**Introduction**

Poisson regression is an underutilized but powerful regression model. In this blog entry, we’ll show you to run and interpret a Poisson regression model in R.

**Access Data and Libraries**

Install ggplot if you have not already done so, and load ggplot2:

install.packages("ggplot")

library(ggplot2)

Now access the dataset warpbreaks:

warpbreaks

head(warpbreaks)

**Why Poisson Regression?**

Poisson regression is typically used when your outcome / dependent variable is a count variable. In warpbreaks, breaks is a count variable: It represents the number of times a break occurs given a specific wool and tension level. That makes Poisson regression well-suited to the warpbreaks data.

**Run the Poisson Regression**

Let’s try to quantify the number of breaks as a function of wool, tension, and wool-tension. Try the following code:

poisson.output <-glm(formula = breaks ~ wool+tension, data = warpbreaks, family = poisson)

print(summary(poisson.output))

Here’s what you get:

Note that the model returned three statistically significant results. Wool B is associated with e^-0.20 (about 0.81) fewer breaks than Wool A, tension M is associated with e^-0.32 (about 0.73) fewer breaks than tension L, and tension H is associated with e^-0.52 (about 0.60) fewer breaks than tension M.

You can also get the exponentiated results in a table instead of calculating them as we did. First, note that you will need to install broom through the command:

install.packages("broom")

Next:

library(broom)

tidy(poisson.output, conf.int = TRUE, exponentiate = TRUE)

**Visualize Data**

Try the following R code:

library(ggplot2)

boxplot.wool<-ggplot(warpbreaks, aes(x=wool, y=breaks)) + geom_boxplot(col="firebrick")

boxplot.wool

Here, you get a sense of there being fewer breaks associated with B. Next, try the following R code:

boxplot.tension<-ggplot(warpbreaks, aes(x=tension, y=breaks)) + geom_boxplot(col="firebrick")

boxplot.tension

And here, you get a sense of there being fewer breaks associated with tensions M and H.

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