Use Poisson regression when the Y values are the actual number of objects or events counted. Be sure the values are not normalized in any way but represent the number of objects or events actually counted. Let's say that the Y values are radioactivity, you counted each sample for 10 minutes, but the instrument reported counts per minute. It would be a mistake to analyze the counts per minute data with Poisson regression, since those are not the actual number of radioactive decay events that were counted. You'd need to multiply all those values by 10 (the number of minutes each sample was counted) to have the actual number of events counted.
Since the Y values are counts, they can't be negative or fractional.
These options are not available with Poisson nonlinear regression
•No standard errors of parameters.
•Confidence intervals of parameters are always computed using an algorithm that usually produces asymmetrical confidence intervals. There us no option for a simpler method that reports symmetrical confidence intervals.
•No confidence or prediction bands.
•No normality tests of residuals (since the residuals are not expected to be Gaussian).
Ordinary regression (assuming residuals are Gaussian) works by minimizing the sum-of-squares of the residuals. This works because minimizing the sum-of-squares is the same as maximizing likelihood when the residuals are sampled from a Gaussian distribution.
Poisson regression works differently, directly maximizing the likelihood.