What are my rights if I got attacked by a dog at a friend's house but the dog is not owned by the people who live in the house?

Generally, the dog owner is responsible for any damages or injuries their dog causes.  In this instance, there could be some liability with the dog sitters, depending upon why the dog bit you or what provoked the bite.  If the dog owners can show that the dog sitters were providing an environment or put the dog in a situation which would have incited the dog or provoked him to bite, the dog owners could point to the dog sitters and expect them to assume liability or share it.