Poisson or quasipoisson

One of the assumptions of Poisson regression to predict counts is that the event you are counting is Poisson distributed: the average count per unit time is the same as the variance of the count. In practice, "the same" means that the mean and the variance should be of a similar order of magnitude.

When the variance is much larger than the mean, the Poisson assumption doesn't apply, and one solution is to use quasipoisson regression, which does not assume that \(variance = mean\).

For each of the following situations, decide if Poisson regression would be suitable, or if you should use quasipoisson regression.

For which situations can you use Poisson regression?

  1. Number of days students are absent: mean 5.9, variance 49
  2. Number of awards a student wins: mean 0.6, variance 1.1
  3. Number of hits per website page: mean 108.2, variance 108.5
  4. Number of bikes rented per day: mean 273, variance 45863.84
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