Chinese Agricultural Science Bulletin ›› 2020, Vol. 36 ›› Issue (33): 31-37.doi: 10.11924/j.issn.1000-6850.casb20191100838
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Tian Yixin(), Gao Fengju, Cao Pengpeng, Gao Qi, Li Hongbo
Received:
2019-11-15
Revised:
2019-12-11
Online:
2020-11-25
Published:
2020-11-18
CLC Number:
Tian Yixin, Gao Fengju, Cao Pengpeng, Gao Qi, Li Hongbo. Orthogonal Polynomial Regression: Application in the Prediction Model of High-protein Soybean Fertilization and Economic Benefit[J]. Chinese Agricultural Science Bulletin, 2020, 36(33): 31-37.
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URL: https://www.casb.org.cn/EN/10.11924/j.issn.1000-6850.casb20191100838
N/(kg/hm2) | K/(kg/hm2) | P | |||||
---|---|---|---|---|---|---|---|
50 kg/hm2 | 80 kg/hm2 | 110 kg/hm2 | |||||
30 | 40 | 2615.21 | (27) | 2730.24 | (24) | 2855.02 | (20) |
70 | 2645.33 | (25) | 2756.57 | (22) | 2883.68 | (17) | |
100 | 2629.14 | (26) | 2747.21 | (23) | 2863.33 | (19) | |
60 | 40 | 2992.33 | (12) | 3114.23 | (8) | 3174.69 | (3) |
70 | 3140.85 | (6) | 3174.78 | (2) | 3282.48 | (1) | |
100 | 3031.76 | (9) | 3148.11 | (5) | 3151.24 | (4) | |
90 | 40 | 2832.17 | (21) | 2954.02 | (16) | 3015.02 | (11) |
70 | 2981.34 | (15) | 3015.21 | (10) | 3122.47 | (7) | |
100 | 2872.21 | (18) | 2988.05 | (14) | 2991.03 | (13) |
N/(kg/hm2) | K/(kg/hm2) | P | |||||
---|---|---|---|---|---|---|---|
50 kg/hm2 | 80 kg/hm2 | 110 kg/hm2 | |||||
30 | 40 | 2615.21 | (27) | 2730.24 | (24) | 2855.02 | (20) |
70 | 2645.33 | (25) | 2756.57 | (22) | 2883.68 | (17) | |
100 | 2629.14 | (26) | 2747.21 | (23) | 2863.33 | (19) | |
60 | 40 | 2992.33 | (12) | 3114.23 | (8) | 3174.69 | (3) |
70 | 3140.85 | (6) | 3174.78 | (2) | 3282.48 | (1) | |
100 | 3031.76 | (9) | 3148.11 | (5) | 3151.24 | (4) | |
90 | 40 | 2832.17 | (21) | 2954.02 | (16) | 3015.02 | (11) |
70 | 2981.34 | (15) | 3015.21 | (10) | 3122.47 | (7) | |
100 | 2872.21 | (18) | 2988.05 | (14) | 2991.03 | (13) |
N/(kg/hm2) | K/(kg/hm2) | P | |||||
---|---|---|---|---|---|---|---|
50 kg/hm2 | 80 kg/hm2 | 110 kg/hm2 | |||||
30 | 40 | 10730.71 | (25) | 11100.14 | (22) | 11511.69 | (16) |
70 | 10691.93 | (26) | 11044.98 | (23) | 11466.60 | (18) | |
100 | 10453.08 | (27) | 10835.65 | (24) | 11209.79 | (21) | |
60 | 40 | 12230.57 | (9) | 12629.67 | (5) | 12763.36 | (2) |
70 | 12703.27 | (4) | 12722.35 | (3) | 13060.11 | (1) | |
100 | 12063.10 | (10) | 12438.24 | (6) | 12324.26 | (7) | |
90 | 40 | 11409.37 | (19) | 11808.27 | (14) | 11944.29 | (11) |
70 | 11884.89 | (13) | 11903.71 | (12) | 12239.57 | (8) | |
100 | 11244.55 | (20) | 11617.48 | (15) | 11502.85 | (17) |
N/(kg/hm2) | K/(kg/hm2) | P | |||||
---|---|---|---|---|---|---|---|
50 kg/hm2 | 80 kg/hm2 | 110 kg/hm2 | |||||
30 | 40 | 10730.71 | (25) | 11100.14 | (22) | 11511.69 | (16) |
70 | 10691.93 | (26) | 11044.98 | (23) | 11466.60 | (18) | |
100 | 10453.08 | (27) | 10835.65 | (24) | 11209.79 | (21) | |
60 | 40 | 12230.57 | (9) | 12629.67 | (5) | 12763.36 | (2) |
