Statistics for Economics and Business

Master Program:	Economics & Enterpreneurship
Credits:	10 ECTS
Start date:	21 September 2015
End date:	08 March 2016
Class calendar:	Monday, 12:00 - 14:00 Tuesday, 12:00 - 14:00
Room:	0.05 / 1.05

Language: English

Description

AIMS
Aim of the course is to provide students with a broad overview of statistical methods and models which may be exploited to tackle economics and business issues starting from data. Students will learn statistics by doing, exploiting R, a popular open-source software for data analysis. Emphasis on the applications of the techniques and on the interpretation of results will help students to appreciate the relevance of the statistical tools in real life applications.

REQUIRED BACKGROUND
A basic knowledge of elementary calculus is required. The course will start assuming a previous knowledge of statistics at an undergraduate level: the minimal prerequisite is a undergraduate course in probability and basic statistics.

TEACHING
Lectures and lab sessions.

EXAMINATION METHODS
Written + oral final exam.

Syllabus

DETAILED SYLLABUS
(for further details, see the diary of class, weekly updated with the topics covered in the classroom)

CONTENTS
Gathering and Exploring Data: data description, graphical and numerical summaries, association, gathering data. Probability distributions and sampling distributions. Inferential statistics: confidence intervals and significance tests about population central values, for comparing two population central values, about population variances, for comparing two variances. Analzying associations: association between categorical variables and between numerical variables. Statistical models: multiple regression, analysis of variance, analysis of covariance. Nonparametric statistics.

PREREQUISITE (basic requirements)

Basic Business Statistics, Thelfth edition. - FIRST SIX CHAPTERS
Berenson, D.M. Levine, T.C. Krehbiel (2005)
Prentice Hall.

EXTRACTS FROM THE FOLLOWING BOOKS

An introduction to Mathematical Statistics and Its Applications, Fifth edition
Larsen R.J., Marx M.L. (2012)
Prentice Hall
Introduction to Probability and Statistics for Engineers and Scientists, Fifth edition
Sheldon Ross (2014)
Academic Press
Regression models for categorical and limited dependent variables
J. Scott Long (2007)
Sage Pubblications
Basic Econonometrics, Fifth edition
Gujarati D.N., Porter D.C., Gunasekar S. (2015)

ADDITIONAL READINGS (EXTRACTS)

Discovering Statistics Using R
Field A., Miles J., Field Z. (2012)
Sage Pubblications
Econometrics by example
Gujarati D.N. (2015)
Palgrave

