# Bisector Method: Adjustment for Linear Regression

Article

Wong, Henry H.   (1991, ASQC)   Polysar Rubber Corporation, Sarnia, Ontario, Canada

Annual Quality Congress, Milwaukee WI    Vol. 45    No. 0
QICID: 9622    May 1991    pp. 890-895
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## Article Abstract

This abstract is an edited version of the author's original.

This paper points out the potential problems in applying linear regression when the measurement of an independent variable is imprecise and suggests methods to reduce the impact of these problems. One simple method is the Bisector Method, which reduces the impact of measurement errors by doing a second linear regression, switching the dependent variable with the independent variable. You can then use the bisector of the two regression line as the most probable cause. This method can often be further simplified by using the Average Method, which takes the average of the two solutions as an estimate.

The Bisector Method and the Average Method work well when the absolute sizes of the two variables are similar. When they are significantly different, you must normalize the data sets before applying the methods. The fundamental assumption for these methods is that the test errors, found in the measurements of the two variables, are very similar in size.

The solutions are not appropriate when the sizes of the test errors differ significantly in size. In these cases, you must modify the methods, adjusting the distances from the middle line to the regression lines, according to the sizes of the test errors. Since this method is based on the sizes of test errors, or the sigmas representing measurement imprecisions, it is called the Sigma method.

## Keywords

Linear regression,Manufacturing,Statistics,Average Method

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