Estimating Uncertainty of Economically Optimum N Fertilizer Rates

Table 3

The comparison of the quadratic model and the linear-plus-plateau model with regards to the coefficient of determination, 𝑅², the point estimation, 𝑁_opt, and the 95% confidence set, where the ratio between 𝑁 fertilizer price 𝑟 and crop price 𝑝 is 𝑟⋅𝑝⁻¹=5.4545, for example, 𝑟=0.60€kg⁻¹ and 𝑝=110€Mg⁻¹.

Model	Design: all 𝑁  levels^1				Design: all 𝑁  levels except the zero 𝑁  rate^2
	𝑅^2	𝑁opt	95 % CI	length	𝑅^2	𝑁opt	95 % CI	length
		kg ha^−1				kg ha^−1
	High yield zone
Quadratic	0.863	240	[204,328]	124	0.707	249	(−∞,−657]∪[203,∞)	∞
Lin. + plat.	0.849	179	[158,200]	42	0.708	206	[178,235)	057
	Low yield zone
Quadratic	0.739	199	[173,260]	87	0.355	227	(−∞,155]∪[162,∞)	∞
Lin.  + plat.	0.715	127	[106,148]	42	0.314	174	[118,229)	110

1 The confidence sets are based on all measured yields at the 𝑁 rates 𝑁₁-𝑁₁₁according to Table 1.
2 The confidence sets are based on all measured yields at the N rates 𝑁₂-𝑁₁₁according to Table 1.