Table 3 The quadratic polynomial trend surface equations, and yield, PFPN and NER.

From: Optimizing planting density and nitrogen application to enhance profit and nitrogen use of summer maize in Huanghuaihai region of China

Year

Equation

R2

p

x

y

z

GY

PFPN

NER

2017

z =  − 3978 + 7.421x + 0.154y + 1.205E−05xy − 0.0211x2 − 9.659E−07y2

0.992

**

199

81,081

3012

12.13

60.90

41.12

2018

z =  − 2897 + 4.029x + 0.124y − 1.593E−05xy − 0.0065x2 − 7.121E−07y2

0.989

**

205

84,782

2774

11.32

54.66

38.56

Mean

z =  − 3438 + 5.725x + 0.139y − 1.942E−06xy − 0.0138x2 − 8.390E−07y2

0.992

**

201

82,680

2890

11.71

57.97

39.92

  1. R2 the coefficient of determination, x represents the N application rate (kg ha−1), y represents the planting density (plant ha−1), z represents the profit, GY represents the grain yield (t ha−1), PFPN represents partial factor productivity of applied N (kg kg−1), NER represents nitrogen efficiency ratio (%).
  2. **Represents significance at the 0.01 probability level.
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