Editing Logistic regression (section)

===Definition of the inverse of the logistic function===
We can now define the [[logit]] (log odds) function as the inverse <math>g = \sigma^{-1}</math> of the standard logistic function. It is easy to see that it satisfies:

:<math>g(p(x)) = \sigma^{-1} (p(x)) = \operatorname{logit} p(x) = \ln \left( \frac{p(x)}{1 - p(x)} \right) = \beta_0 + \beta_1 x ,</math>

and equivalently, after exponentiating both sides we have the odds:

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