## 4 Discussion
In this study, GNDVI, GCI, and NDE demonstrated the ability to discriminate the soybean vigor, yield, and SCN conditions which is similar to the findings by [PERSON] et al. [6]. These results demonstrate the use of aerial multispectral imagery data as a quick, non-destructive, and an economical way for SCN infestation detection and characterization. Out of the 24 initially derived VIs, six VIs and five REFs that showed strong correlation with SY were selected as inputs for ML and statistical modeling to avoid overfitting and improve accuracy of the estimates. The reflectance in blue (r = \(-\)0.62) followed by the reflectance in green (r = \(-\)0.39) wavebands had the highest correlations with SY, while NIR had low correlation with SY (r = 0.15) possibly due to lowered chlorophyll levels at the later stage [50]. The reflectance in the red waveband had the lowest correlation due to its lower sensitivity to chlorophyll variations (r = \(-\)0.0046) [38]. NDE had the highest correlation with SY out of all 24 derived VIs, followed by GCI, GOVAVI, GSOVI, and VARI, among others (r = \(-\)0.57-0.75). The lowest (in magnitude) correlation (r = 0.36) was found with GDVI. The strong correlation is supported by the composition of NDE and GCI, with NIR (840 \(\pm\) 20 nm), red edge (RE: 730 nm \(\pm\) 16 nm), and green (560 nm \(\pm\) 16 nm) wavebands that are relatively more sensitive to the chlorophyll content [38]. However, due to the mathematical nature of GDVI and the use of low-correlated NIR waveband in its computation, it could have exhibited lower correlation of GDVI with SY. Strongercorrelations between SY and VIs like NDRE and GCI are possibly because those indices account for dynamic variations in the visible-NIR region related to nitrogen and chlorophyll content [51]. It is also the reason for higher correlations of NDRE (which uses the red-edge band in its computation) and GCI (which requires the green band) compared to IPVI, and NDVI [52; 53; 54]. Although using either the broadband spectral bands (REFs) or VIs as standalone inputs in linear models may be feasible for SY estimation, these may not stand robust when crops are subjected to high variations in agroclimatic conditions [24; 28]. On the contrary, non-linear combination of spectral indices, REFs, and texture features could improve the prediction accuracy of the models [24; 54]. Following that, this study went a step further to estimate SY (output) using only REFs as well as their non-linear combination with VIs as inputs in statistical and ML models for more accurate, robust, and intricate predictions. In this study, REF in blue, green, red, RE, and NIR wavebands, and Vis, NDRE, GCI, GOAVI, GSAVI, GDVI and VARII, were identified as not to have absolute correlations (i.e., r = 1) among each other using PCA. This aided dimensionality reduction and eliminating collinear variables prior to SY modeling. NDRE is able to overcome saturation limitation [55; 56] when the crop canopy reached 100% [55; 57] due to linear correlation with biomass and yield [56]. Studies that have carried out crop yield and nitrogen estimations using spectral wavebands or a combination of wavebands and VIs through ML [53; 28] have not assessed or removed inter-correlations among the input variables (VIs) prior to output estimation [58; 59]. This may highly result into overfitting and reduced the robustness of the developed and tested models [26]. For model training and validation, the majority of machine learning-based prediction studies have by default used train-test data split ratios of 70:30 or 80:20 [42; 60; 61; 62]. However, there has not been much research conducted on determining the ideal train-test data splits while considering total dataset size. This could form another factor impacting robustness and over fitness of the models [26]. All these factors were considered in this study especially due to the moderate size of the involved dataset.