## 3 Results
### Accuracy of PLS and RF Regression Model  
We created six models using different predictor variable combinations for the regression analysis using PLS and RF regression. The names and details of the models are listed in Table 3. In general, the RF regression outperformed the PLS regression in all combinations of predictors for both the training and test data sets (Table 3). The results showed that the high accuracy in the training data set did not always represent high accuracy in the test data set. In the test data, the PLS regression models scored an RMSE between 2.08 and 3.67 plants m\({}^{-2}\) (\(r^{2}\) = 0.19-0.56), while the RF regression models scored between 1.78 and 1.92 plants m\({}^{-2}\) (\(r^{2}\) = 0.60-0.67). The partial least squares regression models with different variable combinations showed different results in estimating plant density as presented in Figure 6. The partial least squares regression model using variables SR + NDVI (SR + NDVI-PLS) gave the highest accuracy to estimate the test dataset (\(r^{2}\) 0.56 and RMSE 2.08 plants m\({}^{-2}\)). Partial least squares regression using the SR-only predictor (SR-only PLS) performed similar results to SR + NDVI-PLS, with higher plant density variation, ranging from -0.95 to 12.41 plants m\({}^{-2}\). In contrast, PLS regression using the NDVI-only predictor (NDVI-only PLS) scored the lowest variance, ranging from 1.04 to 8.04 plants m\({}^{-2}\). Figure 5: Relationship between manually observed and automatically counted soybean plant density (plants m\({}^{-2}\)) in the YOLOv3 best model with a confidence threshold value of 0.50 for the test dataset (\(n\) = 248). The solid line represents a regression line. The dashed line represents a 1:1 reference line. The results of the RF regression models using different variable combinations presented in Figure 7. The RF model using NDVI and climate data as variable predictors (NDVI + Climate-RF) that scored the highest accuracy was NDVI + Climate-RF (\(r^{2}\) 0.67 \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model Combination 1  & **PLS Regression** & & & & & \\ \cline{2-7}
**Model Combination 2  & **Training** & **Test** & **Training** & **Test** \\ \cline{2-7}
**SR** & \(\mathbf{r^{2}}\) & **RMSE** & \(\mathbf{r^{2}}\) & **RMSE** & \(\mathbf{r^{2}}\) & **RMSE** & \(\mathbf{r^{2}}\) & **RMSE** \\ \hline SR only & 0.71 & 1.81 & 0.50 & 2.17 & 0.84 & 1.37 & 0.63 & 1.82 \\ NDVI only & 0.58 & 2.20 & 0.56 & 2.37 & 0.79 & 1.54 & 0.60 & 1.92 \\ SR + NDVI & 0.74 & 1.74 & **0.56** & **2.08** & 0.84 & 1.35 & 0.67 & 1.81 \\ SR + Climate & 0.76 & 1.65 & 0.19 & 3.67 & 0.84 & 1.36 & 0.63 & 1.83 \\ NDVI + Climate & 0.74 & 1.72 & 0.46 & 2.22 & 0.81 & 1.49 & **0.67** & **1.78** \\ SR + NDVI + Climate & 0.77 & 1.62 & 0.28 & 2.95 & 0.84 & 1.35 & 0.65 & 1.79 \\ \hline \hline \end{tabular}  
* Model combination: SR only—model using predictors from surface reflectance data of PlanetScope imagery only (number of predictors: 16); NDVI only—model only using predictors from NDVI data of PlanetScope imagery only (number of predictors: 4); SR + NDVI—model using predictors from a combination of surface reflectance data and NDVI data of PlanetScope imagery (number of predictors: 20); SR + Climate—model using predictors from a combination of surface reflectance data of PlanetScope imagery and climate data (number of predictors: 22); NDVI + Climate—model using predictors from a combination of NDVI data of PlanetScope imagery and climate data (number of predictors: 10); SR + NDVI + Climate—model using predictors from combination of all PlanetScope imagery data and climate data (number of predictors: 26); the best models for each case are highlighted with bold letters. The best scores for each regression model are marked in bold.  
\end{table} 
Table 3: Comparison of partial least squares (PLS) and random forest (RF) regression models using several combinations of predictors.