## 3 Climate-Related Production Prediction Model for Forage Crops
### Italian Rgegrass Production Prediction Model
Experiments were conducted for cases where the numbers of x_features were seven, four, and three, respectively, by varying the composition of the independent variables. Table 4 shows the comparison results of several models, summarizing the experimental results. When applying the Lasso model with x_features = ['PREOCT', 'PRESUM', 'PREAFOVWIN', 'MINTDEC', 'MINJTAN', 'MINTFE', 'MINTMAR', 'GDDFJTA'], which included all seven selected independent variables in the IRG dataset with N = 304, the value of the adjusted R2 was confirmed to be 0.601. In the case of the Lasso model with x_features = ['PREOCT', 'MINJTAN', 'MINTFE', 'GDDFJTA'], which selected four attributes with high importance from the independent variables in the IRG dataset with N = 304, the value of the adjusted R2 was confirmed to be 0.627. When applying the Lasso model with x_features = ['PREOCT', 'MINJTAN', 'GDDFJTA'], which represented a multivariate regression model using a stepwise selection method among independent variables in the IRG dataset with N = 304, the value of the adjusted R2 was 0.629, which was confirmed to be the highest determination coefficient. As a result, the climate factors, most influencing to the production of IRG, were the precipitation in October (PREOCT), minimum temperature in January (MINJTAN), and GDD from January to April (GDDFJTA). Considering Lasso's ability to enhance prediction accuracy by forcing regression coefficients of irrelevant variables to become zero, along with its capacity to yield a more interpretable model, it could be inferred that appropriate variables were selected. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & & & (a) & & \\ \hline \multicolumn{7}{c}{Model Summary} \\ \hline Model & R & R Squared & Modified R Squared & Standard Error of the Estimate & Darwin-Watson \\ \hline
3 & 0.672 & 0.451 & 0.446 & 3197,9769 & 0.744 \\ \hline \multicolumn{7}{c}{(b)} \\ \hline \multicolumn{7}{c}{ANOVA *} \\ \hline Model & Sum of Squares & Degree of Freedom & Mean Square & F & Significance Probability \\ \hline \multirow{3}{*}{3} & Regression & 2,498,119,243,996 & 3 & 832,706,414,665 & 81.422 & 0.000 \\  & Residual & 3,037,435,744,456 & 297 & 10,227,056,379 & & \\  & Total & 5,535,554,988,452 & 300 & & & \\ \hline \multicolumn{7}{c}{(c)} \\ \hline \multicolumn{7}{c}{Coefficient *} \\ \hline \multicolumn{7}{c}{Model} & Non-Standardized Coefficient & Standardized Coefficient & \multirow{2}{*}{t} & \multirow{2}{*}{Significance Probability} & \multicolumn{2}{c}{Cillimentarity Statistic} \\ \cline{3-3} \cline{5-6}  & B & Standard Error & & & Tolerance & VIF \\ \hline \multirow{3}{*}{3} & (Constant) & 6167.375 & 1046.588 & 5,893 & 0.000 & 0.000 & 0.392 & 2.551 \\  & MINJTAN & 231.498 & 58,153 & 0.273 & 3.981 & 0.000 & 0.925 & 1.081 \\  & PREOCT & 19.046 & 2.746 & 0.310 & 6.935 & 0.000 & 0.925 & 1.081 \\  & GDDFJTA & 9.382 & 2.166 & 0.291 & 4.332 & 0.000 & 0.411 & 2.435 \\ \hline \end{tabular}  
* Dependent variable: DMY1; Predictor: (Constant), MINJTAN, PREOCT, GDDFJTA.  
\end{table} 
Table 3: Results of IRG multivariate regression analysis (stepwise selection method) (a): coefficient of determination (R2) of the final selection model. (b): outcome variable of final selection model. (c): coefficient of final selection model.