Estudio del Análisis Discriminante. Aplicación a datos reales

Abstract

The main aim of the study is to analyze Fisher’s Linear Discriminant Analysis and to later apply real data using the R statistics software. The LDA came about from a study made by Fisher in 1936 where, apart from the morphology of flowers, he studied and evaluated a lineal function to establish the differences between varieties of Iris (Setosa, Versicolor and Virgnica). Fisher did not verify all the hypotheses that are currently considered when applying said technique, but established their foundations. It consists in using a variable category that is a lineal combination of discriminating variables, measured at intervals or through use of reason, to find existing differences between the groups. The LDA has two main aims. The first being to build discriminating functions, that allow us to explain the belonging of an individual to a group, as well as establish the weight of each variable in the discrimination. The second objective is to predict to which group it is most probable the individual belongs, knowing only certain variables. This classifying technique, included in multivariable dependency techniques ( those where variables are divided into two groups: dependent variables and independent variables), is applicable to many areas of knowledge. For example, in education, one tries to estimate students’ academic performance based on educational and social factors. In medicine, it’s used to diagnose illnesses and prescribe the most adequate treatment based on the characteristics of the patient. Finally, one of the most remarkable uses is in the economic scope for estimating cost effectiveness of a business based on variables such as income, debts and the patrimony of said business. Furthermore, it deduces whether it would be beneficial for a financial entity to approve a mortgage to its customers.