What do the various unit stats do?

Units all have the following basic stats:

HP: When this number reaches 0 in battle, the unit is knocked out (KO)
TP: Required to activate various abilities
AP: Required to activate various abilities including Limit Bursts
ATK: Mainly has an effect on physical attacks
MAG: Mainly has an effect on magical attacks
DEF: Mainly has an effect on defense from physical attacks
SPR: Mainly has an effect on defense from magical attacks
AGI: Mainly has an effect on how quickly your CT builds and on the unit's Evasion rate
DEX: Mainly has an effect on Accuracy and Critical Hit Rate
Luck: Mainly has an effect on Accuracy and Evasion
Bravery: Mainly has an effect on Physical Dmg and Reaction Ability activation
Faith: Mainly has an effect of Magical Dmg and Reaction Ability activation