## 5.2 Interpretation of Parameter Estimates

One source of complication when interpreting parameters in the logistic regression model is that they’re on the logit or log-odds scale. We need to be careful to convert them back before interpreting the terms of the original variables.

• $$\exp \left(\beta_{0}\right)=$$ the odds that the success characteristic is present for an individual for which $$x=0$$, i.e., at the baseline. If multiple predictors are involved, all would need to be set to 0 for this interpretation.
• $$\exp \left(\beta_{1}\right)=$$ the multiplicative increase in the odds of success for every 1 unit increase in $$x$$. This is similar to simple linear regression but instead of an additive change, it is a multiplicative change in rate. If multiple predictors are involved, others would need to be held fixed for this interpretation.
• If $$\beta_{1}>0$$, then $$\exp \left(\beta_{j}\right)>1$$, indicating a positive relationship between $$x$$ and the probability and odds of the success event. If $$\beta_{j}<0$$, then the opposite holds.