The intelligence stat determines the mana regeneration of pets.  

It also to a very small degree determines the spell damage of magical spells.

The above chart shows the effect of Intelligence on mana regen every 10 seconds without additional mana regeneration attributes.

The above chart shows the effect of Intelligence on mana regen every 60 seconds without additional mana regeneration attributes.

The intensity weight of Intelligence is 0.5 when training.

Intelligence has a cap of 700 on a pet.

It should be noted that Intelligence, Strength and Dexterity share an stat intensity cap of 2300 intensity weight points. 

Due to the fact strength has to be sacrificed for Intelligence, it is often not advised to max  Intelligence to 700 unless the pet relies on it's ability use.

This pet has reached a pet 2300 intensity value for Strength (2100), Dex (15) and Intelligence (185) combined. 

The max intelligence it could achieve was 370 due to strength being capped at 700 and Dexterity capped at 150.

To see how different values of Intelligence and Mana Regeneration state affect total Mana Recovery, use our Mana Regen Calc