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Applied Statistics

Applied Statistics

Code	16674
Year	2
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	Does not have.
Learning outcomes	1. Understand and differentiate the most common methods for multivariate data analysis. 2. Identify and adjust the appropriate model to a multivariate data set. 3. Interpret and communicate the results from a multivariate statistical analysis. 4. Know how to use a statistical software in the analysis of multivariate data.
Syllabus	1. Multivariate probability distributions: joint probability; marginal distribution; covariance and correlation; multinomial distribution; multivariate normal distribution and its properties. 2. Multiple Regression Models: 2.1. Linear Regression: model; parameter estimation (least squares method); inferences about the model; validation of model assumptions. 2.2 Logistic Regression: model adjustment (maximum likelihood method); significance and model quality. 3. Principal Components Analysis: model; estimation of principal components; rotation and interpretation of the main components. 4. Factor Analysis: model; estimation of common and specific factors; factor rotation; oblique rotation methods; factor scores. 5. Cluster Analysis: probabilistic formulation; hierarchical and non-hierarchical methods; cluster number choice. 6. Discriminant Analysis: selection of discriminant variables; estimation of discriminant functions; classification trees.
Main Bibliography	Principal: - Hardle, W.K., Simar, L. (2019) Applied Multivariate Statistical Analysis (5th ed.), Springer - Johnson, R.A. e Wichern, D.W. (2007) Applied Multivariate Statistical Analysis (6th ed.), Prentice-Hall - Mardia, K.V., Kent, J.T., Bibby, J.M. (1979) Multivariate Analysis, Academic Press - Johnson D. E. (1998) Applied Multivariate Methods for Data Analysts, Duxbury Press & Brooks/Cole Complementar: - Everitt, B., Hothorn, T. (2011) An Introduction to Applied Multivariate Analysis with R, Springer (Use R! Series) - Denis, D. (2020) Univariate, Bivariate, and Multivariate Statistics using R, Quantitative tools for data analysis and data science, John Wiley and Sons Ltd
Teaching Methodologies and Assessment Criteria	The classes are of a theoretical-practical nature with exposure of fundamental concepts for the understanding of the multivariate statistical techniques presented, exemplified with applications and problem solving using a statistical software, by students with professor guidance, of multivariate data exploration and modelling. The assessment consists of two written tests using statistical software.
Language	Portuguese. Tutorial support is available in English.