## 4 Experimental Setting
### Statistical Analysis  
For this investigation, this study chose to use parametric statistical analysis because the assumptions of normality and equal variance are likely to be met given the data and the fact that we are comparing means within each regression model. Additionally, parametric tests are generally more powerful than non-parametric tests, meaning they have a greater ability to detect differences between groups when they exist. Figure 11: Stdev performance for each nutrient prediction model. Figure 10: RMSE performance for each nutrient prediction model. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Method** & **Ca** & **Mg** & **K** & **P** & **N** & **All** & **AVG** & **STDEV** \\ \hline EN & 0.0362 & 0.0193 & 0.3991 & 0.0651 & 0.6326 & 0.2376 & 0.2305 & 0.2738 \\ PN & 0.0255 & 0.0395 & 0.1726 & 0.0267 & 0.4866 & 0.1502 & 0.1502 & 0.1979 \\ SW & 0.0357 & 0.0184 & 0.4241 & 0.0497 & 0.5741 & 0.2572 & 0.2204 & 0.2601 \\ RR & 0.0345 & 0.0176 & 0.2860 & 0.0402 & 0.5070 & 0.1949 & 0.1771 & 0.2152 \\ LS & 0.0297 & 0.0193 & 0.4131 & 0.0651 & 0.6768 & 0.2494 & 0.2408 & 0.2934 \\ LR & 0.0345 & 0.0175 & 0.2852 & 0.0400 & 0.5056 & 0.1949 & 0.1766 & 0.2146 \\ AVG & 0.0327 & 0.0219 & 0.3300 & 0.0478 & 0.5638 & 0.2140 & & \\ STDEV & 0.0042 & 0.0086 & 0.0993 & 0.0153 & 0.0777 & 0.0412 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 13: RMSE with averages and STDEV. The normality assumption was evaluated through the Shapiro-Wilk test, which is a commonly used test for normality. This test checks whether the data follows a normal distribution. The equal variance assumption was examined using [PERSON]'s test. The Shapiro-Wilk test for normality was applied to the residuals of the regression models, and the results indicated that the residuals were normally distributed (\(p\)-value \(>\) 0.05). Additionally, [PERSON]'s test was employed to assess the equality of variances among the groups, and the results did not suggest any significant deviation from homogeneity of variances (\(p\)-value \(>\) 0.05). The application of these tests supports the validity of the ANOVA results presented in Table 14. These tests, along with the reported F-statistics and \(p\)-values, confirm that the assumptions necessary for ANOVA were satisfied. Therefore, we can observe differences among the six designed regression models that are statistically significant and not a result of violations of normality or equal variance assumptions. Table 14 presents the ANOVA test for six designed regression models using different regression methods of \"Elastic Net Regression\", \"Polynomial regression\", \"Stepwise regression\", \"Ridge regression\", \"Lasso regression\" and \"Linear Regression\". Based on the ANOVA test with a \(p\)-value of 2.3253 \(\times\) 10\({}^{-17}\) and an alpha level of 0.05, we can conclude that there is a statistically significant difference among the six designed regression models. Therefore, we reject the null hypothesis that there is no significant difference and accept the alternative hypothesis that at least one of the regression models has a different performance value than the others. Post hoc analysis was conducted using the Tukey Honestly Significant Difference (Tukey HSD) test to determine specific pairwise differences between the regression models. This test accounts for multiple comparisons and provides valuable insights into which models significantly differ in performance. Based on the results of the ANOVA test, Model 5 demonstrated better performance compared to other designed feature set models (refer to Table 4). As a result, to gain insight into the impact of each nutrient on N% nutrient concentration, we utilized SHAP visualization. Figure 12 illustrates the effect of each nutrient on N% nutrient concentration. Referring to Figure 12, the attributes K (potassium), Mg (magnesium), Day, Season, Ca (calcium), Plot, SubPlot, and P (phosphorus) appear to have varying levels of impact on N% nutrient concentration.