## 2 Materials and Methods
### Topographic Features and Rainfall Effects on Performance  
OLS and GWR are both models that seek to explain the relationship between a dependent variable, in this case the calculated grain yield at all the classified wheat parcels, and explanatory independent variables, topographic features (aspect, slope, and altitude), and rainfall for this study. Table 10 presents GWR as the most suitable model for explaining these effects. In this case AIC, sigma and both R\({}^{2}\) and adjusted R\({}^{2}\) improved with GWR in comparison with OLS for the three zones (II, V, and VI) (Table 11). For instance, OLS yielded an adjusted R\({}^{2}\) of 0.05, 0.06, and 0.07 for zones II, V, and VI respectively. Meanwhile, for the statistically significant (\(p<0.05\)) independent variables (rainfall and altitude in zone II; rainfall, slope, and altitude in zone V; and rainfall, slope, and altitude in zone VI) OLS can explain a 5%, a 6%, and a 7% of grain yield variability at each zone (II, V, and VI). On the other hand, GWR presents an adjusted R\({}^{2}\) of 0.20, 0.11, and 0.20 for zones II, V, and VI respectively; therefore 20%, 11%, and 20% of GY variability at each zone can be explained with GWR. The local R\({}^{2}\) of each wheat field is shown in Figure 6. Furthermore, in Table 10, the ANOVA results support significant improvement (\(p<0.05\)) when using GWR in all the three studied zones compared to the global model (OLS). The GWR model explains the effects of topographic factors (aspect, altitude, and slope) and rainfall on grain yield significantly better than the OLS model for all three zones by adding information on the spatial variation of grain yield with these local phenomena. The autocorrelation test of both GWR and OLS for the three zones (Table 12) presents [PERSON]'s I values closer to the expected for GWR in comparison with OLS. The complete spatial randomness of GWR residuals was accepted as the \(p\)-value is not statistically significant, making the null hypothesis, that there is not significant spatial autocorrelation, correct. In contrast with this, \(p\)-value is statistically significant for OLS and therefore shows spatial autocorrelation of OLS residues. Regarding the rainfall interpolation, kriging interpolation outperformed IDW (RMSE = 91.90 mm and 105.08 mm respectively), hence the previous was used. Grain yield correlated positively with rainfall, namely when rainfall increased, so did grain yield. Although in GWR models the regression coefficients vary locally, the fact that in zone II the mean coefficient is 13.87 (Table 11) suggests the strong effect of the rainfall gradient distribution on wheat grain yield in this northern area. Regarding rainfall at the southern region (Zone VI), the mean coefficient is also positive and relatively high, 12.32 (Table 11). Meanwhile, the mean regression coefficient in zone V was lower at 1.73. Concerning the topographic variables, they were spatially heterogeneous except for aspect in the middle zone. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**ZONE-II** & **Sum of Square** & **Degree of Freedom** & **Mean Square** & **F** & \(p\)**-Value** \\ \hline Global Residuals & 7,843,015,749.31 & 3147.00 & & & \\ GWR Improvements & 1,747,830,060.01 & 239.72 & 7,291,131.57 & & \\ GWR Residuals & 6,095,185,689.30 & 2907.28 & 2,096,525.17 & 3.48 & \textless{}0.05 \\ \hline
**ZONE-V** & SS & DF & MS & F & \\ \hline Global Residuals & 1,137,248,334.91 & 2439.15 & & & \\ GWR Improvements & 401,137,210.77 & 338.37 & 1,185,498.75 & & \\ GWR Residuals & 736,111,124.14 & 2100.78 & 350,529.11 & 3.38 & \textless{}0.05 \\ \hline
**ZONE-VI** & SS & DF & MS & F & \\ \hline Global Residuals & 1,023,577,071.92 & 2013.50 & & & \\ GWR Improvements & 300,131,748.19 & 277.42 & 1,081,867.74 & & \\ GWR Residuals & 723,445,323.73 & 1736.08 & 416,711.97 & 2.59 & \textless{}0.05 \\ \hline \hline \end{tabular}
\end{table}