## 3 Climate-Related Production Prediction Model for Forage Crops
### Italian Rgegrass Production Prediction Model
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Variable** & **Meaning** & **Mean** & **S.E.** \\ \hline Yield & DMY1 & First Dry Matter Yield of IRG & 9011.877 & 4295.5617 \\ \hline \multirow{3}{*}{Precipitation} & PREOCT & Precipitation in October & 50.2601 & 69.8917 \\  & PRESUM & Sum of Precipitation & 365.834 & 117.2916 \\  & PREAFTOVWIN & Precipitation Sum Over Winter & 93.315 & 56.7692 \\ \hline \multirow{3}{*}{Temperature} & MINTDEC & Minimum Temperature in December & \(-\)3.323 & 5.1069 \\  & MINTJAN & Minimum Temperature in January & \(-\)5.595 & 5.0707 \\  & MINTFEB & Minimum Temperature in February & \(-\)3.714 & 4.6233 \\  & MINTMAR & Minimum Temperature in March & 1.490 & 3.2148 \\ \hline GDD & GDDFJTA & GDD From January To April & 339.207 & 133.038 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Variables and descriptive statistics of IRG dataset. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **PREOCT** & **PRESUM** & **PREAFOVWIN** & **MINTDEC** & **MINTJAN** & **MINTFEB** & **MINTMAR** & **GDDFJTA** \\ \hline Pearson & DMY1 & 0.445 ** & 0.407 ** & 0.493 ** & 0.574 ** & 0.600 ** & 0.569 ** & 0.583 ** & 0.564 ** \\ \hline \hline \end{tabular}  
* The correlations are statistically significant at the 0.01 level.  
\end{table} 
Table 2: Results of correlation analysis between IRG production and 8 climate indicators. be somewhat insufficient for prediction accuracy. Table 3b shows the selected variables with only the most influence as a result of the stepwise selection method. The results derived that three variables, MINTJAN, PREOCT, and GDDFJTA, were the key impact factors related to IRG production among the climate variables. Table 3c shows the results of summarizing the coefficients and intercepts of the independent variables adopted in the final selection model. As a result of the multiple regression analysis using SPSS, the value of the adjusted R\({}^{2}\) was 0.446, which was somewhat inadequate for determination. In addition, a problem of multicollinearity was identified due to the high correlation among the independent climate factors. Existing linear regression models often suffer from overfitting by closely analyzing the relationship between feature and label values in excessive detail. As a result, their ability to accurately predict new data is diminished due to poor generalization. To address this issue, the Lasso model was employed as a regression technique. In linear regression, the essence lies in discovering suitable weights and biases. The Lasso model achieved this by minimizing the mean squared error (MSE) while introducing supplementary constraints, thereby simultaneously minimizing the sum of absolute weight values. Figure 5: Graphs of correlation analysis results with IRG dataset. The Lasso model addressed the issue of multicollinearity during the modeling process, resulting in the creation of a final model. Therefore, the issue of the multiple regression model could be solved. In addition, the analysis using the Lasso model resulted in an improved determination coefficient (R2) value of 0.6, which demonstrated a greater enhancement in the explanatory power compared to that of the existing multiple linear regression model. Specifically, the application of the Lasso regression model using the climate factors selected through the stepwise selection method resulted in an R2 value of 0.629. As a result, the issue of multicollinearity was resolved, leading to an enhancement in the explanatory power of the prediction model. This improvement enabled the derivation of an IRG production prediction model comprising key climate factors such as the PREOCT (precipitation in October), MINJTAN (minimum temperature in January), and GDDFJTA (growing degree days from January to April), which exerted a significant influence. To find the optimal IRG production prediction model, experiments were performed after reconstructing various datasets.