I was checking if there was a response and upon reading your comments again, looks like your method is less a model and more just some ad hoc procedure. Based on what your conclusion is it sounds like a linear model based on demographic data would work and linear models are easy to train. Though by your summary there are probably going to be issues with the model and you have the same issues with your procedure, you just can't tell because it hasn't been rigorously specified.

There's a channel on YouTube called Statquest that teaches statistics in a pretty accessible way if you're interested in analyzing this sort of data.

I learned my statistics in university, not Youtube. You are confusing yourself about residuals.

To make my point in the original post, I held the group scores fixed and extrapolated combined scores based on changing population sizes. This is straightforward. Simple even.

\(\widehat S=\sum_g p_gS_g,\)

Why did I call this "linear"? (Not a "linear model", your term, because it is not). The model function actually tracks the population function. Over the 25-year period, however, this trend is in fact linear because the White-to-Hispanic population trend is linear on that timescale. Over a longer timescale it would not be.