In terms of adjusted R2 and AICc, GWR models are found here to outperform
classical OLS regressions with the same independent variables (e.g., an OLS regression
with the same regressors as H7 -in Table 3- yields an AICc = 9.33).9 This
indication is also supported by statistically significant joint-parameter spatial nonstationarity
F-tests, especially for primary schools (Table 3, BFC-F: S6-S7; [10]).
Similarly, Monte Carlo significance tests on individual local parameter estimates
partly reject the hypothesis of no spatial variability, particularly for the primary
education sector ([9]). Moreover, the standard errors of parameters turn out to be
underestimated by OLS in some cases, as ranges corresponding to 68% confidence
bands (i.e. β(OLS) } σβ) do not exceed inter-quartile ranges of the respective GWR
parameters, which make up 50% of these estimates (Table 3: (IQR)*). Upper and
lower extreme values of local parameters also show in some cases sign reversal relative
to global regression and median-level GWR parameters, relative to district population (with some negative local parameters in GWRs) and the proxies for
numbers effect (Nhca, Nsch).