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I have two datasets. To simplify, they look something like this:

CountyMonthYear      TotalPop      FatalOverdoses
Brown_2017_01        2546          1
Brown_2017_02        2346          2
Jackson_2017_01      78345         7
Jackson_2017_02      80456         10

And:

CountyMonthYear      TotalPop      DrugSeizures
Brown_2017_01        2546          3
Brown_2017_02        2346          5
Jackson_2017_01      78345         20
Jackson_2017_02      80456         30

I want to find the relationship between drug seizures (predictor) and fatal overdoses, so likely using multiple linear regression. I'm wondering:

Should I use the raw counts of drug seizures and overdoses? Or, should I use seizures per capita as a predictor? Or, should I use population and drug seizures (raw) as separate predictors?

I've ran this model with raw data (i.e. regressing # of fatal overdoses on # seizures and not using population as predictor) and get a very good R-squared. BUT: I'm guessing this model is really just correlating the relationship between population and overdoses.. since clearly more populous counties have more seizures and more overdoses, and less populous counties have less of both.

When I regress per capita overdoses on per capita seizures, the R-squared goes to about 0. I'm struggling with how to proceed here in developing a model and how to transform these variables. Thanks in advance!

kjetil b halvorsen
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DiamondJoe12
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    You would usually model counts with a Poisson regression including (log)-population as an offset. You might want to log transform the count predictor. – mdewey Aug 19 '21 at 15:44
  • So, when you say using log population as an offset, you mean including it as a predictor? By not using per capita, aren't I missing the interaction between pop and seizures? – DiamondJoe12 Aug 19 '21 at 18:54
  • Does this answer your Q? https://stats.stackexchange.com/questions/358980/can-i-model-incidence-per-1000-people-per-month-using-poisson-regression-without – kjetil b halvorsen Aug 20 '21 at 16:24

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