Editing Logistic regression (section)

===Model===
[[File:Exam pass logistic curve.svg|thumb|400px|Graph of a logistic regression curve fitted to the (''x<sub>m</sub>'',''y<sub>m</sub>'') data. The curve shows the probability of passing an exam versus hours studying.]]

The [[logistic function]] is of the form:

:<math>p(x)=\frac{1}{1+e^{-(x-\mu)/s}}</math>

where ''μ'' is a [[location parameter]] (the midpoint of the curve, where <math>p(\mu)=1/2</math>) and ''s'' is a [[scale parameter]]. This expression may be rewritten as:

:<math>p(x)=\frac{1}{1+e^{-(\beta_0+\beta_1 x)}}</math>

where <math>\beta_0 = -\mu/s</math> and is known as the [[vertical intercept|intercept]] (it is the ''vertical'' intercept or ''y''-intercept of the line <math>y = \beta_0+\beta_1 x</math>), and <math>\beta_1= 1/s</math> (inverse scale parameter or [[rate parameter]]): these are the ''y''-intercept and slope of the log-odds as a function of ''x''. Conversely, <math>\mu=-\beta_0/\beta_1</math> and <math>s=1/\beta_1</math>.

Note that this model is actually an oversimplification, since it assumes everybody will pass if they learn long enough (limit = 1).