252 PART 5 Looking for Relationships with Correlation and Regression

In Table 18-1, dose is the radiation exposure expressed in units called Roentgen

Equivalent Man (REM). Because Table 18-1 is sorted ascending by dose, by looking

at the Dose and Outcome columns, you can get a rough sense of how survival

depends on dose. At low levels of radiation, almost all animals live, and at high

doses, almost all animals die.

How can you analyze these data with logistic regression? First, make a scatter plot

(see Chapter 16) with the predictor — the dose — on the X axis, and the outcome

of death on the Y axis, as shown in Figure 18-1a.

In Figure 18-1a, because the outcome variable is binary, the points are restricted

to two horizontal lines, making the graph difficult to interpret. You can get a bet-

ter picture of the dose-lethality relationship by grouping the doses into intervals.

In Figure 18-1b, we grouped the intervals into 200 REM classes (see Chapter 9),

and plotted the fraction of individuals in each interval who died. Clearly,

Figure 18-1b shows the chance of dying increases with increasing dose.

Fitting a function with an

S shape to your data

Don’t try to fit a straight line if you have a binary outcome variable because the

relationship is almost certainly not a straight line. For one thing, the fraction of

individuals who are positive for the outcome can never be smaller than 0 nor

larger than 1. In contrast, a straight line, a parabola, or any polynomial

FIGURE 18-1:

Dose versus

mortality from

Table 18-1: each

individual’s

data (a) and

grouped (b).

© John Wiley & Sons, Inc.