  Thermal microwave emissions detected from stellar atmospheres contain
information on stellar activity. However, even for the Sun, the relationship
between multifrequency microwave data and other activity indices remains
unclear. We investigated the relationships among the thermal microwave fluxes
with 1, 2, 3.75 and 9.4 GHz, their circular polarizations, and several activity
indices recorded during recent solar cycles and observed that these
relationships can be categorized into two groups. In the first group, the
relationship between the microwave fluxes and solar indices, which are strongly
related to the active regions, can be well-fitted by using a linear function.
In the second group, the fitting function is dependent on frequency.
Specifically, the microwave fluxes at 1 and 2 GHz can be well-fitted to the
total unsigned magnetic and extreme ultraviolet fluxes by employing a power-law
function. The trend changes around 3.75 GHz, and of the trend for the 9.4 GHz
fluxes can be fitted by using a linear function. For the first time, we present
the relationship between circular polarization and solar indices. Moreover, we
extrapolated these relationships of the solar microwave fluxes to higher values
and compared them with the solar-type stars. We found that epsilon Eri, whose
microwave emission originates from thermal plasma, follows the extrapolated
relationship. However, to date, only one star's emission at 1--10 GHz has been
confirmed as thermal emission. More solar-type stars should be observed with
future radio interferometers to confirm that relationships based on solar data
can be applied to stellar microwave data.
