## 3 Climate-Related Production Prediction Model for Forage Crops
### Grass Production Prediction Model
When the value of the determination coefficient (R\({}^{2}\)) was satisfied, selecting a smaller number of independent variables could simplify their future use in the analysis of suitable cultivation area changes. It was found that the \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & & & & & & \\ \hline Model & R & R Squared & Adjusted R Squared & Standard Error of the Estimate \\ \hline
2 & 0.482 & 0.233 & 0.230 & 3531.551 \\ \hline  & & & & & \\ \hline \multicolumn{6}{c}{ANOVA *} \\ \hline Model & Sum of Squares & Degree of Freedom & Mean Square & F & Significance Probability \\ \hline \multirow{3}{*}{2} & Regression & 1,879,834,560,268 & 2 & 939,917,280,134 & 75.363 & 0.000 \\  & Residual & 6,198,512,188,682 & 497 & 12,471,855,510 & & \\  & Total & 8,078,346,748,950 & 499 & & & \\ \hline \multicolumn{6}{c}{(c)} \\ \hline Model & \multicolumn{3}{c}{Non-Standardized Coefficient} \\ \cline{2-6}  & \multicolumn{3}{c}{B} & Standard Error & Beta & t & Significance Probability \\ \hline \multirow{3}{*}{2} & (Constant) & 8380.649 & 1779.579 & & 4.709 & 0.000 \\  & PREDAUG & 2.757 & 0.367 & 0.338 & 7.521 & 0.000 \\ \cline{1-1}  & GDDTOTAL & \(-\)211.288 & 43.808 & \(-\)0.217 & \(-\)4.823 & 0.000 \\ \hline \multicolumn{6}{c}{\({}^{\text{a}}\) Dependent variable: DMYT; Predictor: (constant), PREDAUG, GDDTOTAL.} \\ \end{tabular}
\end{table} 
Table 7: Results of the grass multivariate regression analysis (stepwise selection method) (a): determination coefficient (R\({}^{2}\)) of the final selection model. (b): result valuables of the final selection model. (c): coefficients of the final selection model. climate factors that most affected the production of grass were the PREDAUG, GDDTOTAL, MAXJUL, MAXAUG, and DDAYS. Therefore, we selected the Lasso model including five climate factors as an optimal model. The second row of Table 8 specifies the coefficients and intercepts for each variable of the optimal model. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Variables** & **Coefficients** & **Intercept** & **R2** \\ \hline Multivariate Regression & DMY1- & & 8380.649 & 0.23 \\ (Stepwise) & PREDAUG & \(-211.288\) & & \\ (N = 500, X = 5) & GDDTOTAL & 2.757 & & \\ \hline  & DMY1- & & 11,016.29 & 0.4799 \\  & DDAYS & 53.6 & & \\ Lasso Regression & PREDAUG & \(-205.95\) & & \\ (N = 500, X = 5) & MAXJUL & \(-129.12\) & & \\  & MAXAUG & \(-7.35\) & & \\  & GDDTOTAL & 3.244 & & \\ \hline  & DMY1- & & 12,613.215 & 0.367 \\ Lasso regression & PREDAUG & \(-133.099\) & & \\ (N = 400, X = 5) & MAXJUL & \(-97.403\) & & \\  & MAXAUG & 12.386 & & \\  & GDDTOTAL & 2.096 & & \\ \hline  & DMY1- & & 5119.838 & 0.288 \\ Lasso regression & PREDAUG & \(-25.871\) & & \\ (N = 300, X = 5) & MAXJUL & 170.076 & & \\  & MAXAUG & 36.197 & & \\  & GDDTOTAL & 1.1505 & & \\ \hline  & DMY1- & & 13,656.397 & 0.434 \\  & DDAYS & 73.392 & & \\  & PREDAUG & \(-235.871\) & & \\ Lasso regression & MAXJUL & \(-11.940\) & & \\ (N = 500, X = 8) & MAXAUG & 250.936 & & \\  & GDDTOTAL & \(-1.031\) & & \\  & MNITFEB & 314.83 & & \\  & MINITMAR & \(-170.95\) & & \\  & MTMAR & 445.2049 & & \\ \hline  & DMY1- & & 13,581.535 & 0.480 \\  & DDAYS & 64.391 & & \\  & PREDAUG & \(-266.45\) & & \\  & MAXJUL & \(-33.03\) & & \\  & MAXAUG & 378.06 & & \\  & GDDTOTAL & \(-0.7308\) & & \\  & GDDFJTA & \(-3.647\) & & \\ Lasso regression & PREDAOV & 94.77 & & \\ (N = 500, X = 15) & MINITJAN & 11.742 & & \\  & MINITFEB & 282.09 & & \\  & MINTMAR & \(-224.659\) & & \\ MAXTNOV & \(-220.732\) & & \\ MAXTMAR & \(-171.907\) & & \\ MTJAN & \(-224.456\) & & \\ MTFEB & 326.645 & & \\ MTMAR & 915.632 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison of results from analysis of the grass production prediction model.