Table 4 Regression model for crop fertilizer rate optimization

From: Multiobjective spatial optimization of fertilizer rates enables sustainable crop production in southwest China

Crop

Dependent variable

Independent variable

Model

R2

Rice

OYN

x1

0.0475 × 13 + 0.0602 × 12 - 0.1603 × 1 + 14.215

1.00

OYP

x2

0.673 × 23 − 1.2996 × 22 + 0.782 × 2 + 14.209

0.83

OYK

x3

0.0766 × 33 − 0.1254 × 32 + 0.0216 × 3 + 14.213

0.99

OFRN

x1

−8.1756 × 1 + 23.379

1.00

OFRP

x2

2.6425 × 2 + 9.0894

1.00

OFRK

x3

1.6711 × 3 + 8.7415

1.00

Maize

OYN

x1

0.7336 × 13 − 1.5089 × 12 + 0.9009 × 1 + 11.131

0.88

OYP

x2

0.4113 × 23 + 0.0008 × 22 − 0.0095 × 2 + 11.14

0.96

OYK

x3

1.5791 × 33 − 2.7217 × 32 + 1.1573 × 3 + 11.139

0.78

OFRN

x1

−4.4209 × 1 + 32.157

1.00

OFRP

x2

7.8178 × 2 + 11.834

1.00

OFRK

x3

7.1662 × 3 + 9.3479

1.00

Wheat

OYN

x1

−0.0764 × 13 + 0.1283 × 12 − 0.0161 × 1 + 3.1151

0.82

OYP

x2

−0.1503 × 23 + 0.1452 × 22 + 0.0171 × 2 + 3.1183

0.81

OYK

x3

−0.1392 × 33 + 0.2377 × 32 − 0.0826 × 3 + 3.1231

0.99

OFRN

x1

1.273 × 1 + 7.8869

1.00

OFRP

x2

3.382 × 2 + 3.2518

1.00

OFRK

x3

3.1016 × 3 + 2.8368

1.00

  1. Note: the independent variables x1, x2, and x3 denote the adjustment gradients (%) of the nitrogen, phosphorus, and potassium fertilizer rates, respectively; OFRN, OFRP, and OFRK are the total nitrogen fertilizer rate, total phosphorus fertilizer rate, and total potassium fertilizer rate, respectively; OYN, OYP, and OYK denote the total nitrogen response yield, total phosphorus response yield, and total potassium response yield, respectively.
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