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Learning Objectives

The course provides an introduction to the modelling of economic and management variables using regression and multivariate methods, both in a parametric than a nonparametric framework; the emphasis is on business, marketing and industrial applications. The program will cover models for the analysis of dependence (linear regression, ANOVA, autoregressive model, logit and probit models) and exploratory techniques for data reduction (principal component analysis and clustering analysis).

Knowledge and understanding of parametric and nonparametric statistical techniques applied to marketing, sales and financial problems. At the end of the course students should be able to understand: (i) how to apply statistical models in a supervised and unsupervised approach; (ii) perfectly know the model’s assumptions and understanding of the tools needed to verify these hypotheses; (iii) understand the model selection techniques and measures of the model prediction capability. In particular, students will manage:
• Linear regression model
• Logit and Probit model
• Analysis of Variance
• Autoregressive model AR(1)
• Cluster Analysis
• Principal Component Analysis

Practical evidence of the concepts will be given with examples using statistical software such as STATA and SAS applied on real datasets. The students will have to practice both in class that with homeworks on the use of specific software so to be able to comment and understand the output.

Students will be able to choose the more appropriate statistical techniques and to select the right set of explanatory variables. On the basis of results obtained, they will be able to give an interpretation about the relationship between the variables under study.

Students will be able to prepare statistical reports using graphs, tables, figures and commenting them.

Students will have access to reading and understanding scientific articles using the multivariate methods considered in the course program. They will be able to identify the most appropriate methods to answer specific research questions.


Basic knowledge of descriptive statistics, elements of probability, random variables (Probability density function, Cumulative density function, expected value and variance) and statistical inference (point estimation, properties of estimators, estimation methods, statistical test, confidence interval).


Lecture 1-2
linear regression model
• Statistical model
• Linear regression model
• Parameters estimation and measure of goodness of fit
• Diagnostic tools based on residuals
• Applications and Examples with Stata/SAS
Lecture 3-4
Multiple linear regression model
• matrix approach to linear regression
• Estimation of regression coefficients
• Inferences about regression parameters
• Diagnostic tools based on residuals
• Multicollinearity and VIF index
• Variables Selection methods: Backward, forward, stepwise
• Applications and Examples with Stata/SAS
Lecture 5
Analysis of Variance
• Definition
• Effects Estimation
• Applications and Examples with Stata/SAS
Lecture 6
• Introduction to Multivariate Statistics
• Principal components Analysis (PCA): Introduction and Motivation (Data dimension reduction, linear combination of variables)
• PCA: Presentation of Method (eigenvalues and eigenvectors, loadings, scores)
Lecture 7
• Graphical Methods (Biplots)
• PCA: Applications and Examples with Stata/SAS
Lecture 8
• Cluster Analysis: Overview, Partitional clustering: K-means
• Cluster Analysis: Applications and Examples with Stata/SAS
Lecture 9
• Agglomerative Hierarchical clustering (single linkage, complete linkage, group average)
• Cluster evaluation (unsupervised, supervised, relative)
• Cluster Analysis: Applications and Examples with Stata/SAS
Lecture 10
Logit and probit
• Statistical model
Assesment method: AIC and BIC
• Estimation and goodness of fit
• Classification matrix
• ROC curve
Lecture 11
• Autoregressive model
• Estimation and inference
Lecture 12
• Applications with SAS on real data sets


Slides and other teaching material will be available on the course website.
- J. Neter, M. Kutner, C. Nachtsheim, W. Wasserman, 1996, Applied Linear Regression Models, Irwi
- J. Lattin, J. Carroll, P. Green, 2003, Analyzing Multivariate Data, Thomson

Teaching methods

Classroom teaching, exercises, discussion of case studies, 6 hours of practical exercising by using statistical software (LAB). Examples of applications are shown using STATA and SAS statistical software. Students can replicate the examples at home using the free SAS University Edition software and download numerous datasets from the course website.
To check the preparation, the course of self-assessment texts and exam simulations can be downloaded from the website. At the end of the LAB, an optional final test will be held which will allow to obtain up to 2 points to be added to the final test grade.

Exam Rules

The preparation will be verified through a final exam consisting of a test with multiple-choice and open-ended questions. The final exam is a 1 hour written exam. It will be a test with multiple-choice questions and open-ended questions. The questions will mainly focus on the hypotheses underlying the statistical models, on the interpretation of the outputs, on the properties of some statistical indexes. For each question with a closed answer it will be given as a score 1 if correct, 0 if incorrect; each open question will be given a score between 0 and 2; the final evaluation will be proportionally reported in thirtieths.