# Improvement of Wheat Grain Yield Prediction Model Performance Based on Stacking Technique
## 3 Results
### Correlations between Hyperspectral Vegetation Indices and Grain Yield  
A correlation analysis between GY and 15 hyperspectral vegetation indices and LAI at the jointing, flagging, antibesis, and grain filling stages of wheat was conducted, as shown in Figure 4. The results showed that at the jointing stage, the absolute value of the correlation coefficient (\(\,\mathrm{|\,r\,|}\) ) between GY and 15 vegetation indices and LAI ranged from 0.39 to 0.49, and the absolute value of the correlation coefficient between NDWI and GY was the highest, with the best correlation (\(\,\mathrm{|\,r\,|}\) = 0.49). At the flagging stage, the \(\,\mathrm{|\,r\,|}\) value between GY and indices ranged from 0.47 to 0.67, among which the absolute value of the NDWI and GY correlation coefficient was the highest, that was, the strongest correlation (\(\,\mathrm{|\,r\,|}\) = 0.67). At the antibesis stage, the \(\,\mathrm{|\,r\,|}\) value between GY and the indices ranged from 0.48 to 0.81, and the absolute value of the correlation coefficient between NDWI and GY was the highest (\(\,\mathrm{|\,r\,|}\) = 0.81). In the grain filling period, the \(\,\mathrm{|\,r\,|}\) value between GY and the indices was between 0.7 and 0.82, and the correlation between the VREI and GY was the strongest (\(\,\mathrm{|\,r\,|}\) = 0.82). The results showed that the correlation coefficients of LAI and GY were 0.47, 0.67, 0.68, and 0.78 at the jointing, flagging, antibesis, and grain filling stages, respectively. Overall, the correlation between GY and the hyperspectral vegetation indices and LAI showed the gradually increasing trend as the growth period progressed. All indices of each growth period were significantly correlated with GY (\(p\) < 0.001), which could be used to predict the yield of winter wheat. The correlations between different indices were shown in the attached Figure A2.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Measurement Dates** & **MEAN (t ha\({}^{-1}\))** & **SD (t ha\({}^{-1}\))** & **CV (\%)** \\ \hline
2016–2017 & 5.84 & 0.95 & 16.27 \\
2017–2018 & 6.35 & 1.12 & 17.64 \\
2016–2018 & 6.10 & 1.24 & 20.33 \\ \hline \hline \end{tabular} SD means standard deviation; CV means coefficient of variation.  
\end{table}
Table 2: Main statistical parameters of grain yield from different growing seasons.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Measurement Dates**} & \multicolumn{3}{c}{**2016–2017**} & \multicolumn{3}{c}{**2017–2018**} & \multicolumn{3}{c}{**2016–2018**} \\ \cline{2-10}  & **MEAN** & **SD** & **CV (\%)** & **MEAN** & **SD** & **CV (\%)** & **MEAN** & **SD** & **CV (\%)** \\ \hline Jointing & 2.71 & 0.52 & 19.19 & 3.23 & 0.59 & 18.27 & 2.97 & 0.66 & 22.20 \\ Flagging & 3.26 & 0.61 & 18.71 & 3.93 & 0.61 & 15.52 & 3.60 & 0.69 & 19.17 \\ Anthesis & 3.45 & 0.68 & 19.71 & 4.3 & 0.81 & 18.84 & 3.88 & 0.87 & 22.42 \\ Grain filling & 1.85 & 0.71 & 38.38 & 1.97 & 0.74 & 37.56 & 1.91 & 0.76 & 39.79 \\ \hline \hline \end{tabular} SD means standard deviation; CV means coefficient of variation.  
\end{table}
Table 3: Main statistical parameters of LAI from each growth stage in different growing seasons.