Regression studies of salmon stock-recruitment relations require a priori assumptions concerning the nature of stock variability as influenced by smolt populations. Such assumptions can lead to biased estimates of the relationships of smolts to the production of adult salmon. This paper utilizes a statistical method which allows the data to determine the interrelationship of smolts and adult production mean and variability without imposing a priori restrictions on the form of such. The estimation process yields two estimated relationships one explaining the effect of hatchery releases on expected adult production and another explaining the effects of the hatchery releases on the standard deviation of adult production. Application of this model suggests that the standard deviation of adult production increases with the square of the number of seaward migrants both for Hokkaido chum salmon (Oncorhynchus keta) and for Oregon coho salmon (O. kisutch) and that incorrect inferences may have been obtained about density dependence by other authors because of the imposed a priori assumptions and/or data adequacy.