We have seen how locally weighted learning can be used to build accurate models from data, and how predictions can be made from the models. However, predictions are not the only things we would like a model to give us. In many applications, we want estimates of gradients, and of noise, and confidence intervals or distributions for all predictions. As noted in table 1, it can be difficult to get these things from many function approximators, but it can be done easily with locally weighted learning methods. The local models fit by Vizier are well understood statistically, and most common regression analysis techniques can be converted to local forms in order to provide the information we want. In this section, we summarize how prediction, noise, and gradient distributions are done.