My question is in the context of testing and choosing the best weighted linear regression for a calibration model (calibration curves using an internal standard). How to explain the use of the weighting factor 1/y^2, for example, when working on bioanalytical/analytical method validation? What practical factors lead to a verification that the use of 1/y^2 or 1/y, rather than weights related to "x" (1/x or 1/x^2), better describes the data from calibration curves analyzed on an LC/MS-MS system? Signal saturation? Contamination? Accumulation of biological matrix debris? A slight trend in the data that favors 1/y^2?
In addition to the above, if incorporating the weighting factor 1/x^2 (where x reflects the nominal concentrations of the analyte) or 1/y^2 (where y reflects the response of the equipment) into the model results in similar performances in terms of the sum of the absolute percentage relative error (%RE) values, which one would be the most appropriate to be assumed in the calibration model? What conclusions can be drawn from the choice of one or the other with regard to the behavior of the data (and the nature of this behavior)?
I must say that I don't have a strong background in Statistics, so I apologize if I've expressed anything incorrectly.
Thank you
The weighing factors in regressions are used to minimized the relative error due to the different variances (concentration or response).
In bioanalytical methods 1/x and 1/x2 are commonly used since the error due to sample preparation (pipetting, extraction steps, balance weighing, analyst to analyst variability, etc.) have more influence on the resulted concentration (x axis) than the detector's response (y axis).
Applying 1/x or 1/x2 will minimize those errors and give the lower concentrations an influence (they will contribute) to the linearity of the curve, specially in bioanalysis where the calibration curve spans 200-1000 fold. On the other hand, when the response's error would have more influence than the concentrations, it would make sense to use 1/y or 1/y2 to minimize it.