interpreting random effects in a GLMM

#1
I just want to check with everyone about my interpretation of a model results. I am beginning to second guess myself so I want to make sure I am correctly interpreting results.

my abbreviated model is:
athletic funding = rurality + variable_1 ... + variable_n + u_rurality + error

where rurality is the fixed effect of rurality and u_rurality

Rurality is a binary variable where 1 = rural and 0 = non-rural

Say my output gives me the following estimate for my fixed effect of rurality is $1000.

My random effects give me a correlation between u_rurality and the intercept as -.5.


Would it be fair for me to interpret this result as saying that as rural areas spend more on athletic funding, the effect of their "rurality" is diminished?