ABSTRACT: This article proposes a new regression model for a dependent fractional random variable on the interval (Formula presented.) that takes with positive probability the extreme values 0 or 1. Our model relates the expected value of this variable with a linear predictor through a special parametrization that let the parameters free in the parameter space. A simulation-based study and an application to capital structure choices were conducted to analyze the performance of the likelihood estimators in the model. The results show not only accurate estimations and a better fit than other traditional models but also a more straightforward and clear way to estimate the effects of a set of covariates over the mean of a fractional response.