260 PART 5 Looking for Relationships with Correlation and Regression

»

» ^{There’s one row for the constant term labeled Intercept.»}

» ^{The first column usually lists the regression coefficients (under Coeff. in}

Figure 18-4a).»

» ^{The second column usually lists the standard error (SE) of each coefficient}

(under StdErr in Figure 18-4a).»

» ^{A p-value column indicates whether the coefficient is statistically significantly}

different from 0. This column may be labeled Sig or Signif or Pr(> lzl), but in

Figure 18-4a, it is labeled p-value.

For each predictor variable, the output should also provide the odds ratio (OR) and

its 95 percent confidence interval. These are usually presented in a separate table

as they are in Figure 18-4a under Odds Ratios and 95% Confidence Intervals.

Predicting probabilities with the

fitted logistic formula

The output may include the fitted logistic formula. At the bottom of Figure 18-4a,

the formula is shown as:

Prob Death = 1/ 1 + Exp - -4.828 + 0.01146 * Dose

You can write out the formula manually by inserting the value of the regression

coefficients from the regression table into the logistic formula. The final model

produced by the logistic regression program from the data in Table 18-1 and the

resulting logistic curve are shown in Figure 18-5.

Once you have the fitted logistic formula, you can predict the probability of having

the outcome if you know the value of the predictor variable. For example, if an

individual is exposed to 500 REM of radiation, the probability of the outcome is

given by this formula: Probability of Death

1

1

4 828

0 01146

500

/

_

,

.

(

)

e

, which

equals 0.71. An individual exposed to 500 REM of radiation has a predicted proba-

bility of 0.71 — or a 71 percent chance — of dying shortly thereafter. The predicted

probabilities for each individual are shown in the data listed in Figure 18-4b. You

can also calculate some points of special significance on a logistic curve, as you

find out in the following sections.

Be careful with your algebra when evaluating these formulas! The a coefficient in

a logistic regression is often a negative number, and subtracting a negative num-

ber is like adding its absolute value.