# interpretation of slope estimate of Poisson regression

I have seen the other posts regarding interpretation of slope estimates of a Poisson regression and based on that, this is my interpreation of a poisson regression. Can anyone advise me if I can write the below statement:

mdl<-glm(y ~ year, family="quasipoisson")
summary(mdl)

Deviance Residuals:
Min       1Q   Median       3Q      Max
-2.8258  -1.4108  -0.5760   0.8562   3.2575

Coefficients:
Estimate Std. Error t value  Pr(>|t|)
(Intercept) 68.918820  14.838432   4.645 0.0000216 ***
year        -0.034351   0.007531  -4.561 0.0000289 ***

slope<-exp(mdl$coefficients[2]) # 0.9662321 slope - 1 # -0.03376786  Can I make the following statement: one unit increase in year causes y to decrease by 0.033units? Thanks • It's possible that you have missed that the link function is not linear here, but log. Matthew Drury's answer correctly deals with the consequences of this fact but didn't explicitly mention it; and given the form of the question - most particularly that you call it the slope (it isn't) - I am concerned that you might not have realized that was the case. On the other hand, you do exponentiate the coefficient (even while still calling it the slope) so the issue might be more a language one than an issue of actually thinking of it as the slope of a line in the scale of the response. Sep 8, 2016 at 23:44 • Thank you for the comment. Your comment and the answer below was really helpful for my work. Sep 12, 2016 at 10:36 ## 1 Answer No. There are two problems, one is an arithmetic to english translation, and one is philosophical. The phrase "decrease by 0.033 units" is to be interpreted as "subtract 0.033 units from y", which is incorrect. Better is either One unit increase in year corresponds to multiplication of y by 0.966. or One unit increase in year corresponds to a$3.3\%\$ decrease in y.

The percentage sign is very important, it carries the information that the decrease is multiplicative, not additive.

The other is your use of the word causes. That is a heavy word, you should not use it without serious consideration. Certainly a regression cannot demonstrate causation alone, it must be combined with either a randomly assigned experiment, or some scientific reasoning to believe that causation exists (in which case the regression is but estimating its effect size).

• Thanks a lot. For the second part, I understand my choice of predictor variables has to be based on scientific reasoning. For the first part, I will follow the second sentence. Sep 8, 2016 at 21:19