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Not sure of the best way to word the title but this is the scenario:

I am running MLR and GLMs to predict a numeric count response. Lets say one of my predictors is binary with two levels, "Yes" and "No". If the variable is a "No" the response variable is always 0 indicating no response activity on those observations.

I have about 8760 observations and 295 have this "No" category in tis specific variable. Including this variable of course makes my model better but from an information perspective, is it really lending anything useful or insightful to my overall model if I automatically know that having a "No" makes the response a 0? Is there a term for this type of phenomenon and how is it beneficial?

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Yes, that's an important variable!

You basically assure yourself of getting a count of zero if that one predictor is "no", seemingly regardless of the other predictors. If you get a "yes" then perhaps it doesn't help you, but you certainly get a lot predictive power out of that one variable when it is "no".

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  • $\begingroup$ Thank you! My question might seem silly or intuitive but I suppose I was just trying to grasp the fact that if this variable accounts for a lot of predictive power in the model, since it is obvious what it predicts (we can see by just looking at summary statistics), is it taking away statistical utility of other variables? In the case of inference and not purely producing a model that predicts the best results I suppose is where my mind is going. $\endgroup$
    – Coldchain9
    Nov 3, 2020 at 21:24

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