Definition:Logistic Regression Equation

Definition

Consider a logistic regression experiment in which the $i$th Bernoulli trial gives rise to a binary variable $Y_i$.

Let $p_i := \map \Pr {Y_i = 1}$.

Let $\theta_i$ denote the odds on $\map \Pr {Y_i = 1}$:

$\theta_i = \dfrac {p_i} {1 - p_i}$

The logistic regression equation is the equation:

$\map \ln {\theta_i} = \alpha + \beta x_i$

where $x_i$ is the treatment level of the $i$th Bernoulli trial.

Also see

• Results about the logistic regression equation can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): logistic regression
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): logistic regression