This paper investigates a simple, yet effective method for regression on graphs, in particular for applications in chem-informatics and for quantitative structure-activity relationships (QSARs). The method combines Locally Weighted Learning (LWL) with Maximum Common Subgraph (MCS) based graph distances. More specifically, we investigate a variant of locally weighted regression on graphs (structures) that uses the maximum common subgraph for determining and weighting the neighborhood of a graph and feature vectors for the actual regression model. We show that this combination, LWL-MCS, outperforms other methods that use the local neighborhood of graphs for regression. The performance of this method on graphs suggests it might be useful for other types of structured data as well.