## BUSINESS STATISTICS

## Syllabus

### Obiettivi Formativi

Il corso di Metodi Statistici per il Management fornisce allo studente un'introduzione alla modellizzazione delle variabili economiche e gestionali utilizzando metodi di regressione e tecniche multivariate, sia parametriche che non parametriche; l'accento è posto sulle applicazioni commerciali, di marketing e industriali (ad es. controllo della qualità, analisi delle vendite, customer satisfaction, analisi di mercato). Il programma riguarda i modelli di supervised statistical learning correntemente utilizzati per l'analisi della dipendenza (regressione lineare, ANOVA, modello autoregressivo, modelli logit e probit) e le tecniche di unsupervised statistical learning utilizzate per l’esplorazione e la riduzione dei dati (analisi in componenti principali e analisi dei gruppi).

CONOSCENZA E CAPACITÀ DI COMPRENSIONE:

Conoscenza e comprensione di tecniche statistiche parametriche e non parametriche applicate a problemi di marketing, previsione delle vendite e problemi finanziari. Alla fine del corso gli studenti dovrebbero essere in grado di comprendere: (i) come applicare modelli statistici in un approccio supervisionato e non supervisionato; (ii) conoscere le assunzioni e saper formulare ipotesi in merito ad un modello insieme alla conoscenza/comprensione degli strumenti necessari per verificare queste ipotesi; (iii) comprendere le tecniche di selezione del modello e le misure della capacità di previsione del modello. In particolare, gli studenti sapranno dominare:

• Il Modello di regressione lineare

• Il Modello Logit e Probit

• L’Analisi della varianza (ANOVA)

• Il Modello autoregressivo AR (1)

• L’Analisi dei gruppi

• L’Analisi delle componenti principali

CAPACITÀ DI APPLICARE CONOSCENZA E COMPRENSIONE:

Attraverso esempi su insiemi di dati reali e l’utilizzo di software statistici come STATA e SAS, verranno mostrate diverse applicazioni dei concetti illustrati a lezione. Agli studenti verrà richiesto di esercitarsi, sia in classe sia a casa, applicando le metodologie statistiche a insiemi di dati e fornendo un commento e una interpretazione dei risultati ottenuti.

AUTONOMIA DI GIUDIZIO:

Gli studenti saranno in grado di scegliere le tecniche statistiche più appropriate e di selezionare il giusto set di variabili esplicative. Sulla base dei risultati ottenuti, saranno in grado di fornire un'interpretazione sulla relazione tra le variabili oggetto di studio. Gli studenti aumenteranno la capacità di analizzare in modo critico e oggettivo situazioni concrete, fenomeni reali e casi di studio.

ABILITÀ COMUNICATIVE:

Gli studenti saranno in grado di preparare report statistici utilizzando grafici, tabelle, figure e più in generale output di software statistico e di corredarli con commenti appropriati.

CAPACITÀ DI APPRENDIMENTO:

Gli studenti potranno accedere alla lettura e alla comprensione di articoli scientifici che utilizzano i metodi multivariati considerati nel programma del corso. Saranno in grado di individuare i metodi più appropriati per rispondere a delle specifiche domande di ricerca.

### 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:

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

APPLYING KNOWLEDGE AND UNDERSTANDING:

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.

MAKING JUDGEMENTS:

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.

COMMUNICATION SKILLS:

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

LEARNING SKILLS:

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.

### Prerequisiti

### Prerequisites

### Programma

Modello di regressione lineare

• Introduzione al Modello Statistico

• Modello di regressione lineare

• Stima dei parametri e bontà di adattamento

• Strumenti diagnostici basati sui residui

• Applicazioni ed esempi con Stata/SAS

Lezione 3-4

Modello di regressione lineare multipla

• Algebra matriciale per la regressione lineare

• Stima dei coefficienti di regressione

• Inferenza sui parametri del modello

• Strumenti diagnostici basati sui residui

• Multicollinearità e indice VIF

• Selezione delle variabili: Backward, forward, stepwise

• Applicazioni ed esempi con Stata/SAS

Lezione 5

Analisi della Varianza

• Definizione

• Stima degli effetti

• Applicazioni ed esempi con Stata/SAS

Lezione 6

• Introduzione ai metodi di Associazione

• Analisi in Componenti Principali (ACP): Introduzione e motivazione (riduzione del numero di variabili, combinazione lineare delle variabili)

