If this man is Olof Nilsson in Bäck in Svensbyn his father was Nils Michelsson.
I have the family here: https://minaslaktanor.wordpress.com/svensbyn-nr-14/
The similarity is that Olof Nilsson on Bäck no 14 in Svensbyn had a daughter named Karin. And Daniel Olofsson had a sister named Karin.
But Svensbyn was big with 42-44 homesteads, so...
Do anyone know if this family is another one?