I'm curious what typical software packages do if the covariate is continuous?
Essentially you need to maximize
$logit(P(Y=1 | X)) = \alpha + \beta*x$
for the simplest case.
However, but if X is continuous how exactly do we calcualte the probability to put into the logistic function since we don't know it?
Once we have it, it's easy to minimize $\sum_i (logit(Pr(Y_i = 1| X)) - \alpha + \beta * x_i)^2$ but I'm unclear how the machine mechanically calculates the probability?