In the process of solving real-world multi-objective problems, many existing studies only consider aggregate formulations of the problem, leaving the relationships between different objectives less visited. In this study, taking the software upgradability problem as a case study, we intend to gain insights into the inter-objective relationships of multi-objective problems. First, we obtain the Pareto schemes by uniformly sampling a set of solutions within the Pareto front. Second, we analyze the characteristics of the Pareto scheme, which reveal the relationships between different objectives. Third, to estimate the inter-objective relationships for new upgrade requests, we build a predictive model, with a set of problem-specific features. Finally, we propose a reference based indicator, to assess the risk of applying single-objective algorithms to solve the multi-objective software upgradability problem. Extensive experimental results demonstrate that, the predictive models built with problem-specific features are able to predict both algorithm independent inter-objective relationships, as well as the algorithm performance specific indicator properly.