Geographically Weighted Regression (GWR)
Also known as: GWR, local regression, spatially varying coefficient regression, Coğrafi Ağırlıklı Regresyon (GWR)
Geographically Weighted Regression is a local regression method, introduced by Fotheringham, Brunsdon and Charlton (2002), that allows the regression coefficients to vary across space. Instead of one global equation, it fits a separate set of coefficients at every location, capturing spatial heterogeneity in the relationships.
Key highlights
- Reveals spatial heterogeneity by estimating a separate set of coefficients at every location.
- Produces mappable coefficient surfaces showing where and how a predictor's effect changes across space.
- Captures local relationships that a single global regression would average away and hide.
Intuition
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How it works
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When to use it
Use GWR when each observation carries geographic coordinates (latitude/longitude) and you suspect that the effect of a predictor differs across space — that is, when relationships are spatially non-stationary. It needs a reasonable sample (at least about 50 observations) on cross-sectional, geo-referenced data, and the bandwidth must be selected by cross-validation. Beyond the usual regression assumptions, spatial autocorrelation should be checked. If no coordinates are available, GWR cannot be applied and standard OLS regression should be used instead.
Strengths & limitations
- Reveals spatial heterogeneity by estimating a separate set of coefficients at every location.
- Produces mappable coefficient surfaces showing where and how a predictor's effect changes across space.
- Captures local relationships that a single global regression would average away and hide.
- Requires geographic coordinates; without them the method cannot be applied and OLS is the fallback.
- Results depend heavily on the bandwidth, which must be tuned by cross-validation.
- Needs an adequate sample (about 50+) and can give unstable local estimates where data are sparse, and global regression assumptions plus spatial autocorrelation still need checking.
Common pitfalls
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Applications
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Frequently asked
How is GWR different from ordinary OLS regression?
OLS estimates one global set of coefficients assumed constant everywhere. GWR relaxes that, estimating coefficients that vary by location, so it can capture spatial heterogeneity that a single global model would miss.
What is the bandwidth and why does it matter?
The bandwidth controls how quickly the weight given to neighbouring observations decays with distance — effectively how local each regression is. A small bandwidth gives very local, more variable estimates; a large one approaches the global model. It should be chosen by cross-validation.
What data do I need for GWR?
You need geo-referenced, cross-sectional data with coordinates (latitude/longitude) for each observation and ideally at least about 50 observations. Without coordinates GWR cannot run.
What should I do if my data have no coordinates?
GWR is undefined without spatial coordinates. In that case use standard OLS regression, which estimates a single global relationship.
Sources
- 1.Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically Weighted Regression: The Analysis of Spatially Varying Relationships. Wiley.ISBN 978-0471496168
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Cite this page
ScholarGate. (2026, June 1). Geographically Weighted Regression. ScholarGate. https://scholargate.app/spatial-analysis/geographically-weighted-regression