The radius of an exoplanet may be affected by various factors, including irradiation, planet mass and heavy element content. A significant number of transiting exoplanets have now been discovered for which the mass, radius, semi-major axis, host star
metallicity and stellar effective temperature are known. We use multivariate regression models to determine the dependence of planetary radius on planetary equilibrium temperature T_eq, planetary mass M_p, stellar metallicity [Fe/H], orbital semi-major axis a, and tidal heating rate H_tidal, for 119 transiting planets in three distinct mass regimes. We determine that heating leads to larger planet radii, as expected, increasing mass leads to increased or decreased radii of low-mass (<0.5R_J) and high-mass (>2.0R_J) planets, respectively (with no mass effect on Jupiter-mass planets), and increased host-star metallicity leads to smaller planetary radii, indicating a relationship between host-star metallicity and planet heavy element content. For Saturn-mass planets, a good fit to the radii may be obtained from log(R_p/R_J)=-0.077+0.450 log(M_p/M_J)-0.314[Fe/H]+0.671 log(a/AU)+0.398 log(T_eq/K). The radii of Jupiter-mass planets may be fit by log(R_p/R_J)=-2.217+0.856 log(T_eq/K)+0.291 log(a/AU). High-mass planets radii are best fit by log(R_p/R_J)=-1.067+0.380 log(T_eq/K)-0.093 log(M_p/M_J)-0.057[Fe/H]+0.019 log(H_tidal/1x10^{20}). These equations produce a very good fit to the observed radii, with a mean absolute difference between fitted and observed radius of 0.11R_J. A clear distinction is seen between the core-dominated Saturn-mass (0.1-0.5M_J) planets, whose radii are determined almost exclusively by their mass and heavy element content, and the gaseous envelope-dominated Jupiter-mass (0.5-2.0M_J) planets, whose radii increase strongly with irradiating flux, partially offset by a power-law dependence on orbital separation.
