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A bit of a newbie statistics question. In a GLM, would it be sound to use a dependent variable that incorporates one (or more) independent variables? For example, if my dependent variable is number-of-occurences-per-sq-km of a site ("density"), could I use site area (measured in sq km) as one of my independent variables? My intuition says that's a bad idea, but I'm not sure if that's the case.

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I do not know the exact problem you are looking to solve. But If I was to extrapolate from what you are suggesting, we can look at something like number of fire stations in a city.

It would absolutely matter how big the city is area wise to look at the trends, and once again its a subjective call based on the problem you are solving and the other variables involved, in my case it could the number of chemical industries around, fuel depots and so on.

So contrary to your intuition might not be a bad idea after all.

Hope my perspective helps!

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  • $\begingroup$ You've got the exactly the right idea. Let's say I have data for a number of cities, and my dependent variable is firestations-per-unit-area. I was wary of using the area of a city in my independent variables, as it's obviously part of the calculations for my dependent variable values. But you're right, cities of different areas could easily have different firestation densities. So I guess using the city area as a predictior in my GLM is OK? $\endgroup$
    – Fishbee
    Jul 23 '15 at 12:05
  • $\begingroup$ Yes! I think it should be okay. Check the accuracy metrics of your model on your test data with and without. I am guessing with Area will be more accurate. (Working with limited information here, so just an intuition!) $\endgroup$
    – CodePhobia
    Jul 23 '15 at 12:38

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