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I have a set of predictor variables (X1, X2...XN) and a single continuous response variable (Y) that I would like to build a prediction model from. The Y in this case, is the Volume of material but it is often expressed in units such as Volume per inch of rain, per foot of length. During the course of my sampling, we will be measuring both the volume, inches of rain, and the length.

My question is: Should these two 'denominator values' be used as predictors (Xs) and the Y is just the volume, or instead, do we first calculate the Y as Vol/rain*feet and use that as the response?

i.e.: is Vol = f(X1, X2, X-rain, X-length) or is it: Vol /(X-rain * X-length) = f(X1, X2)

kjetil b halvorsen
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DarwinsBeard
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  • Which (other) predictors do you have? Would they be more related to volume or to density? See https://stats.stackexchange.com/questions/58664/ratios-in-regression-aka-questions-on-kronmal – kjetil b halvorsen Apr 01 '21 at 01:06
  • The volume being measured is street trash, and the other predictors would be more things like median income, street sweeping frequency, street cleanliness score, etc. and therefore more related to volume (I think). THinking about it more, we suspect that the volume of trash measured to be related to the quantity of rainfaill and the curb length so (I think) I would answer my own question that I would want to include those 2 vars as predictors? Thanks! – DarwinsBeard Apr 01 '21 at 01:56

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