Statistics
PROFESSOR ENRICO FABRIZI
COURSE AIMS
To provide students with the basic tools they need to analyse data, which are
useful for tackling decision-making and research problems in uncertain conditions
systematically, and to provide students with a few essential conceptual tools in
order to tackle the statistical subjects they will meet during the rest of their degree
course.
LEARNING OUTCOMES
To provide students with a set of tools useful for scientifically tackling information
analysis, research and decision-making problems in uncertain conditions, and to
provide students with a few essential conceptual tools in order to tackle the
statistical subjects they will meet during the rest of their degree course.
COURSE CONTENT
PART I: DESCRIPTIVE STATISTICS
Introduction: Tabulation and graphical representations. Histograms.
Means: Arithmetic and geometric means, median and mode.
Other position indices: Quartiles and percentiles.
Measures of variability: Variance, standard deviation, coefficient of variation,
absolute deviation from the median, and interpercentile ranges.
Skewness: Basic concepts and Fisher index.
Bivariate descriptive statistics: Two-way tables. Odds ratios. Conditional means
and variances, scatter plots, covariance and correlation between quantitative
variables.
Index numbers: simple index numbers, change-of-base formulas, Laspeyers,
Paasche and Fisher index numbers.
PART II: PROBABILITY THEORY
Introduction: Probability theory axioms and fundamental theorems of calculus.
Conditional probability and independent events. Bayes' formula.
Theory of discrete random variables: Probability distribution, cumulative
distribution function, expected value and variance.
Families of discrete random variables: Bernoulli, binomial, Poisson and discrete
uniform.
Theory of continuous random variables: Probability density function, cumulative
distribution function and moments.
Notable families of continuous random variables: Continuous uniform,
exponential, normal, gamma, beta and log-normal.
Discrete and continuous dual random variables: Conditional distributions;
conditional moments. Independence between random variables.
Theories of convergence: Strong law of large numbers and central limit theorem.
PART III: STATISTICAL INFERENCE
Sampling and sampling distributions. Statistics and their sampling distributions.
Point estimate: Concept of estimator. Unbiasedeness, mean-square error, and
efficiency of an estimator. Point estimation of the mean and variance of a
population. Maximum likelihood estimators.
Interval estimate: Introduction. Confidence intervals for the mean of a population;
confidence intervals for a proportion. Confidence intervals for the variance of a
normal population. Calculation of sample size.
Hypothesis testing theory: Definition of the problem, acceptance and rejection
regions, decision error classification, and power function.
Specific tests: Test for the mean of a population; test for a proportion; test for the
difference between two means. Chi-square independence test and Chi square
goodness of fit test.
PART IV: REGRESSION MODELS
Simple linear regression model: Basic model assumptions. Estimation of
parameters. Least-squares and maximum likelihood. Variance decomposition
formula and measures of fit. Statistical properties of estimators.
Inference on the parameters of the simple linear model: Tests on the significance
of coefficients, analysis of variance and F-test. Predictions. Analysis of the
residuals.
Multiple linear regression model: Model specification and least-square estimators.
Inference on the parameters of the multiple linear regression model. t-test on the
coefficients and F-test for variance analysis. Analysis of the residuals and other
diagnostics.
Generalized linear regression models. The logit and probit regression models.
Non-linear regression models. Estimation of logistic growth curves. Introduction
basic ideas of non parametric regression.
PART V: STATISTICAL SOFTWARES (ONLY FOR STUDENTS WITH 12 CFU)
Statistical softwares. Introduction to the software R. Basic function and data
management. Data surmmaries and presentation. Hypothesis testing and im
plementation of regression models.
READING LIST
Reference text
S. BORRA-A. DI CIACCIO, Statistica. Metodologie per scienze economiche e sociali, 3nd ed.,
McGraw-Hill, Milan, 2014.
Other suggested readings:
S. M. ROSS, Introduzione alla statistica, Apogeo, Milan, 2008.
C. IODICE, Esercizi Svolti per la prova di Statistica, III Edizione, Edizioni Simone 2007.
TEACHING METHOD
Lectures and assignments.
ASSESSMENT METHOD
Written exams and interviews.
Students can meet with Professor Fabrizi on the days and at the times indicated on the notice
board at the Faculty of Economics.
REMARKS
The program covers parts I,II,III,IV for students with 8CFU. The part V is only for those
with 12 cfu Statistics course in their study plan.