# Poisson Regression and Negative Binomial regression results interpretation

I'm using Poisson Regression and Negative Binomial regression to estimate temporal trends. 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 multiplying them by 100. 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, it has to be multiplied by 100. So the trend = 1.056 count per year

## migrated from stackoverflow.comFeb 14 '17 at 19:20

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