276 PART 5 Looking for Relationships with Correlation and Regression

»

» ^{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 Pr}

| |

z , 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).

Discovering other uses for

Poisson regression

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

Poisson regression.

FIGURE 19-3:

Poisson

regression,

assuming a

constant increase

in accident rate

per year with

trend line.

© John Wiley & Sons, Inc.