Inverse prediction from 2-point response curve

I will have a 2-point line to use for inverse prediction. I can get the estimate of MSE for the model from outside experiments, so there really is a regression model underlying the 2 points. I then need to do inverse regression from a new y-value. From what I read the CI always assume n>2. Is there any work done when the response curve only has a high and low? I can certainly simulate to get results, but I'd like to see some theory if possible.