Decision tree for output prediction I have satellite data that provides radiance which I use to compute the Flux (using surface and cloud info). Now using a regression method, I can develop a mathematical model directly relating radiance and flux and can be used to predict the flux for new radiance values.
Is it possible to do same using decision trees or regression trees? In a regression there is mathematical equation connecting dependent and independent variable? Using decision trees, how  could you develop such a model?
 A: You can do it with decision trees for sure or any other regression model for that matter. Use any of the packages which have this method available (you can find lots of info about how to do it in R or Python or various statistical software programs). They all work exactly the same - have some input x, have some output y, train it mymodel.train(x, y), and you have the model. Do proper cross-validation and you're done. I'm not sure how you are building your regression right now, but I'm sure this is not much different from it.
A: In algorithmic modeling, as opposed to parametric modeling, there is no explicit equation relating input and output variables (see this paper by Breiman). The assumption is that the phenomenon being modeled is complex and unknown, and rather than imposing a formal model (which comes with a suite of assumptions and limitations), algos directly learn the links between predictors and predictand from the data. In the case of a single tree, this is not so much of an issue because the tree explains its predictions in a very visual and intuitive manner, but with ensemble of trees (Random Forests, Boosting), interpretability is definitely traded off for accuracy. 
A: To predict on a continuous variable the decision tree must essentially bin the variable and you are left with terminal nodes each with an average value for your prediction.  Some programs like RapidMiner force you to bin the value yourself before predicting and some do it on the fly, behind the scenes.  But you could always do something like use your tree to score a dataset that contains X values across the full range of X and derive some kind of equation from the prediction results, Y.
But the problem with this is decision trees are not phased by non-linear relationships in your data.  So in your scored dataset you might see several different "strata".
A better solution might be to think of the decision tree as a tool to identify these "linear strata" beforehand and then build a regression model for each, or the most "important", depending on your domain for example.
Hope this helps!
