Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Given an unknown classifier, could someone make assumptions for the linearity of this model from the fact that

$$y=\left\{ \begin{aligned} 1 &\;\mathrm{if}\;& p(y=1\,|\,x) \geq 0.5 \\ -1 &\;\mathrm{otherwise} \end{aligned} \right.$$ ?

Is that the reason we conclude logistic regression is linear?

share|improve this question

No, many nonlinear equations could satisfy $y=\left\{ \begin{aligned} 1 &\;\mathrm{if}\;& p(y=1\,|\,x) \geq 0.5 \\ -1 &\;\mathrm{otherwise} \end{aligned} \right.$

The logistic model can be represented as a regular linear equation except the left-hand side of the equation is transformed through a link function. So for logistic regression, you have $\ln \left( \frac{\hat{p}}{1-\hat{p}} \right) = B_0 + B_1 X$, where $\hat{p}$ is the probability that $Y=1$. You see the coefficients on the right-hand side ($B_0$ and $B_1$) enter the model linearly just like in simple linear regression. The left-hand side of the equation represents the logit function of $\hat{p}$, or the log odds. So you could could intuitively interpret that we are modeling the log odds using simple linear regression. It is only when we back-transform the predictions that we get the nice logistic curve that does not look linear.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

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