Editing Logistic regression (section)

===As a single-layer perceptron===
The model has an equivalent formulation

:<math>p_i = \frac{1}{1+e^{-(\beta_0 + \beta_1 x_{1,i} + \cdots + \beta_k x_{k,i})}}. \, </math>

This functional form is commonly called a single-layer [[perceptron]] or single-layer [[artificial neural network]]. A single-layer neural network computes a continuous output instead of a [[step function]]. The derivative of ''p<sub>i</sub>'' with respect to  ''X''&nbsp;=&nbsp;(''x''<sub>1</sub>, ..., ''x''<sub>''k''</sub>) is computed from the general form:

: <math>y = \frac{1}{1+e^{-f(X)}}</math>

where ''f''(''X'') is an [[analytic function]] in ''X''. With this choice, the single-layer neural network is identical to the logistic regression model. This function has a continuous derivative, which allows it to be used in [[backpropagation]]. This function is also preferred because its derivative is easily calculated:

: <math>\frac{\mathrm{d}y}{\mathrm{d}X} = y(1-y)\frac{\mathrm{d}f}{\mathrm{d}X}. \, </math>