In regression analysis, such as other statistical inference problems, imprecise data may be encountered. In this paper, we focused on some statistical inferences in fuzzy regression model on the basis of information the supplied by the available fuzzy data based on imprecise data. For these, we consider the maximum likelihood estimates of linear regression parameters based on fuzzy data for the variety of membership functions. Numerical example is given for estimating the regression parameters in order to provide an illustration of the proposed maximum likelihood estimation.