In this note we apply the sequential theory developed by Chow and Robbins  and Gleser ,  to the inverse linear regression problem. A two-stage sequential procedure has been proposed for the construction of a fixed-width confidence interval for $x$ (an unknown parameter). It is shown that the limiting probabilities of "correct decision" are equal to $P^\ast$ (pre-assigned).
"A Sequential Solution to the Inverse Linear Regression Problem." Ann. Statist. 2 (3) 535 - 539, May, 1974. https://doi.org/10.1214/aos/1176342713