Multivariate Statistics
Keywords |
Classification |
Keyword |
OFICIAL |
Quantitative Methods |
Instance: 2020/2021 - 2S
Cycles of Study/Courses
Acronym |
No. of Students |
Study Plan |
Curricular Years |
Credits UCN |
Credits ECTS |
Contact hours |
Total Time |
MIEGI |
100 |
Syllabus since 2006/2007 |
2 |
- |
6 |
56 |
162 |
Teaching language
Suitable for English-speaking students
Objectives
The aim of the courses Statistics and Multivariate Statistics is to endow students with an integrated vision of the basic concepts and statistic techniques frequently applied. At the end of these courses, students should be able to use methods of statistic analysis autonomously in statistical decision making.
Learning outcomes and competences
At the end of this course unit students should be able to:
- perform regression analysis;
- perform analysis of variance;
- design simple experiments;
- perform multivariate analysis of variance;
- perform exploratory factor analysis;
- use spreadsheets and statistical packages to apply the above mentioned techniques.
Working method
Presencial
Pre-requirements (prior knowledge) and co-requirements (common knowledge)
Basic spreadsheets skills and matrix calculus.
EIG0072: All topics.
Program
- INTRODUCTION: Introduction to Multivariate Statistics. Statististics and Graphical Representations for Multivariare data.
- 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).
- 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.
- 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.
- MULTIVARIATE ANALYSIS OF VARIANCE (MANOVA): Theory and Application. Assumptions. "Follow-up" Analysis. Interpretation.
Mandatory literature
Rui Campos Guimarães, José A. Sarsfield Cabral;
Estatística. ISBN: 978-989-642-108-3
Joseph F. Hair, Jr., ... [et al.];
Multivariate data analysis. ISBN: 978-0-13-515309-3
Armando Leitão; Factorial Experimentation (Notes available in Moodle)
Complementary Bibliography
Douglas C. Montgomery, George C. Runger;
Applied Statistics and Probability for Engineers, Wiley, 2014. ISBN: 978-1-118-74412-3
S. Christian Albright, Wayne L. Winston; Business Analytics: Data Analysis and Decision Making, College Bookstore, 2011. ISBN: 9781133629603
Andy Field;
Discovering Statistics using IBM SPSS Statistics, SAGE, 2013. ISBN: 978-1446249178
Teaching methods and learning activities
The methods and techniques are introduced using systematically practical examples. The learning process is complemented with problem solving sessions supported by computer software and teamwork assignments.
Software
SPSS
Folhas de Cálculo
keywords
Physical sciences > Mathematics > Statistics
Evaluation Type
Distributed evaluation with final exam
Assessment Components
Designation |
Weight (%) |
Exame |
70,00 |
Trabalho prático ou de projeto |
15,00 |
Teste |
15,00 |
Total: |
100,00 |
Amount of time allocated to each course unit
Designation |
Time (hours) |
Elaboração de projeto |
50,00 |
Estudo autónomo |
56,00 |
Frequência das aulas |
56,00 |
Total: |
162,00 |
Eligibility for exams
Admission criteria set according to Article 4 of General Evaluation Rules of FEUP.
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 MT + 0.5 x TG
MT - Quizz (in person)
TG - Teamwork Assignment
EF - Final Exam (openbook)
To pass this course, apart from a final grade no less than 10, is required a minimum grade of 7 in the final exam.