# Wheat Yield Estimation Study Using Hyperspectral Vegetation Indices
## 4 Discussion and Conclusions  
The primary focus of this research was to investigate the relationship between wheat canopy hyperspectral data during the crucial growth stage and the subsequent yield of mature wheat. Using hyperspectral data from the wheat grain-filling stage, 27 vegetation indices were calculated and correlated with the measured yield in the experimental area. These vegetation indices exhibited significant correlations at the 0.01 significance level, with correlation coefficients exceeding 0.5. Based on different water treatment tests, [PERSON] (2018) measured the spectral reflectance of the canopy during the key growth period of winter wheat, and calculated 29 kinds of hyperspectral vegetation index. A winter wheat yield estimation model based on the combination of single vegetation index and multiple vegetation index was established, and the accuracy of the model was high. The results showed that the preferred vegetation index could be used for the construction of wheat yield estimation model. Utilizing the selected superior vegetation indices, five different methods were employed to establish wheat yield prediction models: Multiple Linear Regression (MLR), Stepwise Multiple Regression (SMLR), Principal Component Analysis (PCA), Artificial Neural Network (ANN) and Random Forest (RF). The Multiple Linear Regression model yielded an R\({}^{2}\) value of 0.835, and the second model established with Stepwise Multiple Linear Regression achieved an R\({}^{2}\) value of 0.612. However, when evaluating the better of the two methods, the R\({}^{2}\) value was only 0.199. It shows that the methods of multiple linear regression and multiple stepwise regression are less effective than machine learning models in wheat yield prediction, which is consistent \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Modeling Method** & **Modeling Accuracy** & **Verification Accuracy** & **K-Fold Cross-Validation Accuracy** & **RMSE (kg/hm\({}^{-2}\))** \\ \hline PCA & 0.382 & 0.422 & 0.488 & 1201.32 \\ SMLR & 0.612 & 0.398 & 0.493 & 1083.61 \\ ANN & 0.743 & 0.729 & 0.702 & 912.52 \\ MLR & 0.835 & 0.199 & 0.204 & 1123.45 \\ RF & 0.935 & 0.946 & 0.897 & 869.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Modeling accuracy and verification accuracy of different methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Computational Complexity** & **Noise Robustness** \\ \hline SMLR & High, involves evaluating multiple & Sensitive to noise, the model is easily influenced by \\  & variable combinations & noise in the data \\ \hline MLR & Low, capable of directly fitting linear relationships & Good robustness, has some tolerance to minor noise \\ \hline PCA & Low, transforms high-dimensional data into & Some robustness, able to resist some noise interference \\  & low-dimensional data & \\ \hline ANN & High, requires training large numbers of neurons & Some degree of robustness, but may be significantly \\  & and multi-layer network structures & affected by large amounts of noise or outliers \\ \hline RF & Low, integrates multiple decision trees, each tree is & \\  & relatively simple and can be processed in parallel & Strong robustness, able to resist minor noise interference \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Computational complexity and noise robustness of different methods. with the research results of [PERSON] et al. [20]. Because the general linear algorithm model is relatively simple, it is difficult to model nonlinear data or polynomial regression with correlations between data features, and it is difficult to represent highly complex data well, so the fitting accuracy is low. Despite Principal Component Analysis extracting three superior principal components, the accuracy of models built using these components remained relatively low, with the highest R\({}^{2}\) value being 0.398. This is consistent with the conclusion of [PERSON] [25]. For data with a nonlinear relationship, principal component analysis may not be able to accurately extract the main features.