Diary of class

First term

Date	Topics
26/09/2016 - morning	LECTURE 1 Introduction to the class. Basic jargon: population vs sample, parameter vs statistic, exploratory analysis vs inferential analysis. units, variables and their types. Population probability model. Random variable (r.v.), expectation, variability, skewness. The Bernoulli probability model.
26/09/2016 - afternoon 27/09/2016 28/09/2016 29/09/2016 30/09/2016 - morning 30/09/2016 - afternoon 03/10/2016	SHORT COURSE ON R R transcript of the course Plots for the lectures of 30/09: 2D scatterplot - 3D scatterplot
04/10/2016	LECTURE 2 The binomial probability model. The binomial r.v. as sum of n independent Bernoulli r.v.s. Mean, variance and shape of the binomial distribution: the effect of the central limit theorem. The proportion of successes (r.v. relative frequency) as transformation of the binomial r.v. R commands to compute the binomial probabilities. The multinomial r.v. R commands for computing probabilities and plotting for the binomial model an hand-made R function for computing the binomial model
10/10/2016	LECTURE 3 Other special distributions: the hypergeometric distribution, the Poisson distribution, the geometric distribution, the negative binomial distribution.
11/10/2016	LECTURE 4 Relations among the binomial and the Poisson distributions. Special case of continuous r.v.: uniform distribution, negative exponential distribution and normal distribution. Transforming and combining random variables. Mean and variance of a linear transformation of a r.v. Mean and variance of a combination of random variables. The Normal distribution and the central limit theorem. Approximation of the binomial distribution through the normal law. R commands for graphically inspecting the central limit theorem (case of Uniform variables)
17/10/2016	LECTURE 5 The inference problem: parameteter space, sample space and space of the statistic. The problem of estimation. Sufficiency of a statistic. The likelihood function and the method of maximum likelihood (MLE). The likelihood function for the Bernoulli model. R commands for Bernoulli likelihood and log-likelihood function
18/10/2016	LECTURE 6 Likelihood and log-likelihood. Relative likelihood. The maximum likelihood estimation and the Fisher information criteria. The log-likelihood function for the Bernoulli model: derivation of the MLE and of the Fisher information criteria.
24/10/2016	LECTURE 7 Likelihood, log-likelihood and Fisher observed information for the normal model: estimation of the mean (variance unknown), estimation of the variance (mean unknown), joint estimation of the two parameters (profile likelihood and conditional likelihood). R commands for normal likelihood and log-likelihood function: estimation of the mean (variance as nuisance parameter) R commands for normal likelihood and log-likelihood function: estimation of the variance (mean as nuisance parameter) R commands for normal likelihood and log-likelihood function: joint estimation of the mean and of the variance
25/10/2016	LECTURE 8 Taylor series. Quadratic approximation of the likelihood function: the role of the maximum likelihood estimate and of Fisher information for regular probabilistic models. R commands for graphically inspecting the Taylor series: case of the square function and of the exponential function R commands for graphically inspecting the Taylor series: case of the sin function (solution to an exercise of homework #6)
07/10/2016	LECTURE 9 Element of frequentist inference: properties of estimators. Frequentist properties of the likelihood.
08/10/2016	LECTURE 10 The sampling distributions for the main statistics: inference on the mean (case of known and unknown variance), inference on variance, inference on proportion.
14/11/2016	LECTURE 11 Resampling methods: the bootstrap method for deriving the approximate sampling distribution of a statistic. Point estimate and interval estimate. Confidence interval for the mean (case of known and unknown variance), inference on variance, inference on proportion.
15/11/2016	LECTURE 12 Confidence interval for the variance of a normal population. Bootstrap confidence intervals: the percentile method. Introduction to hypothesis testing: type of hypothesis, the spaces involved, the decision rule, the two type of errors, test statistic.
21/11/2016	LECTURE 13 Hypothesis tests for one sample problems.
22/11/2016	LECTURE 14 Inferences on two samples: comparing means, variances and proportions.

Second term

Lezione del:	Argomenti trattati
09/01/2017	LECTURE 15 Anova.
10/01/2017	LECTURE 16 The simple linear regression model: the problem of estimation.
16/01/2017	LECTURE 17 The simple linear regression model: the problem of inference.
17/01/2017	LECTURE 18 The simple linear regression model: the problem of prediction.
23/01/2017	LECTURE 19 The multiple linear regression model.
24/01/2017	LECTURE 20 The multiple linear regression model: use of a dummy regressor.
30/01/2017	LECTURE 21 The multiple linear regression model: use of a nominal/ordinal regressor.
31/01/2017	LECTURE 22 A regression model with a dummy response variable: the linear probability model.
06/02/2017	LECTURE 23 A regression model with a dummy response variable: the logit and the probit model.
07/02/2017	LECTURE 24 Regression model for nominal response.
13/02/2017	LECTURE 25 Regression model for ordinal response.
14/02/2017	LECTURE 26 Regression model for count data: the Poisson regression model.
20/02/2017	LECTURE 27 Regression model for count data: the negative binomial regression model.
21/02/2017	LECTURE 28
27/02/2017	LECTURE 29
28/02/2017	LECTURE 30
06/03/2017	LECTURE 31
07/03/2017	LECTURE 32

Homeworks

First term

Homework n. 1 (lecture of 26/9) - to do before 04/10

Readings (Berenson & al.):
- study chapter 1, chapter 2, chapter 3, chapter 4
- study the R transcript of R short course (available in the Lectures section)

Homework related to the R class (lectures of 26/9, 27/9, 28/9, 29/9, 30/9, 03/10)

Readings:
- Read the Introduction to RStudio (Data & Statistical Services, Princeton University)

Homework n. 3 (lecture of 04/10) - due on 05/10

Readings (Berenson & al.):
- Study chapter 5: sections 5.1, 5.2 (not covered during the lecture) and 5.3
- Study Multinomial distribution:
 * wikipedia link, link to the online multimedia course (Rice University),
 * multinomial coefficient¹, multinomial distribution¹
 ¹An introduction to Mathematical Statistics and its Application, Larsen and Marx, Prentice Hall

