Constructions for regression graphs and verification of the statistical model via linear, linearized, and logistic regressions along them have recently been intensively studied. Given the graph, an iterative regression method, using local averaging estimators, is introduced for prediction, based on a complete training sample. The method makes it possible to perform nonparametric regressions recursively, irrespective of the type of the context and response variables. As a consequence, predictions for the multiple response variables of a test sample are performed in the possession of their context variables only. Consistency is proved if the joint distribution is Markov compatible with a DAG or with a regression graph. In the latter case, the prediction goes on from chain component to chain component, with vector valued smoothers, mainly of product kernel types in the implementation. Practical considerations and application to randomly generated and real-world data are also presented.