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Friendship is basically the "character story" stat. Go to Lin's door and choose "talk" when she isn't in the kitchen and it isn't Wednesday. I'll note now that some events require you find the character in other rooms (or in 1 or 2 cases for Lin, talk to Ellen).

You need to talk to Ellen whilst she is at the reception desk to get the next step of Lin's story. This had me stumped for several in game weeks because I had already bought everything possible from Ellen and at the moment there does not seem to be any other reason to really talk to her most of the time! :P