On the confidence interval of the equivalence point in linear titrations

As the point of intersection in linear-branch titration curves results from two optimized linear regressions, calculated by least-squares from n 1 and n 2 pairs of values of the signal y as a function of the added volume of titrant υ, the value of the equivalence volume V e has the character of an estimated average V e hence a confidence interval is associated with it. If the point of intersection V e belongs concomitantly to both regressions then the same value of y e should correspond to the two extreme values V′ e and V′ e of the confidence interval as to V e itself. Consequently, the two segments of the confidence interval are obtained by averaging each of the two unequal segments of the separate confidence intervals. Alternatively, considering that multiple estimates of V e can be obtained, the confidence interval can be calculated from the normally distributed random variables Δ a′ and Δ b′ of the two linear regressions.