  The dependence of stellar magnetic activity on stellar parameters would be
inspired by the chromospheric activity studies based on the large-scale
spectroscopic surveys. The Ca II H and K lines are employed to construct
indicators for assessing and studying the chromospheric activity of solar-like
stars. We investigate the widely used bolometric and photospheric calibrated
chromospheric activity index $R'_{\rm HK}$, derived from the method in the
classic literature ($R'_{\rm HK,classic}$) and the method based on the PHOENIX
model ($R'_{\rm HK,PHOENIX}$). Since the detailed stellar atmospheric
parameters, effective temperature ($T_{\rm eff}$), surface gravity ($\log\,g$),
and metallicity ([Fe/H]), are available for LAMOST, we estimate the
chromospheric activity index $R'_{\rm HK,PHOENIX}$, along with the
corresponding bolometric calibrated index $R_{\rm HK,PHOENIX}$, taking these
parameters into account. We provide the database of the derived chromospheric
activity parameters for 1,122,495 LAMOST LRS spectra of solar-like stars. Our
calculations show that $\log\,R'_{\rm HK,PHOENIX}$ is approximately linearly
correlated with $\log\,R'_{\rm HK,classic}$. The results based on our extensive
archive support the view that the dynamo mechanism of solar-like stars is
generally consistent with the Sun; and the value of solar chromospheric
activity index is located at the midpoint of the solar-like star sample. We
further investigate the proportions of solar-like stars with different
chromospheric activity levels (very active, active, inactive and very
inactive). The investigation indicates that the occurrence rate of high levels
of chromospheric activity is lower among the stars with effective temperatures
between $5600$ and $5900 \,{\rm K}$.
