  Stellar activity is inherently time variable, therefore simultaneous
measurements are necessary to study the correlation between different activity
indicators. In this study we compare X-ray fluxes measured within the first
all-sky survey conducted by the extended ROentgen Survey with an Imaging
Telescope Array (eROSITA) instrument on board the Spectrum-Roentgen-Gamma (SRG)
observatory to Ca II H & K, excess flux measurements R+, using observations
made with the robotic TIGRE telescope. We created the largest sample of
simultaneous X-ray and spectroscopic Ca II H & K observations of late-type
stars obtained so far, and in addition, previous measurements of Ca II H & K
for all sample stars were obtained. We find the expected correlation between
our log(L_X/L_bol) to log(R+) measurements, but when the whole stellar ensemble
is considered, the correlation between coronal and chromospheric activity
indicators does not improve when the simultaneously measured data are used. A
more detailed analysis shows that the correlation of log(L_X/L_bol) to log(R+)
measurements of the pseudo-simultaneous data still has a high probability of
being better than that of a random set of non-simultaneous measurements with a
long time baseline between the observations. Cyclic variations on longer
timescales are therefore far more important for the activity flux-flux
relations than short-term variations in the form of rotational modulation or
flares, regarding the addition of "noise" to the activity flux-flux
correlations. Finally, regarding the question of predictability of necessarily
space-based log(L_X/L_bol) measurements by using ground-based chromospheric
indices, we present a relation for estimating log(L_X/L_bol) from R+ values and
show that the expected error in the calculated minus observed (C-O)
log(L_X/L_bol) values is 0.35 dex.
