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# Introduction to Statistics

Course director

Dutta R.

Assistant

Legnazzi C.

Assistant

Assistant

## Description

The aim of this course is to introduce to probability theory, descriptive statistics and linear regression, both at a univariate and multivariate level, with applications focusing on finance.

The free-ware statistical software "R" (free version of the commercial software "Splus", one of the main software used for statistical purposes) will be introduced. The software can be downloaded from the website: http://www.r-project.org/.
Data, imported from an Excel spreadsheet into "R", will be analysed. In particular the statistical instruments needed to visualize and summarize data collected on two or more samples and related to two or more characters (both qualitative and quantitative) will be provided.

Prerequisites
No quantitative prerequisite is needed.

Main topics
The course comprises 3 main topics:

Probability Theory
Introduction to probability:
definitions, concept of marginal and joint probability, low of total probability, conditional probability, notion of independence Random variables:
discrete (Bernoulli, Binomial, Geometric, Poisson, Uniform) continuous (Uniform, Gaussian or Normal, Exponential, Student-T, Chi-square)

Descriptive Statistics:
Univariate:
measure of location (mean, median, mode) and dispersion (variance, std deviation, quantiles)
Bivariate:
two way tables, joint and marginal distributions, covariance and correlation
Graphical instruments to visualize data

Linear regression:
Ordinary Least Squared (OLS) method
Properties of OLS
Gauss – Markov theorem
Multiple linear regression

References
Lecture notes will be available on the e-learning website

Textbooks
P. Newbold, W. Carlson, B. Thorne. Statistics for Business and Economics, Prentince Hall, 2010. 7th Edition, (also available in Italian).
M.J. Crawley. Statistics: An Introduction using R, Wiley, New York, 2005.