Value of information analysis is useful for helping a decision maker evaluate the benefits of acquiring or processing additional data. Such analysis is particularly beneficial in the petroleum industry, where information gathering is costly and time-consuming. Furthermore, there are often abundant opportunities for discovering creative information gathering schemes, involving the type and location of geophysical measurements. A consistent evaluation of such data requires spatial modeling that realistically captures the various aspects of the decision situation: the uncertain reservoir variables, the alternatives and the geophysical data under consideration. The computational tasks of value of information analysis can be daunting in such spatial decision situations; in this paper, a regression-based approximation approach is presented. The approach involves Monte Carlo simulation of data followed by linear regression to fit the conditional expectation expression that is needed for value of information analysis. Efficient approximations allow practical value of information analysis for the spatial decision situations that are typically encountered in petroleum reservoir evaluation. Applications are presented for seismic amplitude data and electromagnetic resistivity data, where one example includes multi-phase fluid flow simulations.