Though nowadays people are probably more familiar with this tale as the plot of the 1979 horror film When a Stranger Calls (or its 2006 remake), "The Babysitter and the Man Upstairs" dates from the 1960s, when cell phones didn't exist and the notion of a stranger calling you from inside your own house had a bit more of a shock factor than it does now.
That doesn't mean it won't creep you out.

Comments
That is a creepy story! I wonder if it is based on any truth