• ACP: Introduzione del metodo (autovalori e autovettori, loadings, scores)

Lezione 7

• Metodi grafici (Biplots)

• ACP: Applicazioni ed esempi con Stata/SAS

Lezione 8

• Analisi dei Gruppi: Introduzione, Partizione dei gruppi: K-medie

• Analisi dei Gruppi: Applicazioni ed esempi con Stata/SAS

Lezione 9

• Metodi di raggruppamento gerarchico agglomerativi (legame singolo, legame completo, legame medio)

• Valutazione dei gruppi (non supervisionato, supervisionato, relativo)

• Analisi dei Gruppi: Applicazioni ed esempi con Stata/SAS

Lezione 10

Logit e Probit

• Modello statistico

• Stima dei parametri e bontà di adattamento

Comparazione tra modelli: indici AIC e BIC

• Matrice di classificazione

• Curva ROC

Lezione 11

Previsione

• Modello Autoregressiovo di lag 1

• Stima dei parametri e inferenza

Lezione 12

• Applications with SAS su dati reali

### Program

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

Forecasting

• Autoregressive model

• Estimation and inference

Lecture 12

• Applications with SAS on real data sets

### Testi Adottati

• 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

### Books

- 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

### Modalità di svolgimento

Per valutare la propria preparazione sono presenti sul sito test di autovalutazione ed esempi di esame. Al termine ddel LAB sarà svolta una prova finale facoltativa che permetterà di ottenere fino a 2 punti da aggiungere al voto del test finale.

### Teaching methods

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.

### Regolamento Esame

### Exam Rules

### Updated A.Y. 2021-2022

### Updated A.Y. 2021-2022

**Overview**

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).

**Pre-requisites**

Basic knowledge of descriptive statistics, elements of probability, random variables and statistical inference.

Learning objectives

** Knowledge and understanding**

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

** Applying Knowledge and Understanding**

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.

** Making Judgements**

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.

** Communication Skills**

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

** Learning Skills**

Analyzing in a critical way concrete situations and case studies, working in team and comply with mandatory deadlines.

**Program a.y. 2021-2022**

**Lecture 1-2**

linear regression model

- Statistical model
- Linear regression model
- Estimation and goodness of fit
- Diagnostics for residuals
- Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

- matrix approach to linear regression
- Estimation of regression coefficient
- Inferences about regression parameters
- Diagnostics for residuals
- Multicollinearity
- Model Selection
- 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 vectors, 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
- Estimation and goodness of fit
- Classification matrix
- ROC curve

**Lecture 11**

Forecasting

- Autoregressive model
- Estimation and inference

**Lecture 12**

- Applications with SAS on real data sets

**Teaching methods**

Classroom teaching, exercises, discussion of case studies, 12 hours of practical exercising by using statistical software.

**References**

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

- M. Mazzocchi, Statistics for Marketing and Consumer Research, 2008, Sage (chapters: 7.1, 7.3, 8, 10.3.1, 10.3.2, 10.4.2, 12.1, 12.2.1, 12.2.2, 12.2.3, 12.2.4, 12.2.5, 12.2.6, 12.3.2)

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2019-2020

**Overview**

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).

**Pre-requisites**

Basic knowledge of descriptive statistics, elements of probability, random variables and statistical inference.

Learning objectives

** Knowledge and understanding**

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

** Applying Knowledge and Understanding**

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.

** Making Judgements**

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.

** Communication Skills**

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

** Learning Skills**

Analyzing in a critical way concrete situations and case studies, working in team and comply with mandatory deadlines.

**Program a.y. 2019-2020**

**Lecture 1-2**

linear regression model

- Statistical model
- Linear regression model
- Estimation and goodness of fit
- Diagnostics for residuals
- Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

- matrix approach to linear regression
- Estimation of regression coefficient
- Inferences about regression parameters
- Diagnostics for residuals
- Multicollinearity
- Model Selection
- 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 vectors, 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
- Estimation and goodness of fit
- Classification matrix
- ROC curve

**Lecture 11**

Forecasting

- Autoregressive model
- Estimation and inference

**Lecture 12**

- Applications with SAS on real data sets

**Teaching methods**

Classroom teaching, exercises, discussion of case studies, 12 hours of practical exercising by using statistical software.

