# Protection of Digital Elevation Model--One Approach
## 4 Discussion
### Discussion on the Impact of Changing DEM Data
Linear regression was used as a statistical indicator of the results, which in statistics refers to each approach for modeling relations between one or more variables marked with Y, as well as one or more variables marked with X, in such a way that the model linearly depends on unknown parameters collected from the data. The following statistical indicators were also obtained based on differences in height, such as root mean squared error (1) and standard deviation (2). \[RMSE =\sqrt{\frac{\sum_{i=1}^{n}(Pi-Oi)^{2}}{n}} \tag{1}\] \[\sigma =\sqrt{\frac{\sum_{i=1}^{n}\left(\Delta i-\overline{\Delta}i\right) ^{2}}{n}} \tag{2}\]  
The root means squared error (\(RMSE\)) measures how much error exists between two sets of data. In other words, it compares the predicted value, \(Pi\), and the observed or known value, \(Oi\). In the continuation of the determination of \(RMSE\) for the predicted value, the values of the LiDAR digital models of various spatial resolutions were used, and for the observed value, the values of the digital models created by the radar method of recording were used. The standard deviation shows how much on average the elements of a set deviate from the arithmetic mean of the set. Figure 13a shows the linear regression for LiDAR and SRTM digital elevation models based on the sample value of hundred points. The equation that is derived is the relationship between the LiDAR and radar digital models, and for the Center area reads y = \(-0.0408x+82.74\), where the value of x represents the radar DEM, and y represents the LiDAR DEM. The percentage value determination is also calculated, which in statistics represents the percentage of variation of the dependent variable that is predictable from the other independent variable. Figure 12: Movement of the height of the DMV of the Petrovaradin Fortress area. If the regression line does not miss any of the points significantly, then the determination percentage is relatively high. The average percentage of determination of the height values for the Center area is about 3%. Also, in Figure 13b, referring to the Petrovaradin Fortress area, linear regression of the height values from which the linear equation y = 1.0061x + 2.1308 is performed, but in contrast to the previous area, the average determination percentage is about 86%. The average percentage of determination of altitude values based on the same calculations for the Spens area is about 6%, whereas for the Campus area it is about 11%. In addition, during the analysis, RMSE and standard deviations of the difference in the value of the heights of all areas are calculated (Tables 1 and 2). \begin{table}
\begin{tabular}{c c c c c} \hline  & **Center** & **Petrovaradin** & **Campus** & **Spens** \\ \hline RMSE (Lidar1 \(\times\) 1-SRTM) & 4.614 & 7.206 & 2.858 & 2.078 \\ RMSE (Lidar2 \(\times\) 2-SRTM) & 4.617 & 7.179 & 2.849 & 2.083 \\ RMSE (Lidar5 \(\times\) 5-SRTM) & 4.614 & 7.144 & 2.864 & 2.055 \\ RMSE (Lidar10 \(\times\) 10-SRTM) & 4.576 & 7.160 & 2.870 & 2.083 \\ RMSE (Lidar20 \(\times\) 20-SRTM) & 4.571 & 6.860 & 2.934 & 2.073 \\ RMSE (Lidar30 \(\times\) 30-SRTM) & 4.616 & 7.642 & 2.962 & 1.998 \\ \hline \end{tabular}
\end{table} 
Table 1: Calculated RMSE values. Figure 13: Linear regression of LiDAR and radar DEMs. (**a**) Linear regression based on the collected sample of the Center area; (**b**) Linear regression based on the collected sample of the Petrovaradin area. \begin{table}
\begin{tabular}{c c c} \hline  & **LiDAR DEM** & **LiDAR and SRTM DEM** \\ \hline Center & 0.717 & 2.622 \\ Petrovaradin & 2.822 & 4.951 \\ Campus & 0.544 & 2.547 \\ Spens & 0.427 & 1.910 \\ \hline \end{tabular}
\end{table} 
Table 2: Standard deviations of LiDAR DEM differences and LiDAR and SRTM DEM spatial resolutions 30 \(\times\) 30. By determining the statistical indicators, it was concluded that there are large differences between the digital models created by LiDAR and the radar method.