In logistic regression, input features are linearly scaled just as with linear regression; however, the result is then fed as an input to the logistic function. This function provides a nonlinear transformation on its input and ensures that the range of the output, which is interpreted as the probability of the input belonging to class 1, lies in the interval [0,1]. The form of the logistic function is as follows:
Here is a plot of the logistic function:
When x = 0, the logistic function takes the value 0.5. As x tends to +∞, the exponential in the denominator vanishes and the function approaches the value 1. As x tends to -∞, the exponential, and hence the denominator, tends to move toward infinity and the function approaches the value 0. Thus, our output is guaranteed to be in the interval [0,1], which is necessary for it to be a probability.
