The answer is, we don't ever know, and we aren't meant to know. The characters in the film suspect Peter, but obviously it wasn't him, because the killer is still in the attic at the end of the movie. Although the movie toys with the idea that 'Billy' (as the killer refers to himself in the bizarre phone calls he makes) might be one of the girls' boyfriends (like Chris or Peter), in the end we can only assume that Billy is a stranger. There are several clues during the film indicating that crimes have been commited recently on campus, such as the rape mentioned at the beginning of the movie. You're not meant to be sure if those references, the killings inside the house or the young girl that is murdered in the park is the work of a single killer, multiple killers or if it's a series of coincidences.
1. Clare - Suffocated with plastic sheeting2. Ms. MacHenry - Hook pulley thrown into face/neck3. Janice - Found dead in the park4. Barb - Stabbed to death with a glass unicorn figurine5. Phyllis - Kiled off-screen6. Officer Jennings - Found with throat slit7. Peter - Bludgeoned with a fireplace poker (Killed by Jess)A girl is mentioned to have been raped in the park a few weeks before.Jess is implied to have been killed during the credits but it is unconfirmed.