# Predicting student enrollment based on school demand and birth rate

I want to know whether the decreasing number of students enrolled at an all-male school is due to decreasing birth rate, or to decreased demand for single-sex schools. I have the following data:

1. Birth rate in the city where the school is located, in total and by borough, 2004-2019.
2. Projected birth rate for the city, 2018-2037.
3. Number of births in the city where the school is located, in total and by borough, 2004-2019.
4. Number of births by city and gender in the country, 2006-2037 (real/projected).
5. Number of single-sex and mixed schools in the country, 2001-2020.
6. Number of families that are seeking single sex schools and mixed schools, 2015-2021 (sample size: 850 families, population size: 8000 families).
7. Number of students admitted to all schools in the country, in pre-k, 2010-2019.

I have already carried our an ARIMA model, seeking to cross-correlate number of births and number of students enrolled at the all-boys school. However, lag for number of births is 1, and lag for enrollment is 0, so I can't really predict future enrollment with this data.

Is there any other way I could predict enrollment rate at single-sex schools, and test whether the change is due to change in birth rate or in demand? I have thought of the following options (potential drawbacks I came up with are in parenthesis).

• a. Compare rate of change for single-sex schools vs. mixed schools. i.e. number of students enrolled in 2010 vs. 2019.

• b. As the lag in number of births is 1, years would seem to be an independent variable, so maybe some sort of regression? (The best fit I have is a quartic regression, but prediction power is low, as after a few years the number of births is negative, and I do not like this approach as the N for number of years is low, 10, and I am not considering many factors, such as migration, or death rate).

• c. ARIMA model with birth rate instead of number of births? (I don't know if you can carry out ARIMA with proportions, and the N is still low, 10 years).

As you can see, I am at a loss as to what to do next. Maybe the answer I will get from you is that we simply cannot predict the enrollment rate in schools with the data we have, but I hope this is not the case.

offtopic, but in school at 1st semester we had "econometry" and it was about installing Gretl software (i dont know if its free) and we try different data and looking st things like R^2 and p-value i clicked yt first video saga https://www.youtube.com/watch?v=lsWUy3ALDmw

i feel its more about testing "relationships" in your data mess. you jumped straight into prediction, you did fast choose for arima model family and now diving all direction withouse stable base

i mean, maybe start over and go step 1, 2, 3 (adding problems to problems is like running from solutions to technologies.

2. then look and write few paragraph about each data (as you mentioned N=10 its very short length

3. then maybe set advices which data to try to use/involve

4. open prognostic part, write each paragraph why using some kind of model, why choosing parameters ...do fitting, write plot, check for info criteria, write conclusions on finding results

( in this stage you have good material for someone to look up and give advice or maybe its final stage as not enough data / you found "low correlation" / low forecast precision

good research is better > then none (advice based on data/findings is sometimes much better, it brings peace and stable ground for next)

but i do think after you do these 4 parts and gain cleer sight and organization and little pause, you can start building trustworthy models

(just from my point your goal is more filter which data correlate with wanted one (as a lot of vectors are only 10-30 length

(its just my point of view :-)

edit1:

can I ask, is only for school purpose or for work? I mean, you can model data with linear regression and build simple arima model for prediction (I mean, if you strugle deliver solution at high level, you can create/build really good solution at easy/medium :-)