Example
Christoph Molnar
We use the logistic regression model to predict cervical cancer based on some risk factors. The following table shows the estimate weights, the associated odds ratios, and the standard error of the estimates.
| Weight | Odds ratio | Std. Error | |
|---|---|---|---|
| Intercept | -2.91 | 0.05 | 0.32 |
| Hormonal contraceptives y/n | -0.12 | 0.89 | 0.30 |
| Smokes y/n | 0.26 | 1.30 | 0.37 |
| Num. of pregnancies | 0.04 | 1.04 | 0.10 |
| Num. of diagnosed STDs | 0.82 | 2.27 | 0.33 |
| Intrauterine device y/n | 0.62 | 1.86 | 0.40 |
Interpretation of a numerical feature (“Num. of diagnosed STDs”): An increase in the number of diagnosed STDs (sexually transmitted diseases) changes (increases) the odds of cancer vs. no cancer by a factor of 2.27, when all other features remain the same. Keep in mind that correlation does not imply causation.
Interpretation of a categorical feature (“Hormonal contraceptives y/n”): For women using hormonal contraceptives, the odds for cancer vs. no cancer are by a factor of 0.89 lower, compared to women without hormonal contraceptives, given all other features stay the same.
Like in the linear model, the interpretations always come with the clause that ‘all other features stay the same’.
