As far as I can tell:
-STR doesn't affect anything;
-INT increases nukes' potency;
-PIE increases nukes and debuff's magic accuracy;
-MND increases Cure and Stoneskin potency and increases max MP;
-DEX increases weapon skills' (such as Radiance) accuracy;
-VIT increases max HP and defense.
I think INT also increases Spirit Darts damage.
Tranquillity (the instant MP recovery ability) might be affected by INT and/or MND but didn't bother to test with its long recast. Maybe it's only affected by the Rank.
As far as I can tell Elemental Resistance stats don't affect the damage you deal, just damage taken.
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