You didn't respond to my point at all. There is a true signal, and there is the measured signal. We're measuring, obviously, the measured signal. It is, accordi

You didn't respond to my point at all. There is a true signal, and there is the measured signal. We're measuring, obviously, the measured signal. It is, according to you, a weak proxy for the true signal. That is, it correlates with it at some level. Secondly, we have another variable 'spending'. We can measure that this 'spending' variable correlates with the measured variable. Therefore, we know that those two variables are related in some way. Now, in terms of getting a bead on the true signal, do we care about the spending variable? The only reason we have to believe it has any relationship to the true signal is that it correlates with the measured signal! If we didn't know the measured signal directly, that might be useful. But we do. What I am saying is this: The performance tests are the best we have. There is no additive value of this 'spending' variable, as far as anyone i'm aware of can tell. If you have information to the contrary, i'm curious to hear it, though. Now, you may, perhaps even rightly, that say that the performance tests we have are so bad that they're useless. Well, i'm not going to take a position on that. The position that i'm taking is that adding 'spending' to your model does not minimize your loss function here, and there is no reason to believe that it would.