In information retrieval, data fusion has been investigated by many researchers. Previous investigation and experimentation demonstrate that the linear combination method is an effective data fusion method for combining multiple information retrieval results. One advantage is its flexibility since different weights can be assigned to different component systems so as to obtain better fusion results. However, how to obtain suitable weights for all the component retrieval systems is still an open problem. In this paper, we use the multiple linear regression technique to obtain optimum weights for all involved component systems. Optimum is in the least squares sense that minimize the difference between the estimated scores of all documents by linear combination and the judged scores of those documents. Our experiments with four groups of runs submitted to TREC show that the linear combination method with such weights steadily outperforms the best component system and other major data fusion methods such as CombSum, CombMNZ, and the linear combination method with performance level/performance square weighting schemas by large margins.