Modelos de regressão para placares de jogos divididos em sets

Abstract

The main objective of this work is to propose regression models for the score of games divided into sets. Initially, we assume that the sets are independent and obtain the bivariate probability distribution associated with this proposal. Then, we propose a regression model assuming this probability distribution for the response variable. Inferential and diagnostic aspects of this model are discussed, the performance of the maximum likelihood estimator is evaluated, and two applications to real data are carried out. Subsequently, we assume Markovian dependence between the sets and, fixing the number of sets required for victory, we obtain the bivariate probability distribution associated with this proposal. To conclude the work, we propose a regression model assuming this probability distribution for the response variable. As in the previous model, we discuss inferential and diagnostic aspects, evaluate the performance of the maximum likelihood estimator in the model, and perform an application to real data. This final application, using Grand Slam tennis data, suggests that the proposed model is appropriate for modeling the scores of these matches as a function of covariates.