Regression Functions and Confidence Regions

By analogy with the confidence range of a single value or a mean, we can calculate a confidence interval for a single predicted value according to  

With one measurement in the analysis step at xj, which is not necessarily identical to one of the previous x, in the calibration process, and, from the mathematical point of view, not even within the regression range of x, s2 (jj) then becomes  

Then the confidence interval can be made smaller by replicate measurements, na, of a sample at xj and s1 (yj) becomes  

On each side of the calibration line the border points of the confidence regions may be connected or smoothed to give a confidence band around the calibration line, see Fig. 2-4. 

We can only note here that, in order to be statistically correct, the procedure used for calculating the confidence band has a very sophisticated basis (see, e.g., [MAGER, 1982 LUTHARDT et al., 1987], 

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