Regression slope of the dependence of photometric brightness variation on HK emission variation, plotted vs. mean chromospheric activity for stars with solar (upper panel), polar (middle panel), and homogeneous (lower panel) active region distributions. The asterisks indicate the observed values for the stellar sample of Lockwood et al. (2007). The diamond indicates 18 Scorpii (HD 146233) from Hall et al. (2009). The light-shaded areas represent the activity levels for which the photometric variability, according to the activity-variability regression from Lockwood et al. (2007), is smaller than the 1σ uncertainty and thus Δ [ (b + y)/2 ]/ΔS values cannot be reliably defined. Colored curves are the output of our model calculated for three values of the stellar inclination: 90° (red curve), 57° (magenta curve), and 0° (blue curve). The dashed lines separate facula-dominated (positive Δ [ (b + y)/2 ]/ΔS) from spot-dominated (negative Δ [ (b + y)/2 ]/ΔS) variability. The solid vertical line in the upper panel denotes the mean level of solar chromospheric activity. The dark-shaded bands indicate the range of chromospheric activities for which according to our model the stars can be observed as either faculae- or spot-dominated, depending on the period of time over which they are observed (see text for details).