Definition:Logistic Regression

Definition

Logistic regression is the name given to the process of setting up a set of independent Bernoulli trials such that the $i$th Bernoulli trial gives rise to a binary variable $Y_i$.

The probability $\map \Pr {Y_i = 1}$ is usually denoted $p_i$.

It is often the case that $p_i$ depends on one or more explanatory variables.

Examples

Insecticide

Consider a logistic regression experiment to investigate the efficacy of a certain insecticide.

The treatment level $x_i$ can be amended according to the response of interest $Y_i$ where:

$Y_i = 1$ denotes death of the insect

$Y_i = 0$ denotes survival of the insect.

The odds of death for the $i$th individual are then:

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

Also see

• Definition:Logit

• Results about logistic regression 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