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Based on a raw sequence with some aberrant data, it is difficult for any prediction technique to give out an accurate point forecasting value. However, an interval forecasting value obtained by one or more different techniques should be reasonable and acceptable. In this paper, a data sequence having a linear tendency with upper/positive and lower/negative aberrances is analyzed. Upon the linear regression analysis, the data sequence is classified into three parts: upper/positive aberrant data, lower/negative aberrant data and normal data. Then introducing the non-equidistant GM(1,1), we establish three models : a non-equidistant GM(1,1) based on upper aberrant data, a non-equidistant GM(1,1) based on lower aberrant data and a linear regression model based on the remaining normal data. Using the established models, we can obtain three prediction intervals. Applying it to the prediction of regional grain production, we demonstrate the good performance and effectiveness of the proposed prediction method.