Download Statistics

. - Statistics
PROFESSORS PIERO GANUGI -LAURA BARBIERI
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. Main Means and their properties. Median and Mode.
Indexes. Simple and composite Indexes. Laspeyers, Paasche and Fischer.
Variability. Variance and its properties. Coefficient of variation, absolute deviation
from the median.
Concentration. Lorenz curve. Gini coefficient. Absolute Mean Differencece
Some univariate models. Discrete Rectangular. Normal. Lognormal..
Bivariate descriptive statistics. Covariance and its properties. Linear Correlation.
Least Squares.
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 (overview).
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.
READING LIST
S. BORRA - A. DI CIACCIO, Statistica. Metodologie per scienze economiche e sociali, 2nd ed.,
McGraw-Hill, Milan, 2008.
Other suggested reading
S. M. ROSS, Introduzione alla statistica, Apogeo, Milan, 2008.
D. M. LEVINE - T. C. KREHBIEL - M. L. BERENSON, Statistica, Apogeo, Milan 2002.
C. IODICE, Esercizi Svolti per la prova di Statistica, III Edizione, Edizioni Simone 2007
TEACHING METHOD
Lectures and class exercises.
ASSESSMENT METHOD
Written examination followed by an oral examination.
NOTES
Further information can be found on the Faculty notice board.