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A quantitative model in which the relationships between variables depend on location is said to be spatially heterogeneous. Quantitative geographical models assume certain mathematical relationships exist between the locations and attributes of geographical entities. These relationships typically involve both a deterministic and a random component. A basic example of this is a standard linear regression model

where y is an attribute that depends on {x1xj } through the linear coefficients {a0aj } and the random term ∊i. Typically, it is assumed that the ∊i 's have a normal distribution and that they are independent. Of note in a model of this kind is the fact that the relationships are only between the attributes of the objects—location plays no role. Since the relationship between ...

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