Exploring spatial patterning in data values - Spatial Data Analysis: An Introduction for GIS Users - page 117

8

9

7

4

3

1

2

6

5

0 10 20 Units

Figure 8.5 Locations of the data in Table 8.3.

È 120.8615 ˘

T

YWx z () = Í

˙

i

3397.6046

Î ˚

- 1.223

È ˘

T - 1 T

b ()= x Y Wx Y ()) Y Wx z () = Í

˙

i i i

1.406

Î ˚

h e intercept, b 0 ( x i ), is therefore -1.223 and the slope, b 1 ( x i ), is 1.406. As an example,
for the i rst case in Table 8.3, the i tted value is -1.223 + 1.406 ¥ 12 = 15.649.
Figure 8.6 shows the ordinary (unweighted) and geographically weighted regres-
sion lines i tted with the geographical weights indicated. Note the ef ect of geographi-
cal weighting on, in ef ect, pulling the line towards the points with larger weights. You
can match the geographical weight and the values of the two variables to the entries in
Table 8.3.
h e goodness of i t of the GWR locally can be assessed using the geographically
weighted coei cient of determination ( r 2 ) (Fotheringham et al. , 2002). h e geographically
weighted r 2 for location i is given by:

TSS RSS
TSS

-

(8.6)

r

2

=

i i

i

i

where TSS i is the geographically weighted total sum of squares given by:

n

Â

2

TSS = wz z ( - )

i ij j

j = 1