Where µ is the average number of accidents occurring in the given year. The
regression of the Poisson distribution is the logarithm of the response variable is given
as
log Y= β β X βn X n
... 0
+ 1 1
+ and so ( )( )( )
1 1 1 1
x x
Y e e e
βo β β
= . Therefore, Poisson
Regression model expresses the log outcome rate as a linear function of the set of
predictors. The assumptions of the Poisson regression includes: