This should tell you the model as well as when your serial# was authorized for production.
http://www.ismacs.net/singer_sewing_...-database.html
If your machine has a motor that is built in the machine instead of the standard motor and belt setup chances are it's a 15-91.
Moving the feed dog knob to the top of the bed was a brilliant move by the Japanese when they started copying the model 15.
Rodney