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We consider a prediction problem based on opinions elicited from multiple agents. Making an accurate prediction with a minimal cost requires a joint design of incentive mechanisms and prediction algorithms. Such a problem lies at the interface of statistical learning theory and game theory, and arises in many domains such as the consumer surveys and mobile crowdsourcing. Under a fairly general problem setup, we jointly design a mechanism and algorithm to achieve the optimal system objective. Our results offer several valuable engineering insights. When the costs incurred by the agents are linear in the exerted effort, then the optimal mechanism calls for a “crowd-tender”, where the principal only employs the agent with the lowest bid. When the costs are quadratic, then it is optimal to use a “crowd-sourcing” mechanism that employs multiple agents at the same time. Synthetic simulations demonstrate the gains achieved under our proposed mechanism, as compared to those that do not account for the heterogeneity of the agents.