Logistics function formula. To obtain a more "natural" fit, we need a curve that drops off towards 0 and ascends towards 1 more gradually. One formula that produces such a curve is the logistic formula. which is graphed below: The formula is simple in form and has a number of key interpretational advantages, as we will see later. To provide flexibility , the formula can be extended to the form. where and determine the logistic intercept and slope. When , we have , the logistic intercept. Since the relationship between and is non-linear, the slope varies as varies. At the point where the slope is is . and have the same qualitative effect on the logistic regression relationship as they do in the linear case. If is increased, it moves the values of higher overall. If is increase, it accelerates the degree to which changes as changes. Here are some examples of the various forms that these curves can take:
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