Regression Errors and Tests of the Coefficients

Following the laws of error propagation and using the residual variance of regression s2 (e) defined by  

To replace the concentration term by the respective signal term one can use Eq. 2-59. From this result both variances for the special points x, = 0 and x, = x follow immediately. The first variance then characterizes the error of the calibration offset. v2 ( ). The second term, in brackets in Eq. 2-61, shows that we can expect minimum errors of the calibration process around the middle of the calibration (concentration) range, x, xc  

If we generally assume al to be a true but unknown parameter of the regression model we have the following possible hypotheses  

As in previous sections, with these error estimates it is also possible to determine the confidence interval cnf of the parameters  

From the latter it is obviously possible that the true intercept, blank value. may be zero. The statistically based decision, however, depends on the following. 

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