Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
. - 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.