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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?

Thank you!

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You don't estimate $\beta$ by least squares in logistic regression. You estimate $\beta$ by maximizing the bernoulli likelihood.

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  • $\begingroup$ Argh -- you're right. And I knew that which makes it even more frustrating. Thanks for the reminder! $\endgroup$
    – user1357015
    Commented Apr 22, 2016 at 18:23

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