## 3 Results  
### Soybean Yield  
From 2018 through 2020, the seed yield for soybean cultivars planted in two regions of Central Poland averaged 9.81 dt ha\({}^{-1}\) (_cv._ Augusta, at Mochelek in 2018) to 39.29 dt ha\({}^{-1}\) (_cv._ Aligator, at Jedrzejewo in 2020) (data not present). The main factors, e.g., cultivar, site and year, had individually strongly differentiating (_p_! 0.001) effects on yield, and they interacted (Tables 6 and 7, Figure 1). In 2020, across the locations and cultivars, the highest mean of soybean yield, i.e., 32.2 dt ha\({}^{-1}\), which was higher in comparison to the average yield in 2019 (27%) and the average yield in 2018 (40%), was noted (Table 7). In six locations in the growing season in 2018 and in three locations in 2019, soybean plantations received insufficient sums of precipitation, ranging from 132-207 mm. The hydrothermal coefficient \(K\) ranged from 0.4 to 1.2, indicating that half of the plantations experienced drought conditions during the three years of the study (Table 5). The 2020 season had an optimal distribution of rainfall and temperature for soybeans, as both parameters are indicated by the hydrothermal \(K\) coefficient ranging from 1.7 to 2.4, namely, optimal and humid conditions (Table 5). The highest average yield in 2020 was noted on the sandy loam soil (e.g., in Jedrzejewo and Rakowo) obtained from the soybean cultivars at the 3 rd group of earliness (Figure 1). The interaction of soybean yield depending on the sites and years with various precipitation was thoroughly studied by multi-regression analysis (2). We found a significant multivariate relationship (_R_ = 0.67; _p_! 0.001) between the hydrothermal coefficient \(K\) and the vegetation period day VPD as predictors of soybean yield. The standardized multi regression coefficient \(b\) = 0.56 (_p_! 0.001) was found for the relation between \(K\) and yield, while for the VPD and yield, the standardized multi regression \(b\) = 0.25 (_p_! 0.001), which can be quantified with the regression equation:  
\[\mathrm{Y_{(yield)}}=21.8+12.0\ \mathrm{X_{1(K)}}+0.20\ \mathrm{X_{2(VPD)}} \tag{2}\]  
As producers of soybean have no influence on the \(K\) coefficient, they can decide what type of soybean group and the cultivars they choose, which reflects VPD. Each day of VPD from the range 100-155 increases the production of soybeans by 20 kg of seeds per ha. Meanwhile, each unit of hydrothermal coefficient increases the yield of soybean by 1200 kg of seeds per ha (Figure 2). \begin{table}
\begin{tabular}{c c c c c} \hline
**Source of Variation** & _df_ & **Yield** & **Protein** & **Oil** \\ \hline Year & 2 & 4446 *** & 130.1 *** & 0.98 \\ Site & 5 & 430.9 *** & 19.4 * & 1.33 \\ Cultivar & 19 & 151.4 *** & 25.6 * & 1.72 * \\ Year \(\times\) site & 10 & 33.1 *** & 12.8 & 0.75 \\ Year \(\times\) cultivar & 25 & 33.3 *** & 29.7 * & 1.19 \\ Site \(\times\) cultivar & 32 & 46.3 *** & 1.26 & 0.84 \\ Residual & 314 & 4.07 & 12.6 & 0.68 \\ \hline \end{tabular} \(df\)—degrees of freedom; *—\(p\)! 0.05; ***—\(p\)! 0.001.  
\end{table} 
Table 6: Mean squares from the three-way analysis of variance for the seed yield, protein content and oil content of soybean. Figure 1: The seed yield (dt ha\({}^{-1}\)) depending on the earliness of soybean. _Means \(\pm\) confidence intervals_ (\(p=0.95\)) from cultivars planted in 2018–2020 in Central Poland. # Various letters indicate the heterogenous groups according to the [PERSON]’s test at \(p=0.05\).