Oh I forgot to say - the reason you go out with them is so you can give them a treat for pottying right there. Otherwise there is no incentive for them
Plus, if you give the treat when they run back to the door they think it's for coming to the door, not for pottying outside. I believe the reason my dogs are completely housetrained while many Yorkies are not is because we do not have a fence so my dogs go out on leashes (Flexi's) and I either go outside with them or stand in the door and encourage them and praise them when I see them go. If I just let them out to play in a yard they would totally just chase birds and squirrels
I mean, now they are trained and know why they are going outside, but when they were puppies they had no idea. I had to teach them why we were out there!