# Modelling Electricity Consumption in Cambodia Based on Remote Sensing Night-Light Images
## 4 Results
### Coupled Model of Electricity Consumption and Total Night-Light Values in Cambodia  
Electricity consumption from 2012 to 2019 was used as the independent variable and the total night-light values as the dependent variable to construct three regression models using linear, power, and exponential functions. Tables 5-7 show the results, where \(x\) represents electricity consumption, \(y\) represents the total night-light value, and \(e\) is a natural constant in the regression equation. The higher the adj-\(R^{2}\)-value and the lower the \(p\)-value, the more accurate the model. Normally, \(p\)-values \(>\) 0.05 indicate that the regression does not pass the significance test. Tables 5-7 reveal that the \(p\)-values of the nine regression equations obtained in this study were all less than 0.01. Therefore, all these models passed the significance test. The adj-\(R^{2}\)-values of all these equations are greater than 0.83, indicating a high correlation between the total night-light value and the electricity consumption data. The differences in the adj-\(R^{2}\)-value across models reflect the quality of the different models and the annual night-light images synthesis methods in Cambodia, as discussed in Section 5.1. The \(a\)-values for the three linear regression models in Tables 5-7 are 18.609, 17.716, and 8.802, respectively. A positive \(a\)-value indicates that the total night-light value increases as electricity consumption increases. The \(b\) values for all three linear models are negative, indicating that the total night-light value is only greater than 0 when the electricity consumption is multiplied by the \(a\) value greater than the \(b\) value. The \(a\) and \(b\) values for the power function regression model and the exponential function regression model in Tables 5-7 are greater than zero, indicating that the total night-light value increases as electricity consumption increases. The total night-light value is 0 for a power function regression model with electricity consumption of 0. The total night-light  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Year** & **Annual Average** & **Annual Cloud-Free Averaging** & **Month-Specific Substitution** \\ \hline
2012 & 6103.49 & 11,381.88 & 10,999.01 \\
2013 & 15,477.79 & 15,717.58 & 13,458.87 \\
2014 & 20,513.02 & 17,792.10 & 16,456.33 \\
2015 & 26,199.31 & 27,151.61 & 19,274.36 \\
2016 & 29,259.82 & 31,096.87 & 23,261.00 \\
2017 & 119,668.83 & 115,621.28 & 44,376.24 \\
2018 & 125,776.75 & 124,356.13 & 54,352.43 \\
2019 & 149,365.57 & 142,979.22 & 88,756.83 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Total night-light values of annual images obtained by different processing methods.  
Figure 5: Annual night-light images of Cambodia obtained by month-specific substitution for the years (**a**) 2012, (**b**) 2015, and (**c**) 2018.  
value is equal to \(a\) for an exponential regression model with electricity consumption of 0. In fact, the total night-light value of night-light images is often greater than zero in areas where there is no electricity consumption. This suggests that the exponential function regression model is more appropriate for electricity consumption simulation.  
The total night-light values for Cambodia obtained by the annual average method were fitted to the electricity consumption data using the three regression models. The exponential model produced the smallest adj-\(R^{2}\)-value, with the linear model being the next best and the power model being the best (Table 5).  
Using annual cloud-free average data, the linear regression model had the smallest adj-\(R^{2}\)-value, with the exponential model being the next best and the power model being the best. The results are shown in Table 6.  
Next, models were constructed using the data processed by the month-specific substitution method. The linear model had the lowest adj-\(R^{2}\)-value, the power model was second-best, and the exponential model was the best (Table 7).