, which gives a 95 percent CI of 0.71 to 1.95 (around the estimate 1.33).

The column labeled z value contains the value of the regression coefficient divided by its SE. It’s

used to calculate the p value that appears in the last column of the table.

The last column, labeled

, is the p value for the significance of the increasing trend

estimated at 1.33. The Year variable has a p value of 2.71 e-05, which is scientific notation (see

Chapter 2) for 0.0000271. Using α = 0.05, the apparent increase in rate over the 12 years would be

interpreted as highly statistically significant.

AIC (Akaike’s Information Criterion) indicates how well this model fits the data. The value of

81.72 isn’t useful by itself, but it’s very useful when choosing between two alternative models, as

we explain later in this chapter.

R software can also provide the predicted annual event rate for each year, from which you can add a

trend line to the scatter graph, indicating how you think the true event rate may vary with time (see

Figure 19-3).

© John Wiley & Sons, Inc.

FIGURE 19-3: Poisson regression, assuming a constant increase in accident rate per year with trend line.

Discovering other uses for Poisson regression

The following sections describe other uses of R’s GLM function in performing Poisson regression.

Examining nonlinear trends

The straight line in Figure 19-3 doesn’t account for the fact that the accident rate remained low for the

first few years and then started to climb rapidly after 2016. Perhaps the true trend isn’t a straight line,

where the rate increases by the same amount each year. It may instead be an exponential increase,