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I'm using Poisson Regression and Negative Binomial regression to estimate temporal trends of precipitation events. My understanding is that the coefficients are in log scale and they have to be translated to data-unit (count per time [ year, month...]) by EXP. Is it correct?

Negative binomial example

> library("MASS")
> Y= DF$Counts
> X= DF$ Years
> Nig<- glm.nb(Y~X) 
> summary(Nig)

Call:
glm.nb(formula = Y ~ X, init.theta = 6.190108641, link = log)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.19350  -0.81948  -0.06559   0.47013   1.85608  

Coefficients:
              Estimate Std. Error z value Pr(>|z|)
(Intercept) -18.316582  19.892078  -0.921    0.357
X             0.010564   0.009947   1.062    0.288

(Dispersion parameter for Negative Binomial(6.1901) family taken to be 1)

    Null deviance: 32.207  on 29  degrees of freedom
Residual deviance: 31.059  on 28  degrees of freedom
AIC: 210.93

Number of Fisher Scoring iterations: 1


              Theta:  6.19 
          Std. Err.:  2.23 

 2 x log-likelihood:  -204.928 

The slope (trend) = 0.01056 on Log scale and to change it to count per year= exp(0.01056)= 1.011. So the trend = 1.011 event per year

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