Table 1.
Coding design table of each N, P, and K factor level.
Table 2.
Quadratic orthogonal rotation combination design and results.
Table 3.
Analysis of variance of the effects of N, P, and K fertilizers on yield and yield components.
Fig 1.
Effect of N, P, and K fertilizers on yield and yield components.
a. Effects of N, P, and K fertilizers on yield when N(X1) was within (-1.68, 1.68), Y = 2,306.85 + 113.22X1−104.14X12. When P(X2) was within (-1.68, 1.68), Y = 2306.85 + 96.50X2−74.09X22. When K(X3) was within (-1.68, 1.68), Y = 2306.85 + 129.66X3−99.92X32. b. Effects of N, P, and K fertilizers on pods per plant. When N(X1) was within (-1.68, 1.68), Y = 25.81 + 2.61X1−1.06X12. When P(X2) was within (-1.68, 1.68), Y = 25.81 + 0.99X2−0.91X22. When K(X3) was within (-1.68, 1.68), Y = 25.81 + 1.57X3−2.07X32. c. Effects of single-factor N, P, and K fertilizer on the seeds per pod. When N(X1) was within (-1.68, 1.68), Y = 13.34–0.27X1 + 0.11X12. When P(X2) was within (-1.68, 1.68), Y = 13.34–0.15X2−0.19X22. When K(X3) was within (-1.68, 1.68), Y = 13.34–0.44X3−0.15X32. d. Effects of N, P, and K fertilizers on 100-seed weight. When N(X1) was within (-1.68, 1.68), Y = 6.51 + 0.36X1 + 0.06X12. When P(X2) was within (-1.68, 1.68), Y = 6.51–0.11X2 + 0.02X22. When K(X3) was within (-1.68, 1.68), Y = 6.51–0.01X3 + 0.04X32.
Fig 2.
Effects of N(X1), P(X2), and K(X3) interactions on pods per plant and yield.
The radiation line represents the yield value (Y kg ha-1) and pods per plant. a. Effects of N and P fertilizer interaction on yield (X3 = 0). The radiation angle indicates N fertilizer levels and the series indicates the P fertilizer levels. b. Effects of N and K fertilizer interaction on yield (X2 = 0). The radiation angle indicates the N fertilizer levels and the series indicates the K fertilizer levels. c. Effects of P and K fertilizer interaction on yield (X1 = 0). The radiation angle indicates the P fertilizer levels and the series indicates the K fertilizer levels. d. Effects of N and P fertilizer interaction on pods per plant. The radiation angle indicates the N fertilizer levels and the series indicates the P fertilizer levels (X3 = 0). e. Effects of N and K fertilizer interaction on pods per plant. The radiation angle indicates the N fertilizer levels and the series indicates the K fertilizer levels (X2 = 0). f. Effects of P and K fertilizer interaction on pods per plant (X1 = 0). The radiation angle indicates the P fertilizer levels and the series indicates K fertilizer levels.
Fig 3.
Effects of N(X1), P(X2), and K(X3) interactions on 100-seed weight and seeds per pod.
The radiation line represents the seeds per pod and 100-seed weight (g). a. Effects of N and P fertilizer interaction on the seeds per pod (X3 = 0). The radiation angle indicates the N fertilizer levels and the series indicates the P fertilizer levels. b. Effects of N and K fertilizer interaction on the seeds per pod (X2 = 0). The radiation angle indicates the N fertilizer levels and the series indicates the K fertilizer levels. c. Effects of P and K fertilizer interaction on the seeds per pod (X1 = 0). The radiation angle indicates the P fertilizer levels and the series indicates the K fertilizer levels. d. Effects of N and P fertilizer interaction on 100-seed weight. The radiation angle indicates the N fertilizer levels and the series indicates the P fertilizer levels (X3 = 0). e. Effects of N and K fertilizer interaction on 100-seed weight. The radiation angle indicates the N fertilizer levels and the series indicates the K fertilizer levels (X2 = 0). f. Effects of P and K fertilizer interaction on 100-seed weight (X1 = 0). The radiation angle indicates the P fertilizer levels and the series indicates the K fertilizer levels.
Table 4.
Frequency distribution and fertilization measures for yield and yield components.
Table 5.
Implementation and verification of optimized fertilization.