The question asks about the organization responsible for setting up the Atal Innovation Mission (AIM). Understanding the backdrop and purpose of the AIM is crucial for answering this question correctly.

The Atal Innovation Mission is a flagship initiative set up by the Government of India to promote innovation and entrepreneurship across the country. Here's the step-by-step reasoning:

1. Understanding AIM: AIM aims at fostering innovation and entrepreneurship nationwide through initiatives like Atal Tinkering Labs, Atal Incubation Centers, and programs to support students and startups.
2. Identifying the Ministry/Department: The alignment of AIM with the planning and development policies of India suggests it would be under a body closely related to strategic planning and economic policy.
3. NITI Aayog’s Role: The National Institution for Transforming India (NITI Aayog) is a policy think tank of the Government of India, providing strategic and technical advice across sectors. AIM operates under NITI Aayog, designed to serve as a catalyst for the national growth agenda through entrepreneurial sector development.
4. Ruling out Other Options:
   • Department of Science and Technology: While heavily involved in innovation and development, AIM's strategic alignment with national policy makes NITI Aayog the suitable parent body.
   • Ministry of Statistics and Programme Implementation: Primarily focuses on statistics and program implementations rather than incubating innovation directly.
   • Ministry of Corporate Affairs: Deals mostly with regulation and administration of corporate affairs, not directly involved in fostering innovation ecosystems.

Hence, the correct answer is NITI Aayog.

Conclusion: The Atal Innovation Mission, being a significant component of policymaking and development strategy, is under the auspices of NITI Aayog, reflecting its importance in shaping national economic and innovation strategies.