Geography Reference
In-Depth Information
80
Unweighted
Geog. weights
0.0060
70
60
0.9950
50
0.8825
0.0340
40
0.0002
30
0.7261
20
0.2780
0.0889
10
1.0000
0
0
10
20
30
40
50
60
70
80
Variable 1 (
y
)
Figure 8.6
Regression using the data in Table 8.3: unweighted and geographically (geog.)
weighted, with geographical weights indicated.
h is is the sum of the weights multiplied by the squared dif erence between each
(dependent variable) value and its mean. RSS
i
is the geographically weighted residual
sum of squares given by:
n
Â
ˆ
2
RSS
=
wz z
(
-
)
i
ij
j
j
j
=
1
h is is the sum of the weights multiplied by the squared residual (the dif erence
between each value and the value given the GWR model).
h e calculations following Equation 8.6 are presented in Table 8.4.
In this case, each term is as follows:
n
Â
2
TSS
=
wz z
(
-
)
=
1286.326
i
ij
j
j
=
1
n
Â
ˆ
2
RSS
=
wz z
(
-
)
=
266.227
i
ij
j
j
j
=
1
TSS
-
RSS
1286.326
-
266.227
r
2
=
i
i
=
=
0.7930
i
TSS
1286.326
i
h e unweighted
r
2
is 0.7413 and the geographically weighted
r
2
is 0.7930 (or 0.7966
calculated using purpose-written sot ware, the dif erence being due to rounding
errors). In other words, the GWR model is a better i t than the unweighted model
in this case and this suggests that taking into account distance from the location of
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