## 3 Climate-Related Production Prediction Model for Forage Crops
### Grass Production Prediction Model
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Category** & **Variable** & **Meaning** & **Mean** & **S.E.** \\ \hline Yield & DMYT & Total Dry Matter Yield & 15,854.71 & 4023.565 \\ \hline \multirow{2}{*}{Precipitation} & DDAYS & Drought Days & 1.68 & 3.209 \\  & PREDAUG & Sum of Precipitation Days in August & 14.07 & 4.130 \\ \hline \multirow{2}{*}{Temperature} & MAXJUL & Maximum Temperature in July & 34.0262 & 1.70214 \\  & MAXAUG & Maximum Temperature in August & 34.9328 & 1.71471 \\ \hline \multirow{2}{*}{GDD} & GDDTOTAL & GDD From January to December & 3789.4775 & 493.55510 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Variables and descriptive statistics of forage grass dataset. Figure 6: Graphs of correlation analysis results with the forage grass dataset. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **DDAYS** & **PREDAUG** & **MAXJUL** & **MAXAUG** & **GDDTOTAL** \\ \hline Pearson & DMY1 & 0.444 & \(-\)0.381 & 0.181 & 0.055 & 0.444 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of correlation analysis between grass production and 5 climate indicators. analysis was performed using SPSS, yielding a determination coefficient (R\({}^{2}\)) of 0.23, slightly lower than that of the IRG. Table 7 summarizes the results of the multivariate regression model with the stepwise selection method using SPSS. As shown in Table 7a, as a result of the multiple regression analysis, the value of the determinant coefficient (R\({}^{2}\)) was 0.230, which was considered to be somewhat insufficient for determination. Table 7b shows the selected variables with only the most influential as a result of the stepwise selection method. The results of the final selection model in the stepwise selection method showed that the PREDAUG and GDDTOTAL affected grass production in Table 7b. Table 7c shows the coefficients and intercepts of the final model. Grass was harvested year-round through the establishment of grasslands, showing a distinct contrast from the winter forage crops. Experiments were planned, applying the reorganized multivariate datasets, to figure out the optimal prediction model for forage production. Experiments were performed, varying the sample size (N) and the configuration of the independent variables, as shown in Table 8.  
Table 8 summarizes the experimental outcomes and presents a comparison of several models. When applying the Lasso model with x_features = ['DDAYS', 'PREDAUG', 'MAXJUL', 'MAXAUG', 'GDDTOTAL'], which includes all five selected independent variables in the grass dataset with N = 500, the value of the adjusted R\({}^{2}\) improved to 0.4799, demonstrating an enhanced explanatory power compared to the multiple regression model. When applying quartile refinement to data within the 25% to 75% range and experimenting with data sizes of N = 400 and N = 300, respectively, the values of the adjusted R\({}^{2}\) did not show significant improvement. As shown in Table 8, it was discovered that, in the case with a data size of N = 400, the value of the adjusted R\({}^{2}\) was 0.367, and in the case with a data size of N = 300, the value of the adjusted R\({}^{2}\) was 0.288. This result was interpreted as not requiring additional filtering because the grass data had normality. In the case of the Lasso model, incorporating all 15 climate factors that were initially selected for the first time, the adjusted R\({}^{2}\) value was 0.48, indicating a slight improvement. This outcome can be interpreted as an enhancement in the determination coefficient, attributed to increases in the independent variables. If the R\({}^{2}\) values were comparable, it was desirable to develop a productivity prediction model using the minimum number of indicators. If there were numerous indicators, it became possible to evaluate various factors. However, managing the fundamental data became challenging.