On the analysis of straight line data in pharmacology and biochemistry

The determination of drug potency, efficacy and receptor affinity constants, common calculations in pharmacology and biochemistry, require estimates of the slope and intercept of a linear regression line obtained from measured points ( x i , y i ). Three questions not explicitly covered in the basic statistical literature and, consequently, answered differently by scientists, arise often. (1) When there exist several y's corresponding to each value of the controlled parameter x, should all of these be used as points or only their average value at that x in constructing the line? (2) What are precise confidence limits of an abscissa corresponding to a specified ordinale? (3) What are confidence limits for the intercepts of a regression line whose slope is constrained to +1 or -1? In this paper we show that all the data should be used (question 1) and provide derivations for the formulas used to get the confidence limits mentioned in questions (2) and (3).