They only affect social standing, but you can't unlock certain social links unless a stat is at a specific level. For instance, for Mitsuru you can't have her S Link unless your Academics is at maximum level. You increase stats by answering the right questions at school, doing odd jobs (for instance, having the courage to drink the nurses's disgusting concoction when you are sick), giving money to the shrine (which randomly increases academics), studying, and other things.