Regard for self carriage means that the horse needs to learn to maintain speed, stride length, posture, contact and head position without constant nagging with legs, spurs or reins. You should be able to remove your aids and the horse should maintain the speed, posture and contact. 

Any aid that you are holding on constantly, means the horse is not in self carriage. You can test the self carriage by giving on one or both reins, or removing your legs, and the horse should not change speed or contact. 

The same is true for staying on your line - the horse should remain on your line or on a circle until told otherwise.