**References**

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

- M. Mazzocchi, Statistics for Marketing and Consumer Research, 2008, Sage (chapters: 7.1, 7.3, 8, 10.3.1, 10.3.2, 10.4.2, 12.1, 12.2.1, 12.2.2, 12.2.3, 12.2.4, 12.2.5, 12.2.6, 12.3.2)

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2019-2020

**Overview**

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).

**Pre-requisites**

Basic knowledge of descriptive statistics, elements of probability, random variables and statistical inference.

Learning objectives

** Knowledge and understanding**

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

** Applying Knowledge and Understanding**

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.

** Making Judgements**

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.

** Communication Skills**

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

** Learning Skills**

Analyzing in a critical way concrete situations and case studies, working in team and comply with mandatory deadlines.

**Program a.y. 2019-2020**

**Lecture 1-2**

linear regression model

- Statistical model
- Linear regression model
- Estimation and goodness of fit
- Diagnostics for residuals
- Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

- matrix approach to linear regression
- Estimation of regression coefficient
- Inferences about regression parameters
- Diagnostics for residuals
- Multicollinearity
- Model Selection
- 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 vectors, 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
- Estimation and goodness of fit
- Classification matrix
- ROC curve

**Lecture 11**

Forecasting

- Autoregressive model
- Estimation and inference

**Lecture 12**

- Applications with SAS on real data sets

**Teaching methods**

Classroom teaching, exercises, discussion of case studies, 12 hours of practical exercising by using statistical software.

**References**

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

- M. Mazzocchi, Statistics for Marketing and Consumer Research, 2008, Sage (chapters: 7.1, 7.3, 8, 10.3.1, 10.3.2, 10.4.2, 12.1, 12.2.1, 12.2.2, 12.2.3, 12.2.4, 12.2.5, 12.2.6, 12.3.2)

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2018-2019

Overview

Pre-requisites

Learning objectives

Knowledge and understanding

· Linear regression model

· Logit and Probit model

· Analysis of Variance

· Autoregressive model AR(1)

· Cluster Analysis

· Principal Component Analysis

Applying Knowledge and Understanding

Making Judgements

Communication Skills

Learning Skills

Program

Lecture 1-2

linear regression model

· Statistical model

· Linear regression model

· Estimation and goodness of fit

· Diagnostics for residuals

· Applications and Examples with Stata/SAS

Lecture 3-4

Multiple linear regression model

· matrix approach to linear regression

· Estimation of regression coefficient

· Inferences about regression parameters

· Diagnostics for residuals

· Multicollinearity

· Model Selection

· 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 vectors, 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

· Estimation and goodness of fit

· Classification matrix

· ROC curve

Lecture 11

Forecasting

· Autoregressive model

· Estimation and inference

Lecture 12

· Applications with SAS on real data sets

Teaching methods

References

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

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2018-2019

Overview

Pre-requisites

Learning objectives

Knowledge and understanding

· Linear regression model

· Logit and Probit model

· Analysis of Variance

· Autoregressive model AR(1)

· Cluster Analysis

· Principal Component Analysis

Applying Knowledge and Understanding

Making Judgements

Communication Skills

Learning Skills

Program

Lecture 1-2

linear regression model

· Statistical model

· Linear regression model

· Estimation and goodness of fit

· Diagnostics for residuals

· Applications and Examples with Stata/SAS

Lecture 3-4

Multiple linear regression model

· matrix approach to linear regression

· Estimation of regression coefficient

· Inferences about regression parameters

· Diagnostics for residuals

· Multicollinearity

· Model Selection

· 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 vectors, 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

· Estimation and goodness of fit

· Classification matrix

· ROC curve

Lecture 11

Forecasting

· Autoregressive model

· Estimation and inference

Lecture 12

· Applications with SAS on real data sets

Teaching methods

References

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

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2017-2018

**Overview**

**Pre-requisites**

**Learning objectives**

** Knowledge and understanding**

· Linear regression model

· Logit and Probit model

· Analysis of Variance

· Autoregressive model AR(1)

· Cluster Analysis

· Principal Component Analysis

** Applying Knowledge and Understanding**

** Making Judgements**

** Communication Skills**

** Learning Skills**

**Program**

**Lecture 1-2**

linear regression model

· Statistical model

· Linear regression model

· Estimation and goodness of fit

· Diagnostics for residuals

· Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

· matrix approach to linear regression

· Estimation of regression coefficient

· Inferences about regression parameters

· Diagnostics for residuals

· Multicollinearity

· Model Selection

· 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 vectors, 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

