Answer:
It was based on a story that may or may not be true.
The movie The Exorcist was based on a novel of the same name by William Peter Blatty. The novel is based on the real-life attempt of a priest to exorcise a demon from a young boy (the boy was around the same age Reagan was in the movie). Whether or not the real-life case was a true occurrence of demonic possession, or an elaborate hoax, or just a matter of misdiagnosed mental illness, is debatable.
See the Related Links below for more information. You can try Googling "the Exorcist true story" to find even more of them.