Logistic Regression Example
[Logistic Regression Analysis~6 minutes]
In the following example we would like to predict heart attacks (CORON where 0=no heart attack and 1=heart attack) in males from the following data:
AGE in years
SYSBP
DIABP
CHOLES
HT height in inches
WT weight in pounds
SPSS Analysis
Output
Results
A direct logistic regression analysis was performed on heart attack as outcome (coded 0=no heart attack and 1=heart attack) and six predictors: age, systolic blood pressure, diastolic blood pressure, cholesterol level, height (inches), and weight (pounds). Analysis was performed using SPSS. There were a total of 175 males without a heart attack and 100 males with a heart attack.
A test of the full model with all six predictors against a constant-only model was statistically reliable, c^{2}(6, N=275)=72.25, p<.001, indicating that the predictors reliably distinguished between males who had and did not have a heart attack. The variance in heart attack accounted for is moderate, with Cox and Snell R^{2} equal to .23 and Nagelkerke R^{2} equal to .32. Predicted success was adequate, with 81% of the heart attack participants and 51% of the non heart attack participants identified correctly and an overall success rate of 70.2%.
Table 1 shows the regression coefficients, Wald statistics, statistical significances, and odds ratios for each of the six predictors. According to the Wald criteria only age, cholesterol, and weight reliably predicted heart attack. The odds ratio indicated that for every year in age men were 1.075 times more likely to have a heart attack; in other words, for every one year increase in age there was 7.5% increase in odds of a heart attack. For cholesterol level, for every one increase in cholesterol, there was a 1.01 times greater chance of having a heart attack. For every pound of weight, there was a 1.02 times greater chance that a male would have a heart attack.
Table 1
Logistic Regression Coefficients, Standard Errors, Wald Statistics, and Odds Ratio
Predictors |
B |
S.E. |
Wald |
df |
Sig. |
Odds Ratio |
age |
.072 |
.016 |
19.221 |
1.0 |
<.01 |
1.075 |
sysbp |
.013 |
.015 |
.748 |
1.0 |
.39 |
1.01 |
diabp |
-.029 |
.026 |
1.216 |
1.0 |
.27 |
.97 |
choles |
.008 |
.002 |
10.318 |
1.0 |
<.01 |
1.01 |
ht |
-.053 |
.071 |
.564 |
1.0 |
.45 |
.95 |
wt |
.021 |
.007 |
9.479 |
1.0 |
<.01 |
1.02 |
Constant |
-5.329 |
5.076 |
1.102 |
1.0 |
.29 |
.00 |