*2.4. Statistical Analysis*

Analysis of variance (ANOVA) was conducted using the general linear model procedure in SPSS 25.0 software (SPSS Inc., Chicago, IL, USA). The main e ffects of soil, year, planting density, and N fertilizer rate on yield, AGB, PNC, and NNI were analyzed. Mean values of the aforementioned variables for each N treatment were compared using least significant di fference test (LSD) at the *p* < 0.05 probability level. Three statistical models (quadratic, quadratic-plus-plateau and linear-plus-plateau) were selected to describe the crop yield response to N rate, AGB, PNC, and NNI. The PROC NLIN procedure in SAS software (Version 8.0, SAS, 2013), was used to build and analyze those models. The choice of the best model was based on the coe fficients of determination (R2) and root mean square error (RMSE). The quadratic model had the best fit to describe the crop yield response to AGB, and the

linear-plus-plateau model had the best fit to describe the crop yield response to PNC and NNI at specific soil and specific soil-year respectively. The quadratic-plus-plateau model had the best fit and was therefore used to calculate the EONR and yield at EONR (EOY). The EONR (kg N ha−1) was calculated as:

$$\text{ECONR [kg ha}^{-1}\text{]} = (\text{CP} - \text{b})/2\text{c} \tag{6}$$

where CP was the ratio of the cost of N fertilizer to the price of maize grain, and b and c are the linear and quadratic coe fficients from the quadratic-plus-plateau equation. The EOY was calculated by substituting the EONR value into the quadratic-plus-plateau equation [44].

Additionally, multiple linear regression was used to establish the relationships between EONR (obtained yield) and the soil total N (TN), planting density (D), growing degree days (GDD), and accumulated precipitation (APP) during maize growing season using the SPSS 25.0 software (SPSS Inc., Chicago, IL, USA). The GDD was calculated as follows:

$$\text{GDD} = \sum \left( (\mathbf{T}\_{\text{max}} - \mathbf{T}\_{\text{min}}) / 2 - \mathbf{T}\_{\text{base}} \right) \tag{7}$$

where Tmax, Tmin, Tbase are the daily maximum, minimum, and base temperatures, respectively and Tbase = 10 ◦C.
