You have already investigated Poisson regression models for the total number of plant species in the Galpagos

Question:

You have already investigated Poisson regression models for the total number of plant species in the Galápagos islands. This exercise will examine Poisson models using the number of endemic plant species (species found only on that particular island) as the response.
a. Fit a Poisson regression model to the endemic species count (endemic) with covariates log(area) and log(elevation). Conduct the LRT to determine if at least one of the covariates is significant. Examine the deviance and Pearson statistics for this model, and comment on the model’s goodness of fit.
b. Determine if addition of the covariates nearest, scruz, and adjacent significantly improves the model’s ability to predict the mean number of endemic species. Examine the deviance and Pearson statistics for this model, and comment on the model’s goodness of fit.
c. Based on your answers to Parts A and B, which final model would you select for the endemic species counts? For the model you chose, examine the Pearson residuals to check for overdispersion, and fit an overdispersed model if necessary.