Hi can someone give me a hand?

So we are doing Poisson's Regression right now- we were asked to use the Generalized Linear Model - Distribution: Poisson's - Link function: log. My teacher has asked to write the regression equation with no guidance on how to do so. His advice was go do it in SAS, which would be useful if 1). I had a SAS license and 2). knew how to code in SAS. But without those I am left to JMP, which is in fact what the class is about so hopefully my frustration is understood.

I understand its theoretically "linear" and I understand log is used for our link but can someone help me write it out. I am finding conflicting errors online and I can't complete any of my homework with out this.

My y variable is Length of Stay in hospital, my X-variable is number of factors (number of medical items used during stay) My parameters are as followed:

I attempted to use the "prediction formula column to give me the formula, which said e^B0+B1x1 --> e^1.392+0.0021x. Is this what it is?

Also if whoever answers this has a solid understanding on Poisson's, I have an additional question on model adequacy.

THANK YOU

#STATISTICS