  We consider a simple approach for approximating detailed information about
the conditional distribution of a real-valued response variable, given values
for its covariates, using only the outputs from a standard regression model. We
validate this approach by assessing its performance in the context of quantile
regression; when applied to the outputs of linear, gradient boosted tree
ensemble and random forest models. We find that it compares favourably to the
standard approach for estimating quantile regression functions, especially for
commonly selected tail probabilities, and is highly competitive with the
quantile regression forest model, across a large collection of benchmark data
sets.
