Black Christmas

A disoriented man climbs up into the attic of a sorority house while the occupants hold a Christmas party. Jess Bradford (Olivia Hussey) starts to receives an obscene phone call from "the moaner", a man who has been calling the house. After, she calls sorority friends Barb Coard (Margot Kidder), Phyllis "Phyl" Carlson (Andrea Martin), Clare Harrison (Lynne Griffin), and several other girls to listen. He starts saying perverted things to them before Barb provokes the caller, to which he replies "I'm going to kill you" before hanging up. Barb and Clare slightly argue about the things she said to him and Clare goes upstairs to pack. After she hears the noise of the house's cat and investigates, she is strangled and suffocates by an unseen assailant with plastic wrapping. Her body is brought into the attic and is placed on a rocking chair.
The next day, Clare's father arrives to look for Clare to bring home for the holidays; the housemother Mrs. Mac (Marian Waldman) can't seem to help him and neither can Phyl or Barb. Meanwhile, Jess meets with her boyfriend Peter Smythe (Keir Dullea), a neurotic aspiring pianist at the piano recital hall to inform him that she is pregnant and wants to have an abortion. Peter becomes suspicious and urges her to discuss the situation with him. but she refuses. Elsewhere, Mr. Harrison, Barb, and Phyl go to the police to report Clare's disappearance.
Clare's boyfriend Chris (Art Hindle) is informed by Jess about the disappearance while playing hockey. They then discussed it with Lt. Kenneth Fuller (John Saxon); a mother, Mrs. Quaife (Martha Gibson), reports that her daughter Janice is missing as well. That evening, Mr. Harrison, Chris, and the sorority sisters join a search party for Janice and Clare. Back at the house, Mrs. Mac looks for the cat and discovers Clare's body before she is hooked into the neck by the killer and dragged up. After the search party finds Janice's dead body, Jess returns home and receives another obscene call in which contacts the police to report it. Unaware of Peter in the house, he startles her and starts to argue about her planned abortion before leaving upset after Lt. Fuller arrives at the house to discuss the phone calls. A technician then places a tap "bug tracer" onto the phone and Lt. Fuller informs that there will be another officer stationed outside the house. As Christmas carolers visit to the house and sing, the killer sneaks into Barb's room and stabs her with a glass unicorn head while her screams are drowned out by the carolers. Jess receives another obscene call that quotes a part of the argument she had with Peter.
Phyl goes upstairs to bed and checks into Barb's room before the killer shuts the door from behind and murders her off-screen. Another call comes in and this time, Jess manages to keep Billy on the phone for a minute to allow the police to trace it. Jess is then informed that the calls are coming from the house and is ordered to leave the house immediately. Shocked, Jess puts down the phone and yells up to Barb and Phyl. She arms herself with a fireplace poker and ventures upstairs only to find Barb and Phyl's bodies on the bed. Before leaving, she sees the killer's eye spying on her through the door crack, and she slams the door to flee. Jess is chased through the house before she locks herself in the cellar. Peter appears outside a basement window, telling Jess he heard screaming. He enters and approaches her before she, believing him to be the killer, bludgeons him in self-defense.
Lt. Fuller and the police arrive and finds a fatigue Jess in the basement with Peter's dead body. Later, she is sedated and rest in her bed while the officers discuss about the killer; they believe how Peter must have been the killer and the bodies of Clare and Mrs. Mac have oddly not been found yet. The officers leave the house for Jess to sleep and stations an cop outside for the forensics to arrive. As the house becomes quiet, the camera pans to the attic door opening up, discovering the killer was not Peter and says "Agnes, it's me Billy" before the telephone begins to ring while the credits roll.

Question: who is this person came into room?