Beta regression models are useful for modeling random variables that assume values in the standard unit interval, such as rates and proportions. Such models cannot be used when the data contain zeros and/or ones. The main aim of this work is to propose a mixed continuous-discrete distribution to model data observed on the intervals [0, 1) or (0, 1] and its associated regression model. The GJS distribution is used to describe the continuous component of the model. The parameters of the mixture distribution are modelled as functions of regression parameters. We study the performance of the maximum likelihood estimators through Monte Carlo simulations. Also, we define a residual for the proposed regression model to assess departures from model assumptions as well as to detect outlying observations, and discuss some influence methods such as the local influence. Finally, applications to real data are presented to show the usefulness of the new regression model.