Minitab provides three link functions, allowing you to fit a broad class of Poisson regression models. These are the log link function, the square root link function, and the identity link function. The log and square root link functions transform the mean response. The identity link function does not.

You want to choose a link function that results in a good fit to your data. You can use goodness-of-fit statistics to compare fits using different link functions. Certain link functions may be used for historical reasons or because they have a special meaning in a discipline.

For the resin defect data, the quality analysts at the company chose to use the natural log link function. If the lack-of-fit tests were significant, the analysts could try a different link function to improve the fit.