# Logistic Regression Probabilities

I have performed a logistic regression on some data, and the function is:

$p(x,y) = \frac{\exp(4.5 + 3.5x - 0.1y)}{1+\exp(4.5 + 3.5x - 0.1y)}$

This also gives you the probability of observing some event $(x,y)$ as I understand it. My question is, what does it mean in this case that probabilities should sum to 1? I.e., if I take various inputs $(x,y)$, and get lets' say 0.4916,0.3379,0.3381,0.289, etc... these don't add to 1, but they are probabilities, so how does one interpret the whole "summing to 1" in this case?

Thanks!

You are misunderstanding the outcome of logistic regression. A logistic regression will model $P(Y=1 | X)$. Thus since there are 2 classes, 0 and 1 for instance, this is what should sum to 1: $$P(Y=1 | X) + P(Y=0|X) = 1$$ And you can see that this is always true.