Several methods were suggested for constructing a fuzzy relationship between fuzzy independent and dependent variables. This paper reviews the use of the method by minimizing the square of the difference between an observed and a predicted fuzzy number in an ${alpha}$-level linear regression model. We introduce a new distance between fuzzy numbers on the basis of a mode, a core point and a radius of an ${alpha}$-level set of a fuzzy number an construct the fuzzy regression model using the proposed fuzzy distance. We also investigate sufficient condition for an equivalence in the ${alpha}$-level regression model.