title: An algorithm for finding the linear region in a nonlinear data set.
abstract: 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.
authors.affiliation: Department of Pathology, The Johns Hopkins School of Medicine, Baltimore, MD 21287-7065, USA. mkroll@pathlan.path.jhu.edu
authors.forename: M H
authors.initials: MH
authors.lastname: Kroll
authors.forename: K
authors.initials: K
authors.lastname: Emancipator
authors.forename: D
authors.initials: D
authors.lastname: Floering
authors.forename: D
authors.initials: D
authors.lastname: Tholen
mesh_terms: D000465:Algorithms; D003627:Data Interpretation, Statistical; D006801:Humans; D006854:Hydrocortisone / Q000652:urine; D016014:Linear Models; D008432:Mathematical Computing; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D015203:Reproducibility of Results; D012984:Software
chemical_list: D006854:Hydrocortisone