What function does logistic regression utilize to model a binary dependent variable?

Logistic regression is specifically designed to model binary dependent variables, which means it predicts outcomes that can fall into one of two categories. The correct answer involves the logistic function, which is essential in this context.

The logistic function maps any real-valued number into a range between 0 and 1, making it ideal for predicting probabilities. This characteristic is crucial when dealing with binary outcomes, as it allows analysts to interpret the resultant values as probabilities of the dependent variable belonging to one of the two categories.

By utilizing the logistic function, logistic regression transforms the linear combination of input features into probabilities through the logistic curve, which has an S-shaped or sigmoid form. This transformation ensures that predictions remain bounded within the [0, 1] interval, aligning with the binary nature of the dependent variable.

In contrast, other types of functions mentioned in the choices do not suit this specific modeling purpose in predicting binary outcomes. For instance, exponential functions can grow rapidly and do not constrain the output between 0 and 1, while logarithmic and polynomial functions also do not provide suitable mappings for binary classification scenarios. Thus, the logistic function is essential for effectively modeling and interpreting the results of logistic regression in a binary context.