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I want to see if Wikipedia articles for topics featured in popular documentaries get a boost in page views on the day the documentary is aired. I then want to see if time on screen is a predictor of this boost.

I have to account for baseline popularity but I'm not sure how. For instance, the Wikipedia article for global warming will have a different average number of hits per day than the article for acid rain.

My working solution has been to use the yearly average Wikipedia hits for each article as a baseline. I will have data on the number of hits for each article from the day the documentary aired. So I can calculated a percentage change from baseline to airing date (doc_hits).

Article         Wikipedia_baseline   doc_hits   %_change   seconds_on_screen 
global_warming  300                  450        50         60  
acid_rain       100                  260        30         160
plastics        250                  600        75         140

But if I feed this into a GLM, I'm worried I'm being circular e.g.

glm(%_change ~ seconds_on_screen + Wikipedia_baseline)

Here the %_change has been generated using the Wikipedia_baseline but I obviously need to take the popularity of the articles into account.

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Your basic idea seems sound, but it could be implemented better. doc_hits is a count variable, so a poisson distribution is a good starting point, but I am quite sure we will see overdispersion in this case, so I propose a quasipoisson family. But you are interested in the %_change, that is, a rate. So you need poisson rate regression, then you use the number_of_views as response, and Wikipedia_baseline as an offset:

   glm(number_of_views ~ offset(Wikipedia_baseline) + seconds_on_screen, family=quasipoisson(), data= )

which is the correct form of your proposed model. Your problem also has time-series aspects, which I do not discuss in this answer, which is meant as a point of departure.

(an offset is a variable with a known coefficient of 1, which is not estimated). Poisson rate regression is thoroughly discussed in Goodness of fit and which model to choose linear regression or Poisson Other posts with examples is Poisson Rate Regression: Offset? and How is a Poisson rate regression equal to a Poisson regression with corresponding offset term?

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