Modelando o desempenho dos campeões do Brasileirão através de regressões no intervalo unitário

Abstract

In many contexts, statistical modeling requires consideration of constraints imposed on the response variable, such as the limitation to the unitary interval for proportions. In these cases, it is common to employ distributions compatible with this range, although models with broader support are also applicable. This monograph addresses the Beta, Simplex, and Normal models in the analysis of data between 0 and 1. The Normal distribution is used as a reference to verify its performance parity with that of distributions formulated for this variable profile. Thus, the three regression models and their estimation processes using the Maximum Likelihood Method were discussed. To assess the effectiveness of the models, a simulation study was conducted using the Monte Carlo method to estimate the regression parameters, observing that the estimates approach the true values as the sample size increases. Furthermore, the statistical models were applied to the dataset of Brazilian Championship champion clubs between 2003 and 2024, using points per share as the variable of interest, to demonstrate their practical implementation and the interpretation of the results. Visualization techniques, descriptive statistics, and regressions appropriate to the data were employed in the application. The simulation studies and the application presented in this work confirm the proposed objectives and provide contributions for future research.