Errors in Linear Calibration

Fundamentally, the uncertainties of measured values y estimated by calibration, e.g. according to Eq. (6.6), on the one hand and of analytical results x (analyte contents, concentrations) estimated by means of a calibration function, e.g. according to Eq. (6.17), on the other hand differ from one another as can be seen from Fig. 6.3B,C, and Fig. 6.7. Whereas the uncertainty of y values in calibration is characterized by the confidence interval cnf(y), the uncertainty of estimated x values is characterized by the prediction interval prd(x). 

The uncertainty of OLS calibration is characterized by the following special standard deviations and uncertainty intervals  

In calibration, the number of degrees of freedom depends on the number of parameters estimated by the given model. In case of the two-parametric model (Eq. 6.6) v = n — 2, in case of linear calibration through the coordinate origin (a = 0) v = n — 1, and in case of a three-parametric nonlinear calibration model 

The following uncertainty intervals resulting from Eqs. (6.19) to (6.25) are of practical interest  

The latter is important with regard to the estimation of the detection limit from blanks 

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