Four density-independent "populations" were constructed on a computer, and the simple regression of the log density in one generation (log Nn+1) on the log density in the previous generation (log Nn) was calculated for each of a number of replicates for each population. From the resultant sampling distribution of the regression coefficient for each population, it was found that (i) the mean slope was significantly less than the expected value of 1.0 for a density-independent population, and that (ii) the mean slope was influenced by sample size and the serial correlation between successive values of the rate of increase, ϒ. Despite its demonstrated bias the regression coefficient could still be useful if it were capable of distinguishing between populations with density-dependent processes and populations with no density-dependent processes. So data for a number of natural populations were analyzed by simple regression and each of the slopes so obtained was compared with the mean slopes (for simple regression) for the theoretical populations. These comparisons suggested that the simple regression coefficient was not a good criterion of density dependence.