· Estimation and goodness of fit

· Classification matrix

· ROC curve

**Lecture 11 **

Forecasting

· Autoregressive model

· Estimation and inference

**Lecture 12 **

· Applications with SAS on real data sets

**Teaching methods**

**References**

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

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2017-2018

**Overview**

**Pre-requisites**

**Learning objectives**

** Knowledge and understanding**

· Linear regression model

· Logit and Probit model

· Analysis of Variance

· Autoregressive model AR(1)

· Cluster Analysis

· Principal Component Analysis

** Applying Knowledge and Understanding**

** Making Judgements**

** Communication Skills**

** Learning Skills**

**Program**

**Lecture 1-2**

linear regression model

· Statistical model

· Linear regression model

· Estimation and goodness of fit

· Diagnostics for residuals

· Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

· matrix approach to linear regression

· Estimation of regression coefficient

· Inferences about regression parameters

· Diagnostics for residuals

· Multicollinearity

· Model Selection

· 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

· PCA: Presentation of Method (eigenvalues and vectors, 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

· Estimation and goodness of fit

· Classification matrix

· ROC curve

**Lecture 11**

Forecasting

· Autoregressive model

· Estimation and inference

**Lecture 12**

· Applications with SAS on real data sets

**Teaching methods**

Classroom teaching, exercises, discussion of case studies, 6 hours of practical exercising by using statistical software.

**References**

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

- Press M. Mann, Introductory Statistics, 2010, Wiley, (chapters: 12, 13, 14)

### Updated A.Y. 2016-2017

**Overview**

**Pre-requisites**

**Learning objectives**

** Knowledge and understanding**

· Linear regression model

· Logit and Probit model

· Analysis of Variance

· Autoregressive model AR(1)

· Cluster Analysis

· Principal Component Analysis

** Applying Knowledge and Understanding**

** Making Judgements**

** Communication Skills**

** Learning Skills**

**Program**

**Lecture 1-2**

linear regression model

· Statistical model

· Linear regression model

· Estimation and goodness of fit

· Diagnostics for residuals

· Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

· matrix approach to linear regression

· Estimation of regression coefficient

· Inferences about regression parameters

· Diagnostics for residuals

· Multicollinearity

· Model Selection

· 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

· PCA: Presentation of Method (eigenvalues and vectors, 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

· Estimation and goodness of fit

· Classification matrix

· ROC curve

**Lecture 11 **

Forecasting

· Autoregressive model

· Estimation and inference

**Lecture 12 **

· Applications with SAS on real data sets

**Teaching methods**

Classroom teaching, exercises, discussion of case studies, 6 hours of practical exercising by using statistical software.

**References**

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

### Updated A.Y. 2016-2017

**Overview**

**Pre-requisites**

**Learning objectives**

** Knowledge and understanding**

· Linear regression model

· Logit and Probit model

· Analysis of Variance

· Autoregressive model AR(1)

· Cluster Analysis

· Principal Component Analysis

** Applying Knowledge and Understanding**

** Making Judgements**

** Communication Skills**

** Learning Skills**

**Program**

**Lecture 1-2**

linear regression model

· Statistical model

· Linear regression model

· Estimation and goodness of fit

· Diagnostics for residuals

· Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

· matrix approach to linear regression

· Estimation of regression coefficient

· Inferences about regression parameters

· Diagnostics for residuals

· Multicollinearity

· Model Selection

· 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

· PCA: Presentation of Method (eigenvalues and vectors, 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

· Estimation and goodness of fit

· Classification matrix

· ROC curve

**Lecture 11**

Forecasting

· Autoregressive model

· Estimation and inference

**Lecture 12**

· Applications with SAS on real data sets

**Teaching methods**

Classroom teaching, exercises, discussion of case studies, 6 hours of practical exercising by using statistical software.

