## 8 Simulation Results
### Energy Consumption  
The main goal of our proposed solution is not to reduce energy consumption compared to the existent approaches based on simple linear regression, but rather find the best trade-off between energy consumption and prediction accuracy. In our method we use samples of the temperature variable to predict the humidity and light variables. While we slightly increase energy consumption compared to simple linear regression, we improve the prediction accuracy caused by simple linear regression. \begin{table}
\begin{tabular}{l c c c c} \hline  & **Temperature** & **Humidity** & **Light** & **Time** \\ \hline
**Temperature** & 1.0000 & \(-\)0.7987 & 0.4550 & \(-\)0.2681 \\
**Humidity** & \(-\)0.7987 & 1.0000 & \(-\)0.2489 & 0.1987 \\
**Light** & 0.4550 & \(-\)0.2489 & 1.0000 & \(-\)0.1807 \\
**Time** & \(-\)0.2681 & 0.1987 & \(-\)0.1807 & 1.0000 \\ \hline \end{tabular}
\end{table} 
Table 4: Results of the correlation analysis. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{6}{c}{**Density (nodes/m\({}^{2}\)) by scenarios**} \\ \cline{2-7}
**Nodes** & \#**1** & \#**2** & \#**3** & \#**4** & \#**5** & \#**6** \\ \hline
4 & 0.1600 & 0.1600 & 0.2500 & 0.2500 & 0.2500 & 0.2500 \\
9 & 0.0900 & 0.0900 & 0.1111 & 0.1111 & 0.2500 & 0.2500 \\
16 & 0.0711 & 0.0711 & 0.0625 & 0.0625 & 0.2500 & 0.2500 \\
25 & 0.0625 & 0.0625 & 0.0400 & 0.0400 & 0.2500 & 0.2500 \\
36 & 0.0576 & 0.0576 & 0.0278 & 0.0278 & 0.2500 & 0.2500 \\
49 & 0.0544 & 0.0544 & 0.0204 & 0.0204 & 0.2500 & 0.2500 \\
64 & 0.0522 & 0.0522 & 0.0156 & 0.0156 & 0.2500 & 0.2500 \\
81 & 0.0506 & 0.0506 & 0.0123 & 0.0123 & 0.2500 & 0.2500 \\
100 & 0.0494 & 0.0494 & 0.0100 & 0.0100 & 0.2500 & 0.2500 \\ \hline \end{tabular}
\end{table} 
Table 3: Network density in the simulation scenarios. Figure 14: Average energy of the radio consumed by messages sent to the sink: **(a)** Scenarios #1, #2, #5 and #6. **(b)** Scenarios #3 and #4. Figure 15: Average energy of the radio consumed by messages received for gossip routing: **(a)** Scenarios #1 and #2. **(b)** Scenarios #3 and #4. **(c)** Scenarios #5 and #6. Figures 14 and 15 show the energy consumption results obtained from simulations of the four application versions. They describe the performance of energy consumption for transmission (\(\mathrm{E_{trans}}\)) and reception (\(\mathrm{E_{recp}}\)) of data by sensor nodes. We observed the impact of our method by comparing the energy consumption of the multiple linear regression (our solution) to the simple linear regression (current works). Under all conditions, the energy consumption is greater in the application versions that use simple or multiple linear regression based on the temperature variable instead of the time variable. This happens because when using the independent variable gathered by the sensor nodes, their reading samples have to be sent to the sink. Hence, they consume more energy than the application version that uses time (the counter) as independent variable. The energy consumption due to message exchanges between sensor nodes in scenarios #1, #2, #5 and #6 is presented in Figure 14(a). The \(\mathrm{E_{trans}}\) relation between the approaches remains constant, even when scalability changes and the approaches which use gathered variables consume twice as much \(\mathrm{E_{trans}}\) than approaches which not use it. The relation between the \(\mathrm{E_{trans}}\) of the original application and approaches with gathered variable is about 0.17 and with the current approach is about 0.08. In scenarios #3 and #4, the communication failure affected the energy consumption [Figure 14(b)] of all application versions when density falls below 0.0278 (from 36 to 100 sensor nodes). We checked that the energy consumption of the data sent by sensor nodes in the second application version (a.k.a. SimpleCount) is the lowest [Figure 14(a,b)], due to the fact that this application does not send reading samples to the sink. This application is the one adopted by current approaches.