Evaluating 'goodness-of-fit' for linear instrument calibrations through the origin

Instrument calibrations for environmental analyses frequently entail fitting straight lines forced through the origin, where either the correlation coefficient, Pearson's r, or the percent relative standard deviation, %RSD, for a set of response factors is used to measure the 'goodness-of-fit'. However, these two approaches do not produce comparable linear calibrations. To do this, a weighted regression line needs to be calculated. A weighted regression coefficient is subsequently defined to evaluate the 'goodness-of-fit' and is expressed as function of the %RSD.