A linear regression model for imprecise random variables is considered. The imprecision of a random element has been formalized by means of the LR fuzzy random variable, characterized by a center, a left and a right spread. In order to avoid the non-negativity conditions the spreads are transformed by means of two invertible functions. To analyze the generalization performance of that model an appropriate prediction error is introduced, and it is estimated by means of a bootstrap procedure. Furthermore, since the choice of response transformations could affect the inferential procedures, a computational proposal is introduced for choosing from a family of parametric link functions, the Box-Cox family, the transformation parameters that minimize the prediction error of the model.