Simulated observations of spawning stock size, recruitment, and two random environmental variables were obtained from a density-independent Leslie matrix model. Recruitment to Age 1 was directly proportional to population fecundity but strongly influenced by the effects of the random environmental variables. The simulated observations were subjected to multiple regression analysis which detected the influence of the random environmental variables but did not reliably detect the influence of spawning stock. These results indicate that multiple regression is unreliable in detecting the influence of stock on recruitment when annual variations in recruitment are primarily due to environmental factors.