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Multivariate Statistical Methods for Engineering and. Management – MEGI 2nd Sem. 12/13. General Information. • Schedule: – Theoretical — Wednesday ...

Multivariate Statistical Methods for Engineering and Management – MEGI 2nd Sem. 12/13 General Information • Schedule: – Theoretical — Wednesday, 15h30–17h00 (0.25); Thursday, 15h00–16h30 (0.25). – Laboratory/Practicals — Thursday, 16h30–18h00 (0.14). • Faculty: — Ana Maria Pires • Contacts: — [email protected]; Alameda: 21-8417053 or Ext.1053; Tagus: 21-4233233 or Ext. 5033 Room: 2-N4.12 • Website — https://fenix.ist.utl.pt/disciplinas/memeg4/2012-2013/2-semestre

Classes • Begining: — 13 February 2011.

Syllabus 1. Introduction to Multivariate Analysis 1.1. Overview of multivariate methods and main objectives. 1.2. Some definitions and notation. 1.3. Exploratory analysis: descriptive methods and graphical displays for multivariate data. 2. Regression Analysis 2.1. Multiple linear regression. 2.2. Least squares estimation of the parameters. 2.3. Properties of the estimators. 1

2.4. Tests and confidence intervals for the parameters. 2.5. Prediction. Model adequacy checking. 2.6. Selection of variables and model building. 3. Design of Experiments and Analysis of Variance 3.1. Completely randomized experiment. 3.2. Single-factor analysis of variance, (one-way ANOVA). 3.3. Multiple comparisons. 3.4. Two-factors analysis of variance, (two-way ANOVA). 3.5. Completely Randomized block design. 3.6. Multiple analysis of variance (MANOVA). 4. Principal Component Analysis 4.1. Introduction. 4.2. Definition and derivation of principal components. 4.3. Properties of principal components. 4.4. Geometric properties of principal components. 4.5. Sample principal components. 4.6. Applications of principal components. 4.7. Principal components in multiple linear regression. 5. Factor Analysis 5.1. Introduction. 5.2. Model formulation. 5.3. Estimation of the parameters. 5.4. Factor rotations. 5.5. Scores estimation. 5.6. Applications of factor analysis. 5.7. Factor analysis versus principal component analysis.

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6. Cluster Analysis and Multidimensional Scaling 6.1. Introduction. 6.2. Similarity measures. 6.3. Methods to obtain clusters. 6.3.1. Graphical and visual methods. 6.3.2. Hierarchical methods. 6.3.3. Non hierarchical methods. 6.4. Multidimensional Scaling

Bibliography • Recommended: – Sharma, S. (1996). Applied Multivariate Techniques. John Wiley, New York. – Montgomery, D.C. and Runger, G.C. (2002). Applied Statistics and Probability for Engineers. 3rd edition, John Wiley, New York. • Optional: – Branco, J. A. (2004). Uma Introdu¸c˜ao `a An´alise de Clusters. Sociedade Portuguesa de Estat´ıstica. – Johnson, R. A. and Wichern, D. W. (2002). Applied Multivariate Statistical Analysis. 5th edition, Prentice-Hall, Inc., New York. – Latin, J., Carroll, J. D. and Green, P. E. (2003). Analyzing Multivatiate Data. Thomson, Books/Cole, Ontario. – Rencher, A. C. Methods of Multivariate Analysis. 2nd edition, Wiley, New York. – Trevor C. (2005). An Introduction to Multivariate Data Analysis. Hodder Arnold, London. – Wonnacott, T. H. and Wonnacott, R. J. (1990). Introductory Statistics for Business and Economics. 4th edition, John Wiley, New York.

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Software • SPSS for Windows, Rel. 11.0.1. 2001. Chicago: SPSS Inc. • R Development Core Team. R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria, 2008. http://www.R-project.org.

Evaluation method F G = 0.5 × EG + 0.5 × (P J1 + P J2 )/2, where F G is the final grade of each student, EG is the exam grade (rounded to one decimal), and P Ji , i = 1, 2 is the grade of the i-th project (round to one decimal place). Minimum Grade in the Exam: — 7.0. Projects: • Performed in groups of three students; • Important Dates: Handed out

To be handed back

P J1

21-March

8-April

P J2

08-May

29-May

Exams Schedule: • 1st Date: 8 June 2013, 9-12 am; • 2nd Date: 26 June 2013, 9-12 am.

Recitation Hours • Room: N2 - Meeting Room • Schedule: Thursday — 11-13 am.

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