**References**

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

### Updated A.Y. 2015-2016

**Lecture 1-2**

linear regression model

- Statistical model
- Linear regression model
- Estimation and goodness of fit
- Diagnostics for residuals
- Applications and Examples with Stata/SAS

Lecture 3-4

Multiple linear regression model

- matrix approach to linear regression
- Estimation of regression coefficient
- Inferences about regression parameters
- Diagnostics for residuals
- Multicollinearity
- Model Selection
- 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
- PCA: Presentation of Method (eigenvalues and vectors, 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
- Estimation and goodness of fit
- Classification matrix
- ROC curve

Lecture 11

Forecasting

- Autoregressive model
- Estimation and inference

Lecture 12

- Applications with SAS on real data sets

Textbook:

J. Neter, M. Kutner, C. Nachtsheim, W. Wasserman, 1996, Applied Linear Regression Models, Irwin

J. Lattin, J. Carroll, P. Green, 2003, Analyzing Multivariate Data, Thomson

### Updated A.Y. 2015-2016

**Lecture 1-2**

linear regression model

- Statistical model
- Linear regression model
- Estimation and goodness of fit
- Diagnostics for residuals
- Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

- matrix approach to linear regression
- Estimation of regression coefficient
- Inferences about regression parameters
- Diagnostics for residuals
- Multicollinearity
- Model Selection
- 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
- PCA: Presentation of Method (eigenvalues and vectors, 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
- Estimation and goodness of fit
- Classification matrix
- ROC curve

**Lecture 11**

Forecasting

- Autoregressive model
- Estimation and inference

**Lecture 12**

- Applications with SAS on real data sets

Textbook:

J. Neter, M. Kutner, C. Nachtsheim, W. Wasserman, 1996, Applied Linear Regression Models, Irwin

J. Lattin, J. Carroll, P. Green, 2003, Analyzing Multivariate Data, Thomson

### Updated A.Y. 2014-2015

### Updated A.Y. 2014-2015

**BUSINESS STATISTICS (a.y. 2014/2015)**

(Prof. Simone Borra)

**TEACHING STAFF RESPONSIBLE FOR THE COURSE:**

Simone Borra

Lessons: Monday-Tuesday-Wednesday 14.00-16.00

Laboratory: Thursday 14-16; sometimes Friday 11-13

Office: Room SB5, 3rd floor, Building B

Telephone: 06.72595943

E-mail: borra@economia.uniroma2.it

Office hours: Monday 4-6 pm

**PRE-REQUISITES FOR THE COURSE:**

Basic knowledge of descriptive statistics, elements of probability, random variables and statistical inference.

**LEARNING OBJECTIVES**

The course provides an introduction to modelling economic and management variables using regression and multivariate methods, both in a parametric and a nonparametric framework, with an emphasis on applications in business, marketing and industry. In particular, in the course are presented models for the analysis of dependence (linear regression, ANOVA, autoregressive model, logit and probit model,) and exploratory techniques for data reduction (principal component analysis and clustering analysis).

**TEACHING METHODS**

Lectures

**REFERENCE TEXTBOOK**

J. Neter, M. Kutner, C. Nachtsheim, W. Wasserman, 1996, Applied Linear Regression Models, Irwin

J. Lattin, J. Carroll, P. Green, 2003, Analyzing Multivariate Data, Thomson

**OTHER LEARNING SOURCES**

Slides and other material will be available on the course website. Demonstration of statistical software and use of software to analyse datasets.

**EXAM**

The final exam is a one and half hours written exam. The final exam will be a test with multiple-choice questions and open questions. The exam can only be taken once in each exam session. The score is expressed in thirties (you need at least 18 to pass the exam). Facultative: A report describing a statistical analysis using SAS on a specific dataset. With the report, you may add until 2 points to the score of the final exam.

**PRE-COURSE**

**Lecture 1**

Introduction to Probability, Random Variables, Expectation and Variance operators

**Lecture 2**

The Normal distribution, Bivariate Random Variables, Marginal and Conditional Distributions, Independence of Random Variables, Covariance operator

**Lecture 3**

Sampling distributions, Confidence interval, Hypothesis testing

**ANALYTICAL SYLLABUS**

**Lecture 1-2**

linear regression model

• Statistical model

• Linear regression model

• Estimation and goodness of fit

• Diagnostics for residuals

• Applications and Examples with Stata/SAS

**Lecture 3-4**

Multiple linear regression model

• matrix approach to linear regression

• Estimation of regression coefficient

• Inferences about regression parameters

• Diagnostics for residuals

• Multicollinearity

• Model Selection

• 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 vectors, 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

• Estimation and goodness of fit

• Classification matrix

• ROC curve

**Lecture 11**

Forecasting

• Autoregressive model

• Estimation and inference

**Lecture 12**

• Applications with SAS on real data sets