70 | 12703.27 | (4) | 12722.35 | (3) | 13060.11 | (1) | |
100 | 12063.10 | (10) | 12438.24 | (6) | 12324.26 | (7) | |
90 | 40 | 11409.37 | (19) | 11808.27 | (14) | 11944.29 | (11) |
70 | 11884.89 | (13) | 11903.71 | (12) | 12239.57 | (8) | |
100 | 11244.55 | (20) | 11617.48 | (15) | 11502.85 | (17) |
No | x | y | z | X1(x) | X2(x) | Y1(y) | Y2(y) | X1Y1 | X1Y2 | X2Y1 | X2Y2 | Z1 | W |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 30 | 40 | 50 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -30 | 10731 |
2 | 30 | 40 | 80 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 0 | 11100 |
3 | 30 | 40 | 110 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 30 | 11512 |
4 | 30 | 70 | 50 | -1 | 1 | 0 | -2 | 0 | 2 | 0 | -2 | -30 | 10692 |
5 | 30 | 70 | 80 | -1 | 1 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 11045 |
6 | 30 | 70 | 110 | -1 | 1 | 0 | -2 | 0 | 2 | 0 | -2 | 30 | 11467 |
7 | 30 | 100 | 50 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -30 | 10453 |
8 | 30 | 100 | 80 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 0 | 10836 |
9 | 30 | 100 | 110 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 30 | 11210 |
10 | 60 | 40 | 50 | 0 | -2 | -1 | 1 | 0 | 0 | 2 | -2 | -30 | 12231 |
11 | 60 | 40 | 80 | 0 | -2 | -1 | 1 | 0 | 0 | 2 | -2 | 0 | 12630 |
12 | 60 | 40 | 110 | 0 | -2 | -1 | 1 | 0 | 0 | 2 | -2 | 30 | 12763 |
13 | 60 | 70 | 50 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | 4 | -30 | 12703 |
14 | 60 | 70 | 80 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | 4 | 0 | 12722 |
15 | 60 | 70 | 110 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | 4 | 30 | 13060 |
16 | 60 | 100 | 50 | 0 | -2 | 1 | 1 | 0 | 0 | -2 | -2 | -30 | 12063 |
17 | 60 | 100 | 80 | 0 | -2 | 1 | 1 | 0 | 0 | -2 | -2 | 0 | 12438 |
18 | 60 | 100 | 110 | 0 | -2 | 1 | 1 | 0 | 0 | -2 | -2 | 30 | 12324 |
19 | 90 | 40 | 50 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -30 | 11409 |
20 | 90 | 40 | 80 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 0 | 11808 |
21 | 90 | 40 | 110 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 30 | 11944 |
22 | 90 | 70 | 50 | 1 | 1 | 0 | -2 | 0 | -2 | 0 | -2 | -30 | 11885 |
23 | 90 | 70 | 80 | 1 | 1 | 0 | -2 | 0 | -2 | 0 | -2 | 0 | 11904 |
24 | 90 | 70 | 110 | 1 | 1 | 0 | -2 | 0 | -2 | 0 | -2 | 30 | 12240 |
25 | 90 | 100 | 50 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -30 | 11245 |
26 | 90 | 100 | 80 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 11617 |
27 | 90 | 100 | 110 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 30 | 11503 |
λj | 1 | 3 | 1 | 3 | 1 | 3 | 3 | 9 | 1 | ST= SR= | |||
Aj | 18 | 54 | 18 | 54 | 12 | 36 | 36 | 108 | 16200 | ||||
Bj | 6510 | -21270 | -2439 | -5617 | 47 | -1964 | -45 | 1949 | 138331 | ||||
361.69 | -136 | 3.91 | -1.25 | 8.54 | |||||||||
-393.90 | -104.03 | -54.5 | 18.05 | ||||||||||
Qj= | 2354749 | 330504 | 183.76 | 56.39 | 1181204 | ||||||||
8378285 | 5844323 | 107100 | 35174 |
