## 3 Results and Discussion
### Correlation Analysis
#### 3.4.2 Multiple Linear Regression  
Synergy of the prediction has been obtained when the variables were integrated into an empirical prediction equation derived from multiple line regression. This method was applied to the single PALSAR-2, Sentinel-1A polarization, and also to the variables from the combination of both PALSAR-2 and Sentinel-1A. The best three models have been produced as summarized in Table 8. Evidently the combination of PALSAR-2 L-band and Sentinel-1A able to strengthen the relationship between AGB and the polarization, thus improving the accuracy of estimates. Both datasets have complemented to each other that eliminated the effects of backscattering diffusion.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sensor** & **Variable** & **Scatter** & **Prediction Equation** & \(\mathbf{R}^{2}\) \\  & & **Plot** & \\ \hline \multirow{5}{*}{PALSAR-2} & HH & a & 28.59 HH + 641.68 & 0.119 \\  & HV & b & 47.21 HV + 978.87 & 0.276 \\  & HH \(\times\) HV & c & \(-1.98(\text{HH}\times\text{HV})\) + 608.64 & 0.223 \\  & HH \(-\) HV & d & \(-6.5969(\text{HH}-\text{HV})\) + 369.08 & 0.005 \\  & HV \(-\) HH & e & \(6.5969(\text{HV}-\text{HH})\) + 369.08 & 0.005 \\  & (HH + HV)/2 & f & \(43.49(\text{(HH}+\text{HV)/2})\) + 850.56 & 0.219 \\  & (HH \(\times\text{HV)}^{1/2}\) & g & \(-40.72(\text{(HH}\times\text{HV)}^{1/2})\) + 813.88 & 0.201 \\ \hline \multirow{5}{*}{Sentinel-1A} & VV & h & 15.56 VV + 527.84 & 0.091 \\  & VH & i & 8.48 HV + 518.33 & 0.023 \\  & VV \(\times\) VH & j & \(-0.69(\text{VV}\times\text{VH})\) + 482.13 & 0.090 \\  & VV \(-\) VH & k & \(13.78(\text{VV}-\text{VH})\) + 319.88 & 0.041 \\  & VH \(-\) VV & l & \(-13.328(\text{VH}-\text{VV})\) + 321.76 & 0.038 \\  & (VV + VH)/2 & m & \(14.13(\text{(VV}+\text{VH)/2})\) + 556.84 & 0.062 \\  & (VV \(\times\) VH)\({}^{1/2}\) & n & \(-14.46(\text{(VV}\times\text{VH)}^{1/2})\) + 553.95 & 0.073 \\ \hline \multirow{5}{*}{Combination} & HH \(-\) VV & o & \(-4.11(\text{HH}-\text{VV})\) + 398.50 & 0.004 \\  & HV \(-\) VH & p & \(6.48(\text{HV}-\text{VH})\) + 388.08 & 0.015 \\  & (HH + HV)/(VV + VH) & q & \(-31.53(\text{(HH}+\text{HV)/(VV+VH)})\) + 429.95 & 0.001 \\  & (VV \(-\) VH)/(VH - HV) & r & \(-590.85(\text{(VV}-\text{VH)/(VH-HV)})\) + 269.13 & 0.099 \\  & (HH + HV + VV + VH)/4 & s & \(36.98(\text{(HH}+\text{HV}+\text{VV}+\text{VH)/4})\) + 797.17 & 0.176 \\  & (HH \(\times\) HV)/(VV \(\times\) VH) & t & \(-0.91(\text{(HH}\times\text{HV)/(VV}\times\text{VH)})\) + 400.39 & 0.003 \\  & (HH \(\times\) HV \(\times\) VV \(\times\) VH)\({}^{1/4}\) & u & \(-35.30(\text{(HH}\times\text{HV}\times\text{VV}\times\text{VH)}^{1/4})\) + 764.90 & 0.177 \\ \hline \hline \end{tabular} All polarizations are in sigma nought (\(e^{0}\), dB). All correlations are significant at \(p<0.05\).  
\end{table}
Table 7: Summary of the AGB prediction equations produced from simple linear regression.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Sensor** & **Prediction Equation** & \(\mathbf{R}^{2}\) \\ \hline PALSAR-2 & \(146.90\text{HH}+169.78\text{HV}-7.03(\text{HH}\times\text{HV})+416.96(\text{HH} \times\text{HV})^{1/2}\) + 227.07 & 0.342 \\ \hline Sentinel-1A & \(-17.040\text{VH}-2.344(\text{VV}\times\text{VH})+24.327(\text{HH}\times \text{HV})^{1/2}+181.918\) & 0.138 \\ \hline Combination & \(-10.877\text{VH}-13.292(\text{HH}\times\text{HV})^{1/2}+139.702\text{HH}+162.287 \text{HV}-6.526(\text{HH}\) \\  & \(\times\) HV) + 394.502(\text{HH}\times\text{HV})^{1/2}+238.524 & 0.356 \\ \hline \hline \end{tabular} All polarizations are in sigma nought (\(e^{0}\), dB). All correlations are significant at \(p<0.05\).  
\end{table}
Table 8: The best correlations derived from multiple regression from a single sensor and combination of sensors.