In logistic regression, what does the doubling amount represent?

In logistic regression, the interpretation of a coefficient associated with an input variable indicates the effect of a one-unit increase in that variable on the log-odds of the outcome. Specifically, the doubling amount represents the change in the input variable that is necessary to double the odds of the outcome event occurring.

When the odds are doubled, it implies that the likelihood of the outcome has increased significantly due to a change in the predictor variable. This is grounded in the mathematical relationship between the coefficients in the logistic regression model and the odds ratio. The odds ratio is expressed as ( e^{\beta} ), where ( \beta ) is the coefficient of the input variable. Therefore, if you want to double the odds of the outcome, you need to calculate the necessary change in the input variable that would achieve this, which is exactly what this option describes.

Each coefficient in a logistic regression reflects a multiplicative change in the odds, and thus understanding how to interpret these coefficients in terms of odds is crucial for making informed predictions and decisions based on the model.