Your basic stats in the game never go up. You may be able to get lucky and get some drunk fans or clovers for luck to increase them temporarily. This is where cards come in to boost these stats. Here is a breakdown of the stats for you.

Fans: Increase starbits rewards and allows you to do higher level missions
Luck: Increases average number of drunk fans you get and skill points from lessons
Skill: Used to offset Ego (unlocked at level 15) and ensure your starbits reward is not dropped
Income Modifier: Only for rankings currently.