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.
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