Multivariate Statistics

Code:

M.EGI001

Acronym:

EM

Keywords
Classification	Keyword
OFICIAL	Statistic and Operational Research

Instance: 2023/2024 - 1S

Active?	Yes
Responsible unit:	Department of Industrial Engineering and Management
Course/CS Responsible:	Master in Industrial Engineering and Management

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M.EGI	74	Syllabus	1	-	6	45,5	162

Teaching language

English

Objectives

To allow students to deepen their knowledge about the statistical method at a multivariate level. At the end of the course, students should be able to use the methods and techniques studied critically and autonomously when making decisions.

Learning outcomes and competences

At the end of this course unit students should be able to:

• perform analysis of variance;
• design simple experiments;
• perform regression analysis;
• perform principal components analysis and exploratory factor analysis;
• perform multivariate analysis of variance;
• use spreadsheets and statistical packages to apply the above mentioned techniques.

 

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Knowledge about the statistical method, namely: descriptive statistic and statical inference.

Program

• INTRODUCTION: Introduction to Multivariate Statistics..


• ANALYSIS OF VARIANCE (ANOVA): Introduction. One-Way ANOVA Model (Fixed and Random Effects, Multiple Comparisons). Two-Way ANOVA Model (Fixed and Random Effects, Interation between Factors, Constrasts). Extension to Additional Factors. ANOVA Assumptions.


• DESIGN OF EXPERIMENTS: Introduction to the Design of Experiments. Randomization and Replication. Two Level Factorial Designs (Full and Fractional).


• REGRESSION: Introduction. Simple and Multiple Linear Regression (Parameters Estimation, Inference about Parameters, Predictors Slection, Forecasts based on the Simple and Multiple Linear Regression Model, Qualitative Predictor, Collinearity). Assumptions and Residual Analysis. Linear Regression with variable Tansformations.


• PRINCIPAL COMPONENTS ANALYSIS AND EXPLORATORY FACTORIAL ANALYSIS: Factors and Principal Components (Graphical and Mathematical Representations). Principal Components Analysis. Exploratory Factorial Analysis. Factors e Principal Components Extraction (Eigenvalues and Scree Plot). Rotating Factors and Principal Components. Interpretation.


• MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA): Theory and Application. Assumptions. "Follow-up" Analysis. Interpretation.

Mandatory literature

Joseph F. Hair, Jr., ... [et al.]; Multivariate data analysis. ISBN: 978-0-13-515309-3
Armando Leitão; Nonparametric tests, Analysis of Variance, Factorial Experimentation (Notes available in Moodle)
David Diez, Mine Çetinkaya-Rundel, Christopher Barr; OpenIntro Statistics, OpenIntro, 2022 ((https://leanpub.com/os))

Complementary Bibliography

Douglas C. Montgomery, George C. Runger; Applied Statistics and Probability for Engineers, Wiley, 2014. ISBN: 978-1-118-74412-3
Andy Field; Discovering Statistics using IBM SPSS Statistics, SAGE, 2013. ISBN: 978-1446249178
Rui Campos Guimarães, José A. Sarsfield Cabral; Estatística. ISBN: 978-989-642-108-3

Teaching methods and learning activities

Concepts and techniques are introduced using systematically practical examples. The learning process is complemented with problem solving sessions supported by computer software and teamwork assignment.

Software

Folhas de Cálculo
SPSS
python

keywords

Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	70,00
Teste	30,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Elaboração de projeto	30,00
Estudo autónomo	86,50
Frequência das aulas	45,50
Total:	162,00

Eligibility for exams

To obtain attendance in the course, students must obtain a minimum mark of 7 (out of 20) in the distributed assessment component (intermediate tests).

In addition to the above requirement, students must comply with FEUP's general assessment rules in order to obtain attendance in the course.

Calculation formula of final grade

The final mark (CF) will be obtained by the following formula:

           CF = Maximum( 0.30 AD + 0.70 EF; EF )

AD - Distributed Assessment:

          AD = 0.5 x TI1 + 0.5 x TI2

TI1, TI2 - Quizzes
EF - Final Exam

To pass this course, apart from a final grade no less than 10, is required a minimum grade of 7 in the final exam.

Special assessment (TE, DA, ...)

Written exam.

Classification improvement

Students can choose between:

• overall improvement (exam + distributed assessment) by a two-part written appeal exam;


• improving only the exam component with a one-part appeal exam.