Inverse distance weighting (IDW) is a simple method for multivariate interpolation but has poor prediction accuracy. In this article we show that the prediction accuracy of IDW can be substantially improved by integrating it with a linear regression model. This new predictor is quite flexible, computationally efficient, and works well in problems having high dimensions and/or large datasets. We also develop a heuristic method for constructing confidence intervals for prediction. This article has supplementary material online.