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A reducing variation of quality characteristics is a typical example of quality improvement. In such a case, we treat the quality characteristic, as a response variable and need to find active factors affecting the response from many candidate factors since reducing the variation of the response will be achieved by reducing variation of the active factors. In this paper, we first derive a method of selecting an active factor by linear regression. It is well known that correlation between factors deteriorates the precision of estimators. We, therefore, examine robustness of the selecting method against the correlation in the data set and derive an evaluation method of the deterioration brought by the correlation. Furthermore, some examples of selecting and evaluation methods are shown to demonstrate practical usage of the methods.