GWR (Geographically Weighted Regression)
v1.0.2
Agriculture, Forestry & Aquatic context — regression in which the coefficients vary by location. At each point a local model is fit with the AICc-optimal bandwidth, yielding maps of β₁(s), β₂(s).
🎯 What is it for?
Standard OLS estimates a single global β; GWR produces location-varying β: answering questions such as “Is the effect of X1 stronger in the north or the south?”. For Agriculture, Forestry & Aquatic, it visualizes how the sensitivity of agac_capi_cm to rakim_m and egim_pct varies regionally.
📌 When is it used?
- Spatial clustering in the OLS residuals (Moran’s I significant)
- The discipline-specific question “does the effect differ by geography?”
- A desire to visualize spatial heterogeneity
⚙ Assumptions
- Lat/lon coordinates, continuous DV (agac_capi_cm), continuous X’s.
- Sufficient density: number of points within the bandwidth ≥ 30.
- AICc / CV for bandwidth selection (default AICc).
📊 How to Run It in MerQur?
Panel assignments (form fields in the program):
- Columns:
{'y': 'birim_id', 'x': ['X1', 'X2'], 'lat': 'lat', 'lon': 'lon'} - Parameters:
{'bandwidth_method': 'AICc'}
📊 Sample Dataset — Agriculture, Forestry & Aquatic
ℹ Note: The scenario, MerQur output and interpretation below were produced by actually running the real example dataset in MerQur. Numeric results on your own data will differ; the goal is to show how the analysis is set up and interpreted end-to-end.
🎬 Example File
This analysis is demonstrated on the following example dataset for Agriculture, Forestry & Aquatic:
Ziraat_Orman_Su/107_gwr_local.xlsx
🎬 Scenario
We think the effect of X1, X2 on Y_value is not the same everywhere but varies by location. Classical regression gives a single
global coefficient; GWR estimates local coefficients for each location: a variable’s effect may be strong in one region and
weak/reversed in another. It makes spatial heterogeneity visible on the map.
⚙️ Variable Selection
- Dependent (outcome): Y_value
- Predictors: X1, X2
- Coordinates: lat, lon
Data Preview (First 5 Rows)
| unit_id | lat | lon | X1 | X2 | Y_value |
|---|---|---|---|---|---|
| 1.0 | 40.9141 | 38.4082 | 69.6 | 18.8 | 227.4 |
| 2.0 | 38.892 | 29.2114 | 39.1 | 25.4 | 401.3 |
| 3.0 | 39.2512 | 37.5754 | 24.9 | 34.1 | 495.9 |
| 4.0 | 40.24 | 39.2261 | 51.4 | 51.0 | 437.6 |
| 5.0 | 38.3041 | 29.6453 | 52.7 | 29.6 | 331.8 |
n = 110 · Columns: unit_id, lat, lon, X1, X2, Y_value
📈 MerQur Output
─────────────────────────────────────────────
R² = 0.887 Adj. R² = 0.868 AICc = 1129.9 | local coefficients per location
Y_value ~ X1 + X2 (lat/lon)
💬 Interpretation
We thought the effect of X1, X2 on Y is not the same everywhere but varies by location. Classical regression gives a
single global coefficient; GWR estimates local coefficients for each location. The model fit very well (R² = 0.89).
GWR’s key output is the VARIATION of the coefficients across the map: a variable’s effect may be strong in one
region, weak or reversed in another. This makes “spatial heterogeneity” visible. In practice this is very valuable:
e.g. if precipitation’s effect on yield is strong in an arid region and weak in a humid one, a single global
coefficient hides it — GWR reveals it. Far more informative than global models for region-specific management decisions.
⚠ Common Mistakes
- If too few points fall within the bandwidth in low-density regions, the standard error becomes large.
- If you find the same effect across the entire region, global OLS is sufficient — the complication of GWR is not needed.
- Multicollinearity may vary locally in GWR; checking the VIF at each bandwidth is recommended.
📚 MerQur’a Atıf
Örücü, Ö. K. (2026). MerQur: Integrated Academic Data Analysis & Reporting Platform [Computer software] (Version 1.0.0). https://doi.org/10.53463/merqur.2026001
📝 Üretim Notu — Bu sayfadaki örnek veri sentetik olarak üretilmiştir (sabit SEED=42, generator: samples/Ileri_Duzey_v102/_generate_v102_datasets.py). Sayfa içeriği Anthropic Claude desteği ile hazırlanmış, akademik doğruluk yazar tarafından kontrol edilmiştir.