## 3 Results
### Spatial Modelling of Bacteria Distribution and Water Temperature  
Several studies have attempted to discover the relationship between bacterial distribution [3; 36] and water temperature, but so far we are unaware of any studies that have attempted to perform an analysis for the selected Bay of Bengal region, Bangladesh, using a spatial model. For this reason, we attempted to investigate the relationship between bacterial distribution and water temperature by developing hexagons through a geographically weighted regression model. Firstly, we added water temperature data in each hexagon. Temperatures exceeding 29 \({}^{\circ}\)C were seen mostly in the study area.  
Figure 2 shows the relationship between bacterial distribution and water temperature in each hexagon, revealing the average water temperature within each hexagon. Water temperature and bacterial number data were analyzed and modelled to create a spatial polygon data frame. Importantly, the spatial information allowed relationships to be analyzed on a map. Here, the map displayed hexagons that were colored according to groups defined by a two-way table of bacterial diversity and water temperature using above- and below-median values. The median water temperature and number of bacteria calculated from the data were 28.2 \({}^{\circ}\)C and two, respectively. Red and blue hexagons indicated regions of high or low diversity and high or low water temperature, respectively. Magenta hexagons showed low diversity coupled with a relatively high water temperature, indicating regions with 'under-performing' bacteria numbers. Cyan hexagons showed high diversity coupled with relatively low temperatures, indicating regions with 'over-performing' bacterial numbers.  
Relationships were detected between bacterial diversity and water temperature through the spatial GWR model, in particular with the local regression and the relationship between bacterial diversity and water temperature changes for different water temperature values (Figure 3).  
To assess the model fit, we examined the residuals. A residual was the difference between the observed and predicted diversity in each hexagon. Residuals above zero indicated that the model under-predicted the diversity, whereas residuals below zero indicated that the model over-predicted diversity. A histogram (Figure 4) of the residuals showed the values were centered on zero. The left tails indicate that the model over-predicted diversity in some hexagons. The over-prediction can be associated with other environmental factors.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Survey Zone** & **Name of Bacteria** \\ \hline Zone-1 (Western side-Khulna) & N1, N3, N2, N4, N6, N7, N10, N9, and N11. \\ \hline Zone-2 (Western side-Satkhira) & N1, N4, N7, N9, N10, and N11. \\ \hline Zone-3 (Middle side-Bhola) & N1, N3, N2, N5, N8, N8, N4, N6, N7, and N10. \\ \hline Zone-4 (Eastern side-Chittagong) & N1, N2, N3, N5, N4, N7, N10, N9, and N11. \\ \hline Zone-5 (Eastern side-Cox’s Bazar) & N1, N3, N2, N4, N5, and N11. \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distribution of bacteria in survey site. N1... N11 denote the name of the bacteria.  
Figure 4: Histogram of geographically weighted regression (GWR) residuals. A residual (x-axis) is the difference between the observed and predicted diversity number (y-axis) in each hexagon. Residuals above or below two indicate that the model under-predicted or over-predicts the diversity, respectively.  
Figure 3: Linear (black line) and local linear regressions (red line) between bacterial diversity and water temperature. The relationship between bacterial diversity (x-axis) and water temperature (y-axis) changes for different values of water temperature.  
Figure 2: Water temperature and bacterial diversity over the Bay of Bengal region, Bangladesh. Low and high water temperatures with low and high bacterial diversity regions are shown in blue and red, respectively, whereas low and high water temperatures with high bacterial diversity are shown in cyan.