If b is a very large number, either positive or negative, the logistic curve becomes so steep that

it looks like what mathematicians call a step function, as shown in Figure 18-3b.

© John Wiley & Sons, Inc.

FIGURE 18-3: The first graph (a) shows that when b is negative, the logistic function slopes downward. The second graph (b)

shows that when b is very large, the logistic function becomes a “step function.”

Because the logistic curve approaches the limits 0.0 and 1.0 for extreme values of the

predictor(s), you should not use logistic regression in situations where the fraction of individuals

positive for the outcome does not approach these two limits. Logistic regression is appropriate

for the radiation example because none of the individuals died at a radiation exposure of zero

REMs, and all of the individuals died at doses of 686 REMs and higher. If we imagine a study of

patients with a disease where the outcome is a cure, if taking a drug in very high doses would not

always cause a 100 percent cure, and the disease could resolve on its own without any drug, the

data would not be appropriate. This is because some patients with high doses would still have an

outcome value of 0, and some patients at zero dose would have an outcome value of 1.

Logistic regression fits the logistic model to your data by finding the values of a and b that

make the logistic curve come as close as possible to all your plotted points. With this fitted

model, you can then predict the probability of the outcome. See the later section “Predicting

probabilities with the fitted logistic formula” for more details.

GETTING INTO THE NITTY-GRITTY OF LOGISTIC

REGRESSION

You don’t need to know all the theoretical and computation details for logistic regression because the software will do them

for you. However, you should have a general idea of what it is doing behind the scenes. The calculations are much more

complicated than those for ordinary straight-line or multivariate least-squares regression. In fact, it’s impossible to write down

a set of formulas that give the logistic regression coefficients in terms of the observed X and Y values. The only way to obtain

them is through a complex iterative procedure that would not be practical to do manually.