Abstarct: In many regression models the response variable is continuous‎, ‎restricted to the‎ ‎interval $(0,1)$‎, ‎such as percentages‎, ‎proportions and fractions or rates‎. ‎For analysing such responses‎, ‎the logistic or probit regression models are not adequate and the popular model is beta regression‎. ‎However‎, ‎the beta regression model is not robut when there are outlying observations in the response variable‎. ‎Therefore‎, ‎we consider a new regression model constructed baxsed on the beta rectangular distribution‎. ‎It is shown that beta rectangular regression is more robust than the beta regression model‎. ‎In this thesis‎, ‎we first review the beta rectangular distribution and a new parametrization is introduced‎. ‎Then the beta rectangular regression model is proposed and a Bayesian inference approach is adopted using a Markov chain Monte Carlo (MCMC) algorithm‎. ‎Two simulation studies are carried out to show the better performance of the new model in the presence of outliers‎. ‎Finally‎, ‎application of the proposed model is shown by two applications‎.