Identifying and removing sources of imprecision in polynomial regression

Identification and removal of imprecision in polynomial regression, originating from random errors (noise) in the independent variable data is discussed. The truncation error-to-noise ratio (TNR) is used to discriminate between imprecision dominated by collinearity, or numerical error propagation, or inflated variance due to noise in the independent variable. It is shown that after the source of the imprecision has been identified, it can often be removed by simple data transformations or using numerical algorithms which are less sensitive to error propagation (such as QR decomposition). In other cases, more precise independent variable data may be required to improve the accuracy and the statistical validity of the correlation.