Using a Logit model to predict unknown outcome 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.]
If I understood you correctly, $\Lambda(x_i'\hat\beta)$, where $\Lambda(x) = e^x / (1+e^x)$. You can use predict in both R and Stata. Try in Stata:

clear all
*** Generate data
set obs 10
set seed 1
gen x = rnormal()
gen y = 1+x+rnormal() &gt; 0
replace y = . in 7/10
list
*** Estimate
logit y x
*** Predict
predict phat, p
list


For clarification, I presumed that your outcome variable is in $\{0,1 \}$ (not in $[0,1]$). You observe $y_i$ for some $i$ but not for all, you fitted a logit regression, and then you want to predict the probability for every $i$. Please let me know if I misinterpreted your question.