This is obvious if you have a dog, but cool to see it studied.
My dog is a velcro dog, he follows me everywhere. If I change direction he will too. If I start to run he will too. One amusing thing on our walks is he will walk confidently, determinedly in one direction, as if he is rushing to a destination. Then if I change direction, he immediately does too, as if forgetting about his original destination in the first place. Anthropomorphizing a bit I know.
This article suggests all dogs are like this, mine just might do it to a stronger degree.