Homework n. 4 (lectures of 10/10 and 11/10) - due on 17/10

Readings:
- Study chapter 5: sections 5.4, 5.5, 5.6
- Study chapter 6: sections 6.1, 6.2, 6.3 (not covered during the lecture), 6.4, 6.5, 6.6 (partially covered during the lecture)
 * geometric distribution¹, negative binomial distribution¹
 ¹An introduction to Mathematical Statistics and its Application, Larsen and Marx, Prentice Hall

Homework n. 5 (lectures of 17/10 and 18/10) - due on 24/10

Readings:
- Study chapter 7
* Maximum likelihood estimators¹
 ¹Introduction to Probability and Statistics for Engineerings and Scientists, Sheldon Ross, Academic Press

Homework n. 6 (lectures of 24/10 and 25/10) - due on 07/11

Readings:
- Study (again and in detail) the chapter on Maximum likelihood estimators (see homework #5)
- Study Taylor series: Wikipedia link
* Quadratic approximation of the log-likelihood function¹* Score function and Fisher information¹
 ¹Applied Statistics and Inference, Held and Sabanés Bové, Springer

Homework n. 7 (lectures of 07/11 and 08/11) - due on 14/11

Readings:
- Study chapter 7
- Study chapter 12: section 12.5

Homework n. 8 (lectures of 14/11 and 15/11) - due on 21/11

Readings:
* Bootstrap methods (not considering the Matlab code)¹
- Study chapter 8
- Study chapter 9: section 9.1
¹Computational Statistics Handbook with Matlab, Martinez and Martinez, Chapman and Hall/CRC

Homework n. 9 (lectures of 21/11 and 22/11) - to discuss during office hours

Readings:
- Study chapter 9: sections 9.2, 9.3, 9.4, 9.5 and 9.6 (on-line topic)
- Study chapter 10
- Study chapter 12: section 12.5

Second term

Homework n. 10 (lectures of 09/01 and 10/01) - due on 16/01

Readings (Gujarati and Porter):
- Chapters 1 and 2

Homework n. 11 (lectures of 16/01 and 17/01) - due on 23/01

Readings (Gujarati and Porter):
- Chapter 3

Homework n. 12 (lectures of 23/01 and 24/01) - due on 30/01

Readings (Gujarati and Porter):
- Chapter 4
- download here the dataset for the exercise: Grade Point Average, using the command:
 gpa <- read.table("http://domenicovistocco.it/teachingMaterials/busStats/datasets/grade_point_data.txt")

Homework n. 13 (lectures of 30/01 and 31/02) - due on 06/02

Readings (Gujarati and Porter):
- Chapter 5
- download here the dataset for the exercise: Grade Point Average, using the command:
 gpa <- read.table("http://domenicovistocco.it/teachingMaterials/busStats/datasets/grade_point_data.txt")

Homework n. 14 (lectures of 06/02 and 07/02) - due on 13/02

Readings (Gujarati and Porter):
- Study again chapters 1, 2, 3, 4 and 5
- Study chapter 6: sections 2 and 3

Homework n. 15 (lectures of 13/02 and 14/02) - due on 20/02

Readings (Gujarati and Porter):
- Chapter 7 and 8
- download here the dataset for the exercise: Brand Preference, using the command:
 brand <- read.table("http://domenicovistocco.it/teachingMaterials/busStats/datasets/brand_preference.txt", header = TRUE)

Homework n. 16 (lectures of 20/02 and 21/02) - due on 27/2

Readings:
- Chapter 9

Homework n. 17 (lectures of 27/02 and 28/02) - due on 06/03

Readings:
- Chapter 15

Homework n. 18 (lectures of 06/03 and 07/03) - to discuss during office hours

Readings:
- Chapter 15

Student ID	Student	Mark	Oral timetable (4-th October)
0047951	Boateng Owsu Ose	16	3:00 p.m.
0047963	Dao Khanh Ly	17	3:00 p.m.
0047968	Do Hong Duong	17	3:00 p.m.
0006975	Grossi Fabiola	Failed	---

Statistics for Economics and Business