I am currently working on a problem which involves predicting the value of some variable (which I will call Y), based on a number of input variables (X_i, i = 1..N). The problem is that one of the input values (X_1, say) is actually a prediction of Y produced from an independent model (the form of which is unknown). I want to build a model that combines the prediction, X_1, with my other input variables, X_i, i = 2..N, in order to produce a better estimate of Y.

Can anyone advise me on appropriate approaches for tackling this sort of problem? My initial thoughts were to build a regression model, and simply incorporate X_1 as one of the explanatory variables; does this sound sensible?

I will try to provide more information if necessary -- I know this is all a bit vague.

Many thanks,

Steven