Given the common problem of predicting response variable $Y$ from predictor variables $X$ and $Z$, is there any way to determine the "theoretical best" prediction possible for a response variable?
When I am asked to find a model to do such a prediction, I might try different techniques: e.g. linear regression, KNN, etc. However, if $X$ and $Z$ are simply not predictive at all of $Y$, then no matter how good of a model I have, it is a waste of time. For example, if I am trying to predict a student's grade in a class, then using the temperature in Hawaii and the GDP of France will be a complete waste of time. How can I determine that without trying it (or knowing a priori)?
In other words, how do I find out if I should even be using $X$ and $Z$ to predict $Y$ in the first place? Is there some way to calculate an upper bound for the "best" a model I can possibly hope to generate?