In this study, the soft X-ray luminosity of the solar corona, measured by the Yohkoh spacecraft for 104 well developed and decaying active regions, is compared to the magnetic field parameters determined from SOHO/MDI high resolution magnetograms. We calculated and compared the following parameters: i) two area-independent characteristics of the magnetic field: index (α) of the magnetic power spectrum, E(k) ∼ k −α and the magnetic energy dissipation rate (ε/η) which is a proxy for the energy of random footpoint motions induced by turbulent convection in the photosphere and below; ii) four area-independent parameters of the soft X-ray emission: the area-normalized flux in Yohkoh Al.1 and AlMgMn channels, the emission measure and temperature of the coronal plasma. Here we report that the area-normalized soft X-ray flux correlates with both the power index α (Pearson correlation coefficient ρ = 0.72/Al.1 and 0.73/AlMgMn) and the magnetic energy dissipation rate ε/η (ρ = 0.68/Al.1 and 0.70/AlMgMn). Also, both magnetic parameters are well-correlated with the logarithm of the emission measure (ρ = 0.72) and the logarithm of temperature (ρ = 0.59/α and 0.63/ε/η). Our results present strong observational support to those coronal heating models that rely on random footpoint motions as an energy source to heat the corona above active regions.