Métodos Estatísticos Multivariados para Engenharia e Gestão

Objectives

The aim of the course is to give the students training in areas of multivariate statistics, to analyse data from engineering and management, and also to interpret the output of statistical softwares. Procedures covered in the course include exploratory multivariate data analysis, regression, cluster analysis and topics to analyse means (analysis of variance) and covariance structures (principal components and factorial analysis).

Syllabus

1. Introdution to Multivariate Analysis Overview of multivariate methods and main objectives; Some definitions and notation;Exploratory analysis: descriptive methods and graphical multivariate data display. 2. Regression Analysis Multiple linear regression; Least squares estimation of the parameters; Properties of the estimators; Tests and confidence intervals for the parameters; Prediction. Model adequacy checking; Selection of variables and model building. 3. Design Experiments and Variance Analysis Completely randomized experiment; Single-factor analysis variance, (one-way ANOVA).; Multiple comparisons; Two-factors analysis variance, (two-way ANOVA); Randomized complete block design; Multiple analysis of variance (MANOVA). 4. Principal Components Analysis Introduction; Definition and derivation of principal components; Properties of principal components; Geometric properties of principal components; Sample principal components; Question regarding the application of principal components.; Principal components in multiple linear regression. 5. Factorial Analysis Introduction; Model formulation; Estimation of the parameters; Factors rotations; Scores estimation; Question regarding the application of factor analysis; Factor analysis versus principal components analysis. 6. Clusters analysis and Multidimensional Scaling Introduction; Similarity measures; Methods to obtain clusters: Graphical and visual methods; Hierarchical methods; Non hierarchical methods.Multidimensional Scaling.