How can I predict student enrolment in September based on independent data available earlier in the year? I'd like to predict how many students will enroll in a college in September, based on independent variables which are known earlier in the annual student recruitment cycle.

For example, one independent variable would be the number of accepted offers; I know how many students have accepted an offer from the college for each week from January to August for the last five years, and I know how many of these students actually enrolled in September (generally about 80% of students who accept an offer actually enroll, but this varies year-on-year).

Other independent variables might include: how many students have already paid a deposit on their tuition fee, or even the current exchange rate for students travelling from abroad.

So far, I've used historical conversion rates to predict enrollment, but I am wondering whether I can do something more sophisticated which would allow me to add in other independent variables.

Any ideas of which approaches I should investigate would be very welcome. I'd be particularly interested to hear of any Python libraries which might be relevant.
I would try out regression in Python's scikit-learn library to predict the September headcount given all those other variables you have. Here is a basic example using a linear model. Once you have that working, you could try a more sophisticated algorithm.

http://scikit-learn.org/stable/auto_examples/linear_model/plot_ols.html