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**Course: Advanced Data Analysis and Mathematical Models 1**

## Details

Module I: Statistics

Instructor: Giuliana Passamani, giuliana.passamani [at] unitn.it

Credits: 6

**!!**Students must pass both modules (1 and 2) in order to get 12 credits. No credits are awarded for the single module.

## Course objectives

The aim of the module is to introduce statistical methods for modern econometric analysis, with particular attention to the linear regression model and its application to observed numerical and categorical variables.

In particular, the learning outcomes are:

- knowledge and understanding of statistical methodologies for analysing causal linear relations in economics;
- applying the techniques for analysing observed cross-sectional data;
- evaluation of suitability of particular methods to research in economics;
- making inference using the results of applied research.

## Contents

The syllabus of the module covers the following topics:

The classical linear regression model: assumptions and OLS estimation in the simple and in the multiple regression model.

- Properties of the estimators.
- Sampling distributions of the estimators.
- Single linear hypothesis and multiple linear hypotheses testing.
- Specification problems: omission of relevant variables and inclusion of irrelevant ones.
- Large sample properties of estimators and test statistics.
- Prediction in the classical linear regression model.
- Qualitative information in multiple regression models.
- Consequences of heteroskedasticity for OLS estimation.
- Consequences of serial correlation for OLS estimation.

## Requirements

Familiarity with distributions, densities and moments, both unconditional and conditional; matrix algebra.

## Contents

The syllabus of the module covers the following topics:

- The classical linear regression model: assumptions and OLS estimation in the simple and in the multiple regression model.

- Properties of the estimators.

- Sampling distributions of the estimators.

- Single linear hypothesis and multiple linear hypotheses testing.

- Specification problems: omission of relevant variables and inclusion of irrelevant ones.

- Large sample properties of estimators and test statistics.

- Prediction in the classical linear regression model.

- Qualitative information in multiple regression models.

- Consequences of heteroskedasticity for OLS estimation.

- Consequences of serial correlation for OLS estimation.

## Teaching methods

Traditional lectures and exercise classes.

## Verification of learning

A final written exam, 100% of the module total mark, consisting of four open questions on topics and exercises covered during the course, to be answered in two hours.

## Textbook

Main textbook: Stock J.H. and Watson M.W., "Introduction to Econometrics", Prentice Hall, Updated 3rd Edition, 2015.

Alternatively, Wooldridge J.M., "Introductory Econometrics", Thomson South-Western, 3rd edition, 2006.