We develop an empirical, spatially continuous model for the single-station within-event (ϕ_SS) component of earthquake ground motion variability in the Los Angeles area. ϕ_SS represents event-to-event variability in site response or remaining variability due to path effects not captured by ground motion models. Site-specific values of ϕ_SS at permanent seismic network stations were estimated during our previous work [1]. Here we first fit a model to ϕ_SS conditioned on the time-averaged shear wave velocity in the upper 30 m (V_S30). We observe that stations on soft soil have larger average variability in site response than those on rock, especially at short periods. We use regression kriging to spatially interpolate ϕ_SS to an even grid spacing, using the V_S30-scaling as the background model [2]. This improves on previous work that used ordinary kriging for interpolation [1]. We find that ϕ_SS ranges from about 0.1 to 0.4 natural log units in our study area, representing variations in site response at single locations of a factor of 1.1 up to a factor of 1.5. There is both greater variability and more coherency in the variability for short-period site response than for long periods. We recommend using these ϕ_SS models with the site response models of [1] for applications where quantification of variability is needed, such as probabilistic seismic hazard analyses.