  Using a sample of 11,478 spaxels in 34 galaxies with molecular gas, star
formation and stellar maps taken from the ALMA-MaNGA QUEnching and STar
formation (ALMaQUEST) survey, we investigate the parameters that correlate with
variations in star formation rates on kpc scales. We use a combination of
correlation statistics and an artificial neural network to quantify the
parameters that drive both the absolute star formation rate surface density
(Sigma_SFR), as well as its scatter around the resolved star forming main
sequence (Delta Sigma_SFR). We find that Sigma_SFR is primarily regulated by
molecular gas surface density (Sigma_H2) with a secondary dependence on stellar
mass surface density (Sigma_*), as expected from an `extended Kennicutt-Schmidt
relation'. However, Delta Sigma_SFR is driven primarily by changes in star
formation efficiency (SFE), with variations in gas fraction playing a secondary
role. Taken together, our results demonstrate that whilst the absolute rate of
star formation is primarily set by the amount of molecular gas, the variation
of star formation rate above and below the resolved star forming main sequence
(on kpc scales) is primarily due to changes in SFE.
