Aplicações de estatística multivariada em análise de dados experimentais

Abstract

Multivariate statistics is a branch of statistics responsible for studying situations where statistics models presents more then one variable and their methods can be applied in the most diverse areas of knowledge assisting in decision making, because their methods have as main benefits the reduction of dimensionality of the model studied, making it less complex, in addition to being used in the construction of indexes, classification, association between variables and statistical inference. In this work Multivariate statistics methods were applied in tree different situations, the method of canonical correlation analysis was applied in two different situations and the principal component analysis with experimental errors method was applied in the last one. the first application referring to a socio-environmental analysis where the existence of a correlation between the human development index (HDI) and its sub-indices in relation to water consumption and sewage generation of Brazilian cities was analyzed. While the second analysis is related to high-energy physics involving the collision of heavy lead ions Pb-Pb. The third situation refers to the application of principal component analysis for the dimensionality reduction of a model of characterization of the interstellar medium. As a result, it was possible to generate a model capable of correlating the HDI with water consumption and sewage generation, with a canonical correlation of 62.4%, capable of representing the whole country, and a second model, directed only to the state of Sa˜o Paulo, with a canonical correlation of 83%. For the second scenario, involving the collision of heavy ions a canonical correlation of 99.9% was obtained, confirming the existing correlation between entropy and the number of charged particles. A second correlation, calculated from the second pair of canonical variables, returned a high correlation with 96%, however, in this model the crosssectional moment had the highest canonical weight, and can be calculated from the other variables studied such as centrality, energy and entropy. Regarding the principal component analysis, it was possible to reduce the number of variables used in the explanation of the model significantly, from 23 original variables to 8 main components, in addition to identifying that when considering the experimental errors during the analysis we obtain greater security regarding the number of variables used to explain the model.