This paper investigates the impact of data integrity attacks (DIAs) on cooperative economic dispatch of distributed generators (DGs) in autonomous AC microgrids. To establish resiliency against such attacks and ensure optimal operation, a linear regression based control update is designed in this paper. To improve the robustness against multiple points of intrusion, the design of the resilient control update involves local measurements. As a result, any maloperation due to DIA is prevented from being propagated to the neighboring nodes. The proposed strategy acts immediately upon detection of data integrity attack to ensure maximization in the economic profit.