What is the Difference Between Logit and Logistic Regression?

Logit and logistic regression are the same thing.  However, they actually relate to generalized linear models.  In a generalized linear model, you have some features x, parameters \beta, response y, and link function g.  that relates E(y) to x and \beta.  The relationship is as follows:

(1)   \begin{align*} g(E(y))&=\beta^T x \end{align*}

One choice of g is the logit function \log\frac{x}{1-x}.  Its inverse, which is an activation function, is the logistic function \frac{1}{1+\exp(-x)}.  Thus logit regression is simply the GLM when describing it in terms of its link function, and logistic regression describes the GLM in terms of its activation function.

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