  High-precision time series have recently become available for many stars as a
result of data from CoRoT, Kepler, and TESS and have been widely used to study
stellar activity. They provide information integrated over the stellar disk,
hence many degeneracies between spots and plages or sizes and contrasts. Our
aim is to understand how to relate photometric variability to physical
parameters in order to help the interpretation of these observations. We
computed a large number of synthetic time series of brightness variations for
old MS stars within the F6-K4 range, using consistent modeling for radial
velocity, astrometry, and LogR'HK. We analyzed these time series to study the
effect of the star spectral type on brightness variability, the relationship
between brightness variability and LogR'HK, the interpretation of brightness
variability as a function of spot and plage properties, and the spot-dominated
or plage-dominated regimes. Within our range of activity levels, the brightness
variability increases toward low-mass stars, as suggested by Kepler results.
Brightness variability roughly correlates to LogR'HK level, but with a large
dispersion, caused by spot contrast and inclination. It is also directly
related to the number of structures, and we show that it cannot be interpreted
solely in terms of spot sizes. In the activity range of old main-sequence
stars, we can obtain both spot or plage dominated regimes, as in observation.
The same star can be observed in both regimes depending on inclination. Only
strong correlations between LogR'HK and brightness variability are significant.
Our realistic time series proves to be extremely useful when interpreting
observations and understanding their limitations, most notably in terms of
activity interpretation. Inclination is crucial and affects many properties,
such as amplitudes and the respective role of spots and plages.
