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Geographically Weighted Regression

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Encyclopedia of Mathematical Geosciences

Part of the book series: Encyclopedia of Earth Sciences Series ((EESS))

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Definition

Geographically weighted regression (GWR) (Brunsdon et al. 1996; Fotheringham et al. 2015, 2003) is a technique that extends the traditional regression framework by allowing different linear relationships to exist at various locations in space. It is a local method for analyzing spatial heterogeneities of processes and is widely applied in geography and other related disciplines. The underlying idea of GWR is that each observed point in the study areas borrows a certain number of its nearest neighbor points to build pointwise regression models.

Introduction

The general global linear regression model commonly assumes that the same relationships hold throughout the entire study area (i.e., constant across space). It can build the relationship between a dependent variable and one or more independent variables, whose general form is as follows:

$$ {y}_i={\beta}_0+{\sum}_{i=1}^n{\beta}_k{x}_{ik}+{\varepsilon}_i\, \mathrm{for}\ i=1,2,\dots n $$
(1)...

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Correspondence to Xiang Que .

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Que, X., Su, S. (2021). Geographically Weighted Regression. In: Daya Sagar, B., Cheng, Q., McKinley, J., Agterberg, F. (eds) Encyclopedia of Mathematical Geosciences. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-26050-7_141-1

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  • DOI: https://doi.org/10.1007/978-3-030-26050-7_141-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-26050-7

  • Online ISBN: 978-3-030-26050-7

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