Exploring spatial patterning in data values - Spatial Data Analysis: An Introduction for GIS Users - page 113

Local I
-1.0-0.0
0.1-1.0
1.1-1.5
1.6-3.2
Inland water

N

0 20 40 km

Figure 8.4 Local I for log of persons per hectare in Northern Ireland in 2001 using queen's
case contiguity. Northern Ireland Census of Population data—© Crown Copyright.
Reproduced under the terms of the Click-Use Licence.

h e focus of the chapter now moves onto analysis of spatial patterning in the
relationships between multiple variables.

Regression and correlation

8.5

h e subject of regression and correlation was introduced in Section 3.3. Some regres-
sion-based analyses of spatially referenced variables map the residuals (in the two-
variable case, this means the dif erence between the value indicated by the line of best
i t and the observed value) from the regression (see the example in Figure 3.5). It is
straightforward to take this a step further and explore not just how accurate i tted
values are from place to place but to consider how the relationships between variables
dif er spatially. As with univariate statistics, multivariate approaches (such as correla-
tion and regression) can be conducted in a moving window. h e next section intro-
duces some approaches to regression in the analysis of spatial data. Next, the focus is
on regression conducted in a moving window. Following this, a geographically
weighted approach is detailed and this account makes use of matrix algebra to obtain
regression coei cients.

8.5.1 Spatial regression

An assumption of standard ordinary least squares regression is independence of
observations. As discussed in Section 3.5, this assumption rarely holds true for spatial