  We aim to use statistical analysis of a large number of various galaxies to
probe, model, and understand relations between different galaxy properties and
magnetic fields. We have compiled a sample of 55 galaxies including low-mass
dwarf and Magellanic-types, normal spirals and several massive starbursts, and
applied principal component analysis (PCA) and regression methods to assess the
impact of various galaxy properties on the observed magnetic fields. According
to PCA the global galaxy parameters (like HI, H2, and dynamical mass, star
formation rate (SFR), near-infrared luminosity, size, and rotational velocity)
are all mutually correlated and can be reduced to a single principal component.
Further PCA performed for global and intensive (not size related) properties of
galaxies (such as gas density, and surface density of the star formation rate,
SSFR), indicates that magnetic field strength B is connected mainly to the
intensive parameters, while the global parameters have only weak relationships
with B. We find that the tightest relationship of B is with SSFR, which is
described by a power-law with an index of 0.33+-0.03. The observed weaker
associations of B with galaxy dynamical mass and the rotational velocity we
interpret as indirect ones, resulting from the observed connection of the
global SFR with the available total H2 mass in galaxies. Using our sample we
constructed a diagram of B across the Hubble sequence which reveals that high
values of B are not restricted by the Hubble type. However, weaker fields
appear exclusively in later Hubble types and B as low as about 5muG is not seen
among typical spirals. The processes of generation of magnetic field in the
dwarf and Magellanic-type galaxies are similar to those in the massive spirals
and starbursts and are mainly coupled to local star-formation activity
involving the small-scale dynamo mechanism.