No | x | y | z | X1(x) | X2(x) | Y1(y) | Y2(y) | X1Y1 | X1Y2 | X2Y1 | X2Y2 | Z1 | W |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 30 | 40 | 50 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | -30 | 10731 |
2 | 30 | 40 | 80 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 0 | 11100 |
3 | 30 | 40 | 110 | -1 | 1 | -1 | 1 | 1 | -1 | -1 | 1 | 30 | 11512 |
4 | 30 | 70 | 50 | -1 | 1 | 0 | -2 | 0 | 2 | 0 | -2 | -30 | 10692 |
5 | 30 | 70 | 80 | -1 | 1 | 0 | -2 | 0 | 2 | 0 | -2 | 0 | 11045 |
6 | 30 | 70 | 110 | -1 | 1 | 0 | -2 | 0 | 2 | 0 | -2 | 30 | 11467 |
7 | 30 | 100 | 50 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | -30 | 10453 |
8 | 30 | 100 | 80 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 0 | 10836 |
9 | 30 | 100 | 110 | -1 | 1 | 1 | 1 | -1 | -1 | 1 | 1 | 30 | 11210 |
10 | 60 | 40 | 50 | 0 | -2 | -1 | 1 | 0 | 0 | 2 | -2 | -30 | 12231 |
11 | 60 | 40 | 80 | 0 | -2 | -1 | 1 | 0 | 0 | 2 | -2 | 0 | 12630 |
12 | 60 | 40 | 110 | 0 | -2 | -1 | 1 | 0 | 0 | 2 | -2 | 30 | 12763 |
13 | 60 | 70 | 50 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | 4 | -30 | 12703 |
14 | 60 | 70 | 80 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | 4 | 0 | 12722 |
15 | 60 | 70 | 110 | 0 | -2 | 0 | -2 | 0 | 0 | 0 | 4 | 30 | 13060 |
16 | 60 | 100 | 50 | 0 | -2 | 1 | 1 | 0 | 0 | -2 | -2 | -30 | 12063 |
17 | 60 | 100 | 80 | 0 | -2 | 1 | 1 | 0 | 0 | -2 | -2 | 0 | 12438 |
18 | 60 | 100 | 110 | 0 | -2 | 1 | 1 | 0 | 0 | -2 | -2 | 30 | 12324 |
19 | 90 | 40 | 50 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | -30 | 11409 |
20 | 90 | 40 | 80 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 0 | 11808 |
21 | 90 | 40 | 110 | 1 | 1 | -1 | 1 | -1 | 1 | -1 | 1 | 30 | 11944 |
22 | 90 | 70 | 50 | 1 | 1 | 0 | -2 | 0 | -2 | 0 | -2 | -30 | 11885 |
23 | 90 | 70 | 80 | 1 | 1 | 0 | -2 | 0 | -2 | 0 | -2 | 0 | 11904 |
24 | 90 | 70 | 110 | 1 | 1 | 0 | -2 | 0 | -2 | 0 | -2 | 30 | 12240 |
25 | 90 | 100 | 50 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | -30 | 11245 |
26 | 90 | 100 | 80 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 11617 |
27 | 90 | 100 | 110 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 30 | 11503 |
λj | 1 | 3 | 1 | 3 | 1 | 3 | 3 | 9 | 1 | ST= SR= | |||
Aj | 18 | 54 | 18 | 54 | 12 | 36 | 36 | 108 | 16200 | ||||
Bj | 6510 | -21270 | -2439 | -5617 | 47 | -1964 | -45 | 1949 | 138331 | ||||
361.69 | -136 | 3.91 | -1.25 | 8.54 | |||||||||
-393.90 | -104.03 | -54.5 | 18.05 | ||||||||||
Qj= | 2354749 | 330504 | 183.76 | 56.39 | 1181204 | ||||||||
8378285 | 5844323 | 107100 | 35174 |
来源 | 平方和SS | 自由度DF | 均方MS | F | ||
---|---|---|---|---|---|---|
N(x) | Χ1 | 2354748.601 | 1 | 2354748.601 | 122.5440** | F0.01(1,17)=8.4 |
Χ2 | 8378285.143 | 1 | 8378285.143 | 436.0161** | F0.05(1,17)=4.45 | |
K(y) | Y1 | 330504.0123 | 1 | 330504.0123 | 17.1998** | |
Y2 | 584432.4677 | 1 | 584432.4677 | 30.4146** | ||
交互作用 | X1Y1 | 183.7576 | 1 | 183.7576 | 0.0096 | |
X1Y2 | 107100.1548 | 1 | 107100.1548 | 5.5736* | ||
X2Y1 | 56.3941 | 1 | 56.3941 | 0.0029 | ||
X2Y2 | 35174.1950 | 1 | 35174.1950 | 1.8305 | ||
P(z) | Z | 1181204.174 | 1 | 1181204.174 | 61.4713** | |
