An algorithm for finding the linear region in a nonlinear data set
Finding the linear reportable range is an important procedure for each method in clinical chemistry. One is often called upon to limit the reportable range in order to find the linear region. Limiting the reportable range by visual techniques is subjective, may introduce bias and is not programmable. Using Kroll and Emancipator's polynomial method for linearity, we compare the residuals of a test to determine whether eliminating a point from one end or the other of the data set worsens or improves the data sets' linearity. In an example of urinary cortisol, the root mean squares of the residuals improve by 2% when the lowest point is removed, 39% when the highest point is removed and 82% when the two highest points are removed. The latter data set is the most linear.
linear nonlinear reportable range accuracy