Using the results of our first paper on the Chandra HRC observation of the Orion Nebula Cluster ( ONC ) , here we explore the relation between the coronal activity of its 1-Myr-old pre-main sequence population and stellar parameters . We find that median X-ray luminosities of low mass stars ( M / M _ { \odot } \lesssim 3 ) increase with increasing mass and decreasing stellar age . Brown dwarfs ( 0.03 \lesssim M / M _ { \odot } \lesssim 0.08 ) follow the same trend with mass . From M \sim 0.1 to M \sim 0.5 ~ { } M _ { \odot } , median L _ { X } / L _ { bol } values increase by about half an order of magnitude and then remain constant at \sim 10 ^ { -3.5 } for the mass range from 0.5 to 3.0 M / M _ { \odot } . In these same two mass ranges , L _ { X } / L _ { bol } remains roughly constant with age , until it drops by more than two orders of magnitudes at the epoch when \sim 2 - 4 M _ { \odot } stars are expected to become fully radiative . We find a dependence of L _ { X } and L _ { X } / L _ { bol } on circumstellar accretion indicators and suggest three possible hypotheses for its origin . In spite of improved X-ray and rotational data , correlations between activity indicators and rotation remain elusive for these stars , possibly indicating that stars for which rotational periods have been measured have reached some saturation level . Our study of X-ray activity vs. stellar mass leads us to propose that the few HRC X-ray sources not associated with any optical/infrared counterpart trace a yet to be discovered stellar population of deeply embedded , relatively massive ONC members .