Relation between prediction errors of inverse and classical calibration

The formulae for prediction errors of inverse and classical calibration derived by Centner, Massart and de Jong in the Fresenius' Journal of Analytical Chemistry (1998) 361 : 2-9 are reconsidered. All calculations assume univariate calibration by ordinary least squares regression applied to an infinite number of data pairs. Inverse calibration gives rise to an error variance which is smaller by a certain factor than that of classical calibration. This factor amounts to unity plus the ratio of the variances of the measurement errors and of the responses used for the calibration. The root mean squared error of prediction is also smaller for inverse than for classical calibration, namely by the square root of this factor. A prediction error calculated in that way agrees well with a result obtained by Monte Carlo simulations.