I've been studying to understand the concept of logistic regression and I think I understand the idea more or less, but there are still some gaps to fill. What I'm looking for is an example of logistic regression and multinomial logistic regression to take the point home. Could someone perhaps give me a very simple examples to show me the fundamental steps one needs to take when doing logistic regression?
For example could someone show me what would I have to do If my data set consisted of the following:
$$\textbf{x}_1 = x_{11}, x_{12}, ..., x_{1n}$$ $$\textbf{x}_2 = x_{21}, x_{22}, ..., x_{2n}$$ $$\vdots$$ $$\textbf{x}_m = x_{m1}, x_{m2}, ..., x_{mn}$$
So $\textbf{x}_i$ is the $i$th variable and the observations from that variable I have denoted as $x_{ij}$, $1 \leq j \leq n$. I have $m$ variables and $n$ observations on each of them. Let's say the data described different kind of physiological features from $n$ different persons and I would like to use logistic regression to get the probability that person $A_k$, $1 \leq k \leq n$ gets an heart attack. In this example there are only two possible events: "heart attack" and "no heart attack". Could someone give me a pencil and paper like example what I would need to do to estimate the parameters using maximum likelihood etc. just to make it absolutely clear to me. It would be very nice if I could get examples in the case of two possible events and in the general cases where the number of possible events is $\geq 3$, because I'm using logistic regression in a project work where I have more than three possible events. Hope my question is clear.
The examples don't have to be long or anything. Just a very simple, short, showing all the steps,(e.g. calculating parameter estimates etc.). I have been watching some examples from the web, but in many sources the actual calculations I would like to see are just replaced by the words: "And computer gives us the parameters" :(. I want to see what is going on :)
Thank you for any help :)
P.S. You don't have to present a numeric example (you can if you want ;)). It is enough just to show all the necessary steps so that I'll be able to program the steps in Matlab if I wanted to :) Both logistic and multinomial logistic regression :)
UPDATE: If anyone is interested I found a very good site explaining logistic regression covering the details, etc. The site can be found here:
http://www.real-statistics.com/logistic-regression/basic-concepts-logistic-regression/