaluate which, among the several statistical tools acquired, is 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 summarize and communicate them, also via e.g. graphical representations. 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 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.

KNOWLEDGE AND UNDERSTANDING: The students remember and understand thefundamental theoretical notions of the analysis of any type of statistical data, including summarizing, organizing and graphically representing the data with the most suitable measures and graphs. They will also be able to formulate and conduct simple hypothesis testing and to set basic regression analysis on small datasets.

APPLYING KNOWLEDGE AND UNDERSTANDING: The students will be able to produce and interpret basic statistical analyses. The use of examples based on real data (taken from Bank of Italy, Eurostat, Istat, NBER, etc… ) is focal throughout the entire course. The objectives of the course, thus, include the ability of recognizing the different types of data (cross-section, time-series, panel) and their peculiarities, the ability of producing descriptive

statistics and suitable graphical representations, the ability of remembering and understanding the basics of statistical inference as well as of conducting a correct correlation analysis, via the estimation of linear regression models.

MAKING JUDGEMENTS: The students will be able to autonomously evaluate which, among the several statistical tools acquired, is 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 summarize and communicate them, also via e.g. graphical representations. 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 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.

### Prerequisites

Mathematics: powers, logs, combinatorics, mathematical functions

### Program

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 and multiple inear regression model: Assumptions and properties

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 and multiple inear regression model: Assumptions and properties

### Books

The main textbook is Introductory Statistics (8th Edition), by P. S. Mann, edited by Wiley.

### Teaching methods

During the whole duration of the course (12 weeks), there will be 2 weekly classes of 3 hours each, and 1 practice of 2 hours. In all appointments, an active participation to the class is strongly encouraged.

### Exam Rules

The written exam covers the whole program of the course.

It includes multiple-choices as well as open questions, on both theoretical notions and applied issues, featuring e.g. graphs, computation of descriptive statistics and estimation outputs applied to small datasets. This will allow to evaluate the student in terms of understanding and interpretation of the final results of an basic statistical analysis. Final mark ranges between 18 (minimum to pass the exam) and 30 (maximum mark).

It includes multiple-choices as well as open questions, on both theoretical notions and applied issues, featuring e.g. graphs, computation of descriptive statistics and estimation outputs applied to small datasets. This will allow to evaluate the student in terms of understanding and interpretation of the final results of an basic statistical analysis. Final mark ranges between 18 (minimum to pass the exam) and 30 (maximum mark).