Of course, this type of data does not work very well with a traditional linear regression because the distribution of the dependent variable is not normal. But linear regression is a good place to start with this discussion because it gives me a reference point to show you what I understood about linear regression that I didn't understand about logistic regression.
The first problem in PS#1 in the machine learning class that requires a program is this:
Implement2 Newton’s method for optimizing ℓ(θ), and apply it to
fit a logistic regression model to the data. Initialize Newton’s method with θ = ~0 (the
vector of all zeros). What are the coefficients θ resulting from your fit? (Remember
to include the intercept term.)
And here is the generalization of Newton's method in the notes:
I am embarrassed to say that it took me an incredibly long time to answer these questions. In my defense, the resources on the web are really hard to understand. Did you scroll down far enough so see where part of the information is written as a debate? But here is what I figured out. Once you get the coefficient values (code will come in another post), you can calculate the value of the sigmoid function, h.