回归 | 12971688.9 | 9 | 1441298.767 | 75.0069** | ||
剩余 | 326664.202 | 17 | 19215.5413 | |||
总计 | 13298353.1 | 26 |
来源 | 平方和SS | 自由度DF | 均方MS | F | ||
---|---|---|---|---|---|---|
N(x) | Χ1 | 2354748.601 | 1 | 2354748.601 | 122.5440** | F0.01(1,17)=8.4 |
Χ2 | 8378285.143 | 1 | 8378285.143 | 436.0161** | F0.05(1,17)=4.45 | |
K(y) | Y1 | 330504.0123 | 1 | 330504.0123 | 17.1998** | |
Y2 | 584432.4677 | 1 | 584432.4677 | 30.4146** | ||
交互作用 | X1Y1 | 183.7576 | 1 | 183.7576 | 0.0096 | |
X1Y2 | 107100.1548 | 1 | 107100.1548 | 5.5736* | ||
X2Y1 | 56.3941 | 1 | 56.3941 | 0.0029 | ||
X2Y2 | 35174.1950 | 1 | 35174.1950 | 1.8305 | ||
P(z) | Z | 1181204.174 | 1 | 1181204.174 | 61.4713** | |
回归 | 12971688.9 | 9 | 1441298.767 | 75.0069** | ||
剩余 | 326664.202 | 17 | 19215.5413 | |||
总计 | 13298353.1 | 26 |
序号 | 实测值W | 预测值 | W- | 序号 | 实测值W | 预测值 | W- | |
---|---|---|---|---|---|---|---|---|
1 | 10730.71 | 10832.90 | -102.19 | 15 | 13060.11 | 13001.01 | 59.10 | |
2 | 11100.14 | 11089.07 | 11.07 | 16 | 12063.10 | 12028.89 | 34.22 | |
3 | 11511.69 | 11345.24 | 166.45 | 17 | 12438.24 | 12285.06 | 153.18 | |
4 | 10691.93 | 10841.92 | -150.00 | 18 | 12324.26 | 12541.23 | -216.97 | |
5 | 11044.98 | 11098.09 | -53.11 | 19 | 11409.37 | 11443.50 | -34.12 | |
6 | 11466.60 | 11354.26 | 112.33 | 20 | 11808.27 | 11699.67 | 108.60 | |
7 | 10453.08 | 10551.79 | -98.70 | 21 | 11944.29 | 11955.84 | -11.55 | |
8 | 10835.65 | 10807.96 | 27.69 | 22 | 11884.89 | 11772.02 | 112.87 | |
9 | 11209.79 | 11064.13 | 145.66 | 23 | 11903.71 | 12028.19 | -124.48 | |
10 | 12230.57 | 12319.90 | -89.33 | 24 | 12239.57 | 12284.36 | -44.79 | |
11 | 12629.67 | 12576.07 | 53.61 | 25 | 11244.55 | 11142.58 | 101.96 | |
12 | 12763.36 | 12832.24 | -68.88 | 26 | 11617.48 | 11398.75 | 218.72 | |
13 | 12703.27 | 12488.67 | 214.60 | 27 | 11502.85 | 11654.92 | -152.07 | |
14 | 12722.35 | 12744.84 | -22.49 |
序号 | 实测值W | 预测值 | W- | 序号 | 实测值W | 预测值 | W- | |
---|---|---|---|---|---|---|---|---|
1 | 10730.71 | 10832.90 | -102.19 | 15 | 13060.11 | 13001.01 | 59.10 | |
2 | 11100.14 | 11089.07 | 11.07 | 16 | 12063.10 | 12028.89 | 34.22 | |
3 | 11511.69 | 11345.24 | 166.45 | 17 | 12438.24 | 12285.06 | 153.18 | |
4 | 10691.93 | 10841.92 | -150.00 | 18 | 12324.26 | 12541.23 | -216.97 | |
5 | 11044.98 | 11098.09 | -53.11 | 19 | 11409.37 | 11443.50 | -34.12 | |
6 | 11466.60 | 11354.26 | 112.33 | 20 | 11808.27 | 11699.67 | 108.60 | |
7 | 10453.08 | 10551.79 | -98.70 | 21 | 11944.29 | 11955.84 | -11.55 | |
8 | 10835.65 | 10807.96 | 27.69 | 22 | 11884.89 | 11772.02 | 112.87 | |
9 | 11209.79 | 11064.13 | 145.66 | 23 | 11903.71 | 12028.19 | -124.48 | |
10 | 12230.57 | 12319.90 | -89.33 | 24 | 12239.57 | 12284.36 | -44.79 | |
11 | 12629.67 | 12576.07 | 53.61 | 25 | 11244.55 | 11142.58 | 101.96 | |
12 | 12763.36 | 12832.24 | -68.88 | 26 | 11617.48 | 11398.75 | 218.72 | |
13 | 12703.27 | 12488.67 | 214.60 | 27 | 11502.85 | 11654.92 | -152.07 | |
14 | 12722.35 | 12744.84 | -22.49 |
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