Identifying and removing sources of imprecision in polynomial regression

Identification and removal of imprecision in polynomial regression, origina ting from random errors (noise) in the independent variable data is discuss ed. The truncation error-to-noise ratio (TNR) is used to discriminate betwe en imprecision dominated by collinearity, or numerical error propagation, o r inflated variance due to noise in the independent variable. It is shown t hat after the source of the imprecision has been identified, it can often b e removed by simple data transformations or using numerical algorithms whic h are less sensitive to error propagation (such as QR decomposition). In ot her cases, more precise independent variable data may be required to improv e the accuracy and the statistical validity of the correlation. (C) 1998 IM ACS/Elsevier Science B.V.