Augmenting model predictions with another model

Hello All,

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,
That is definetely one option! Another is Bayesian model averaging, i.e average the predictions from the two models.
Thanks for the reply!

I'm vaguely familiar with Bayesian Model Averaging, but I'm not sure about applying the technique when one of the 'models' is actually just a single point estimate (I am unlikely to get any useful information about the model used to generate the point estimate X_1).

Can you recommend any good sources that might help me incorporate BMA into my analysis?

Thanks again.