Gaussian random noise background-subtracted (top) and residuals (bottom) vs. W, the sum of the weights of the non-rejected local background models that determine the global background model at each point, for 1/10 and 1/5 beamwidth rasters, and for 1, 3, 6, 12, and 24 beamwidth background-subtraction scales (background-subtraction scale times the sampling density of the data sets increases from left to right). The rms of the data varies with W, but not with background-subtraction scale or sampling density independently. Curves are 1, 2, and 3σ model noise envelopes that have been fitted to all of these data simultaneously (Equations (6) and (7)).