The amount of personal information contributed by individuals to digital repositories such as social network sites has grown substantially. The existence of this data offers unprecedented opportunities for data analytics research in various domains of societal importance including medicine and public policy. The results of these analyses can be considered a public good which benefits data contributors as well as individuals who are not making their data available. At the same time, the release of personal information carries perceived and actual privacy risks to the contributors. Our research addresses this problem area. In our work, we study a game-theoretic model in which individuals take control over participation in data analytics projects in two ways: 1) individuals can contribute data at a self-chosen level of precision, and 2) individuals can decide whether they want to contribute at all (or not). From the analyst's perspective, we investigate to which degree the research analyst has flexibility to set requirements for data precision, so that individuals are still willing to contribute to the project, and the quality of the estimation improves. We study this tradeoffs scenario for populations of homogeneous and heterogeneous individuals, and determine Nash equilibrium that reflect the optimal level of participation and precision of contributions. We further prove that the analyst can substantially increase the accuracy of the analysis by imposing a lower bound on the precision of the data that users can reveal.