## 3 Climate-Related Production Prediction Model for Forage Crops
### Italian Rgegrass Production Prediction Model  
To analyze the correlation between Italian ryegrass and climate data, a climate change vulnerability analysis was performed with the selected eight climate factors known to affect the growth of winter forage crops. These selected climate factors have been empirically shown to impact the growth of winter forage crops. These factors were chosen by the Grassland Feed Department of the National Institute of Animal Science. Their selection was based on the department's extensive experience and knowledge, gained over many years of the trial cultivation of grassland forage crops with previously studied climate factors. Dry matter yield (DMY1) was chosen as the dependent variable. The following eight climate factors were selected as independent variables: October precipitation (PREOCT), the sum of precipitation (PRESUM), the precipitation sum over winter (PREAUTOVWIN), the minimum temperature in December (MINTDEC), the minimum temperature in January  
Figure 4: Preprocessed dataset of forage grass. (MINTJAN), the minimum temperature in February (MINTFEB), the minimum temperature in March (MINTMAR), and the GDD From January to April (GDDFJTA). These variables are listed in Table 1. As shown in Section 2, N = 304. The descriptive statistics for each variable are summarized in Table 1. These valuables satisfied the normality of the dry matter yield (DMY1), the dependent variable. Table 2 shows the results of the correlation analysis between the eight climate indicators and the dry matter yield. As a result of the correlation analysis between these eight climate factors and the dry matter yield, variables such as the growing degree days from January to April (GDDFJTA), the minimum temperature in January (MINTJAN), the precipitation in October (PREOCT), and the precipitation sum over winter (PREAFOVWIN) exhibited slightly high correlation coefficients. Additionally, it was evident that all independent variables were correlated with the dependent variable, the dry matter yield (DMY1). These correlations were statistically significant at the 0.01 level. Figure 5 shows a graph of the correlation analysis results for each variable. To select the climate factors with more influence on Italian ryegrass production among the eight climate factors, forecast models were constructed and analyzed in various combinations. While developing a productivity prediction model, several variables, including the soil type, variety, and cultivation management, might exert an influence in addition to climate factors. However, since this study's objective was to analyze the vulnerability of Italian ryegrass (IRG) production to climate change, focusing on climate factors, a data analysis was performed to obtain an optimal model by applying various regression models. A correlation analysis was conducted using the eight climate factors listed in Table 1 as independent variables, while the dry matter yield (primary) data--the Italian ryegrass production data--served as the dependent variable. A production prediction model was then developed through a multiple regression analysis, the Lasso model, and the Ridge model. Subsequently, the production was compared and analyzed using these models. Three regression models were estimated within the multivariate regression framework using a stepwise selection method in SPSS. All three models from the stepwise selection process were found to be significant. However, the model of the result of the third step was chosen because it had the highest value of adjusted R\({}^{2}\). Table 3 summarizes the results of the multivariate regression model with the stepwise selection method using SPSS. As shown in Table 3a, as a result of the multiple regression analysis, the value of the determinant coefficient, R\({}^{2}\), was 0.446, which was considered to