quantify the amount by which a specific predictor influences the chance of getting the outcome. As

an example, you could quantify the amount obesity plays a role in the likelihood of a person being

diagnosed with Type II diabetes.

To develop a formula to predict the probability of getting an outcome based on the values of the

predictor variables. For example, you may want to predict the probability that a person will be

diagnosed with Type II diabetes based on the person’s age, gender, obesity status, exercise status,

and medical history.

To make yes or no predictions about the outcome that take into account the consequences of false-

positive and false-negative predictions. For example, you can generate a tentative cancer diagnosis

from a set of observations and lab results using a formula that balances the different consequences

of a false-positive versus a false-negative diagnosis.

To see how one predictor influences the outcome after adjusting for the influence of other

variables. One example is to see how the number of minutes of exercise per day influences the

chance of having a heart attack after controlling for the for the effects of age, gender, lipid levels,

and other patient characteristics that could influence the outcome.

To determine the value of a predictor that produces a certain probability of getting the outcome.

For example, you could determine the dose of a drug that produces a favorable clinical response in

80 percent of the patients treated with it, which is called the

, or 80 percent effective dose.

Understanding the Basics of Logistic Regression

In this section, we explain the concepts underlying logistic regression using an example from a

fictitious animal study involving data on mortality due to radiation exposure. This example illustrates

why straight-line regression wouldn’t work and why you have to use logistic regression instead.

Gathering and graphing your data

As in the other chapters in Part 5, we present a real-world problem here. This example examines the

lethality of exposure to gamma-ray radiation when given in acute, large doses. It is already known that

gamma-ray radiation is deadly in large-enough doses, so this animal study is focused only at the short-

term lethality of acute large doses. Table 18-1 presents data on 30 animals in two columns.

TABLE 18-1 Radiation Dose and Survival Data for 30 Animals, Sorted

Ascending by Dose Level

Dose in REMs Outcome Dose in REMS Outcome

0

0

433

0

10

0

457

1

31

0

559

1

82

0

560

1

92

0

604

1

107

0

632

0

142

0

686

1

173

0

691

1