A curve that lies between 0 and 1 for all values of X

A linear equation cannot provide adequate predictions of the proportion in a response category at extreme values of X. There are various nonlinear equations that satisfy the requirement that their value is between 0 and 1 for all values of X, but the simplest of these is a logistic curve,

predicted proportion,   

Logistic curves satisfy the requirement because...

The parameters of the logistic curve

The constants b0 and b1 have a similar effect on the shape of the logistic curve to the corresponding parameters of a linear equation.

We again call b0 the intercept of the curve and we call b1 the slope.

The diagram below shows a logistic curve, and has two sliders that can be used to adjust the values of the two logistic parameters.

Use the sliders to observe that ...

These properties are shared with linear models.