2
$\begingroup$

The logistic regression model,

\begin{equation} \operatorname{p}(X) = \frac{\operatorname{e}^{\beta_0 + \beta_1 X}}{1 + \operatorname{e}^{\beta_0 + \beta_1 X}} \end{equation}

is said to create a decision boundary linear in $X$.

As far as I understand, only the logit is linear in $X$. Is this the reason the decision boundary is linear in X? If so, why? And if this is not the case, what is the reason for this phenomenon?

I am confused about this because the decision boundary can be expressed as: \begin{equation} \operatorname{p}(X) = a, a \in [0,\, 1] \end{equation} And $\operatorname{p}(X)$ is not linear in $X$.

$\endgroup$

1 Answer 1

1
$\begingroup$

The decision boundary $p(X)=a, a\in(0,1)$ is

$$\beta_0+\beta_1X=\log\frac{a}{1-a}$$

which is linear in $X$.

$\endgroup$
1
  • 1
    $\begingroup$ Ah, thanks for showing me the relation of the decision boundary to the logit. The decision boundary is thus a hyperplane, and thus linear in $X$. $\endgroup$
    – Nurmister
    Sep 15, 2018 at 16:43

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.