Context : The radius of an exoplanet may be affected by various factors , including irradiation received from the host star , the mass of the planet and its 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 .

Aims : We use multivariate regression models to determine the power-law 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 .

Methods : We fit models initially to all 119 planets , resulting in fairly high scatter between fitted and observed radii , and subsequently to three subsets of these planets : Saturn-mass planets , Jupiter-mass planets , and high-mass planets .

Results : We find models for each subset that fit the observed planetary radii well and show the importance of the various environmental parameters on each subset .

Conclusions : We determine that heating leads to larger planet radii , as expected , increasing mass leads to increased or decreased radii of low-mass ( < 0.5 R _ { J } ) and high-mass ( > 2.0 R _ { 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 } / 1 \times 10 ^ { 20 } ) .
These equations produce a very good fit to the observed radii , with a mean absolute difference between fitted and observed radius of 0.11 R _ { J } , compared to the mean reported uncertainty in observed radius of 0.07 R _ { J } .
A clear distinction is seen between the core-dominated Saturn-mass ( 0.1-0.5 M _ { J } ) planets , whose radii are determined almost exclusively by their mass and heavy element content , and the gaseous envelope-dominated Jupiter-mass ( 0.5-2.0 M _ { J } ) planets , whose radii increase strongly with irradiating flux , partially offset by a power-law dependence on orbital separation .