The dog could also be looking for your blessing.
"If a dog should stare at its owner when relieving itself, he is most likely checking for approval to be sure that he is using the correct location," Nick Jones, dog behaviorist and trainer with Alpha Dog Behaviour in London, told The Dodo. "Perhaps if an owner had previously scolded their dog for pooping in the wrong area, this could cause anxiety in the dog as a result."
Another possibility is more instinctual.
"The pooping position is a vulnerable position for dogs," Friedman said. "The feeling of being vulnerable is left over from their wild ancestor, the wolf, who still has to fend for himself in the wild. I think dogs are making sure we have their backs while they're in that vulnerable position for an extended period of time."