In this paper, we first propose a self-tuning distributed observer for a multi-agent system, which is capable of providing the estimation of the leader's signal to various followers without assuming all the followers know the system matrix of the leader. We then further develop a novel adaptive distributed control law to solve the cooperative output regulation problem for linear heterogeneous multi-agent systems. This control law offers two advantages in that it makes less use of the information of the network as well as the information of the leader and external disturbances, and it avoids calculating the observer gain.