If you want to just have your own yogurt bar then that's cool. If you want to have customers, I don't really think that's a good idea... Not many people would probably come. I would have it at a different location.
Great for family and friends. If you are thinking about selling, that is another story. Residential areas usually do not allow businesses. You need a license and health inspection to be able to sell to the public.
1meeshee is correct..You need to be in a business zone area and have permits like the.Board of Health etc I don't see anything wrong with starting a business in your home if you pass all the criteria and you have an inviting atmosphere in your home. Good luck