Cabrera Cruz, Greichaly

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    Aplicación de las técnicas de componentes principales y componentes independientes como herramientas en los métodos de regresión lineal múltiple y clasificación no supervisada a partir de variables socio-económicas de Puerto Rico
    (2015-06) Cabrera Cruz, Greichaly; Lorenzo González, Edgardo; College of Arts and Sciences - Sciences; Díaz Caraballo, José N.; Santana Morant, Dámaris; Department of Mathematics; Castellano Rodríguez, Dorial
    Studying the socio-economic aspect of Puerto Rico is of utmost importance for decision-making in the country. This thesis presents different findings, by applying the techniques of: Principal Components, Independent Components, Unsupervised Classification and Multiple Linear Regression to socio-economic variables of Puerto Rico for 2010. Using the Principal Components technique, we succeeded in reducing the number of variables to only 3 variables, which absorbed 77% of variability. By applying the Principal Components and Independent Components techniques, new latent socio-economic factors were identified. After applying Unsupervised Classification to the socio-economic variables a regionalization with 7 clusters was obtained. The first two clusters showed poor socio-economic characteristics, the next three mean socio-economic characteristics and the last two had positive socio-economic characteristics. Moreover, the classification obtained by using principal components consisted of seven clusters, which were characterized in terms of the latent factors identified. The classification obtained using the independent component consisted of eight clusters, among them a cluster consisted of the municipalities of Vieques and Culebra, and another had only the municipality of Guaynabo. Interpretability of this classification was more limited than the other classifications. Variable selection methods were applied to the Multiple Regression technique using the principal components as regressors. After applying the Box-Cox transformation, using the response ln(population density) we obtained a valid socio-economic regression model, whose R-squared was 60.6%.