Abstract: In this paper, the distribution model of the regression residue of discrete dependent variables is obtained by general survey of a vast amount of the examples of the weather predictions. The regression diagnosis shows that unidirectional characteristic of the model is caused by some high leverage cases. In the sense of statistical forecasting, the residues of these high leverage cases have no rationality, and the errors of least square (LS) estimation of the regression coefficient are occured. Therefore, the method of discrete regression is proposed in this paper. The results show that the method of discrete regression is superior to general zegression method by mathematical proving and the calculation of the examples.