Usually when fitting a logit or probit model to data, one has a dependent binary outcome variable (say, university attendance = [0, 1]) and the usual set of independent variables (for the sake of it, say, parent income, gender and some measure of ability).
In my case, things are a bit different. To stay within the example, for my main data set I do not know whether people attended university. The only aspects I have information about are parent income, gender and other independent variables. However, I was able to obtain data on university attendance for a random subset of the data. Using this subset I fitted a logistic model, obtaining coefficients for all independent variables.
How can I use these coefficients to predict the probability of university attendance for everyone else?
[Please note that the education example is only made to simplify things.]