**4.8 Geographically weighted regression**

Due to the detection of nonstationary and/or heteroscedasticity in the datasets, a GWR was used to adequately assess the relationship. The Global Moran's Index and

**131**

**Table 3.**

*A GIS-Based Approach for Determining Potential Runoff Coefficient and Runoff Depth…*

AICc produced (AICc = 1522.83) compared to the OLS (1573). The R<sup>2</sup>

= 0.35) with a lower adjusted R2

*Statistical diagnostic results from the ordinary least squares regression.*

*Results from the geographic weighted regression analysis.*

Anselin Local Moran's Index was performed to test for clustering and local patterns of spatial association [37]. The Global Moran's I indicated that the standard residuals produced from the GWR were significantly dispersed indicating the absence of spatial autocorrelation (Moran's I = −0.025, *p* = 0.111). The algorithm calculated an index for every feature, and 96% of the local *p*-values were not significant (*p* > 0.05). The validation for choosing the GWR also can be justified by the smaller

GWR accounts for nonstationary data that contain local trends for the relationship between the variables. Local trends within the dataset relationships were inevitable due to the complexity of different LC/LU within urban communities. The locally weighted regression coefficients can be seen on the coefficient raster produced by the GWR analysis (**Figure 8**). The coefficients show that LDI influences runoff in locations with more impervious surfaces and higher runoff depths, and forested land cover that consists of low LDI values and low runoff. The coefficients increase from blue to yellow to red, indicating higher relationships between the two

**Table 3** shows statistical values generated from the model according to the optimal sampling distance for nearest neighbors (bandwidth). The sampling kernel type for the GWR was fixed, and therefore provides the bandwidth in meters. The Residual Squares is the sum of squared residuals that represent the distance between the observed and estimated values. Therefore, the data are more related when this value is smaller. With a strong influence from bandwidth, the Effective Number is a measure of the complexity of the model that is used to calculate other variables within the GWR model, and it is useful when compared to other models. The sigma is the estimated standard deviation for the residual sum of squares, which shows

**Number of observations: 564 AICc 1573.001** Multiple R-squared 0.151 Adjusted R-squared 0.147 Joint Wald statistic 67.250 Prob(>chi-squared), (2) df: <0.0001 Koenker (BP) statistic 10.963 Prob(>chi-squared), (2) df: 0.004 Jarque-Bera statistic 5.500 Prob(>chi-squared), (2) df: 0.064

**Variable name Values** Bandwidth 11228.83 m Residual squares 406.15 Effective number 66.62 Sigma 0.90 AICc 1522.83 R-squared 0.35 Adjusted R-squared 0.26 Dependent field 0.00 Explanatory field 1.00

for the GWR

of 0.26. As previously stated, the

*DOI: http://dx.doi.org/10.5772/intechopen.87163*

increased (R2

variables.

**Table 2.**
