The character of Laura, although played by a different actress, is the same one who appeared in the episode Monday is Forever. In that episode, Laura is moving to Detroit, but in this episode it's Chicago.
Laura: When we moved to Chicago, I met a bunch of kids, and there were lots of parties, and... Buddy, they all drank! I couldn't believe it! I hated it, but... I wanted to fit in. You understand.
Buddy: I'm sure some of the kids didn't. You're only 15.
Laura: Oh, Buddy... What am I gonna do?
Buddy: What do you wanna do?
Laura: I... just... wanna feel like someone. I wanna feel... like Laura Richardson. Only I don't.... (starts sobbing) I don't know... who that is.
Buddy: I do. Laura Richardson is a friend of mine. I've known her since I was a little kid. She's terrific. Anything you wanna know about her, I can tell you. You'll like her, once you get to know her.