# Logistic regression linear hyperplane

I'm performing logistic regression for binary classification in SAS and it outputs all of the coefficients to the logit model.

I was wondering how you would take those coefficients and use them to convert the model into a linear hyperplane in the original space (i.e., hyperplane that splits the space into two classes, positive and negative).

• Sep 6, 2019 at 11:13

Logistic regression does not predict the class of an observation, just the probability that it will belong to a given class. So it only defines a set of "parallel" hyperplanes $$b_0 + b_1x_1 + \cdots + b_kx_k = A$$, where $$A$$ is any constant. Each choice of $$A$$ will give a different sensitivity/specificity for the resulting classification. There is an entire set of techniques (usually called "ROC analysis") for trying to get a good value for this cutoff.
As @cardinal points out in the comment below, $$A=0$$ is a special case of using $${\rm logit} (p) = 0$$, that is $$p=0.5$$ as a cutoff between the two classes. So it corresponds to the intuitive rule of classifying into the class with the higher predicted probability.
• (+1): A couple comments: (i) The case $A = 0$ is an interesting special case and has an intuitively satisfying interpretation that might be worth remarking on, and (ii) Note that classifying by choosing some $A \neq 0$ is equivalent to ignoring the fitted intercept estimate and instead modifying it to optimize a different criterion conditional on the estimates of the remaining parameters. Oct 3, 2011 at 16:32