multiply by the desired dispersion before adding the shift. Now you have it!

@WangWang if E(Y|Z) differs from E(Y) then you definitely could use Z to predict Y. Otherwise you cannot use it to predict Y's expectation, but this does not mean it could hold other type of information like, for example, variance

It looks to me as if your models had excessive complexity (this has already been pointed out by a previous answer) Could you please provide further information about model specifications and the data you use to train your model?

@Glen_b When I said "high value" I meant "high in magnitude", either positive or negative