With the advent of smart grids, a significant amount of data has become available about the electric infrastructure. Much of research focus has been on exploiting newly available data sources such as smart meters and phasor measurement units. This paper proposes a new class of predictive analytics that can be built to manage existing infrastructure by combining new and old data sources together. Power transformers, one of the most critical assets in the grid, are perhaps frontrunners among 'smarter' set of assets which have significant instrumentation already installed to monitor their operating conditions such as load, voltage, and internal oil temperature. While such advanced instrumentation enables detailed operating condition monitoring, manual measurement of dissolved gas concentration has been the primary fault diagnostic method to identify their fault modes. Dissolved gas analysis (DGA) offers great potential to diagnose fault modes in such oil-immersed transformers. This manual routine DGA, however, is costly and not free from error. Fortunately, it is understood that the loading conditions of transformers are major drivers of fault modes in oil-immersed transformers. In this paper, a predictive model is proposed to predict accumulation of dissolved gas concentration in sealed substation transformers based on its historical loading conditions. A multi-dimensional regression approach is used to predict the concentration level of each gas in real-time. Measurements from historical dissolved gas analyses are used to solve the regression problem with a robust optimization framework. The simulation results show that the forecasting of each dissolved gas based on loading characteristics is possible with high regression accuracy ranging from 84% to 97%. Thus this method can be used to optimize DGA inspection schedules as well as to provide 'virtual DGA instrumentation' without the associated high cost.