4因素二次回归通用旋转组合设计
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9.603
x44 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0
12.407
F 0.03497
Ya 0.654 0.433 0.538 0.321 0.314 0.279 0.295 0.242 0.779 0.594 0.71 0.529 0.481 0.307 0.328 0.291 0.125 0.648 0.785 0.213 0.429 0.198 0.842 0.486 0.797 0.709 0.759 0.694 0.728 0.738 0.746
0.127
x11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
10.187
x22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0
11.087
x33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0
1
1
1
-1
-1
1
-1
-1
-1
1
-1
-1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.051
0.137
x2x4 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.505
x3x4 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.389
结构矩阵和试验计算结 x1x3
1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.019
F-G
G
0.03125 0.00372
误差来源 x1 x2 x3 x4
x1x2 x1x3 x1x4 x2x3 x2x4 x3x4 x11 x22 x33 x44 回归 剩余 失拟 纯误 总误差
b2
0.13188555
b3
0.04371183
b4
0.07563105
b12 -0.0243125
b13 -0.0011875
b14 -0.0031875
b23
0.0085625
b24
0.0315625
b34
0.0079375
b11 -0.09171409
b22 -0.06358909
b33 -0.10996409
1
0.0001626 0.0570826 4.49(0.05)
1
0.0011731 0.4119122
1
0.0159391 5.5968834
1
0.0010081 0.3539737
1
0.240534 84.461731
1
0.1156298 40.602528
1
0.345785 121.41983
1
方差分析表
df
MS
F值
Fa
1
0.1648516 57.886402
1
0.4174178 146.57315 8.53(0.01)
1
0.0458537 16.10119
1
0.1372704 48.201466 3.05(0.10)
1
0.0094576 3.3209528
1
0.0001626 0.0570826
x1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.989
x2 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 3.165
试验号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Bj
x0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15.992
0.0142704 5.0109355
14
0.099151 34.816136 3.45(0.01)
16
0.0028478
10
0.0038706 3.3856559 4.06（0.05）
6
0.0011432
30
结构矩阵和试验计算结果
x1x4
x2x3
1
1
-1
1
1
-1
-1
-1
1
-1
-1
-1
1
1
-1
1
-1
x3 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 0 0 0 0 2 -2 0 0 0 0 0 0 0 0 0 1.049
各参数
T=∑Bjj
K
ELeabharlann Baidu
e-1
43.284 0.14286 -0.03571 0.04167
b0
0.73894548
b1 -0.08288163
SS 0.164852 0.417418 0.045854 0.137270 0.009458 0.000163 0.000163 0.001173 0.015939 0.001008 0.240534 0.115630 0.345785 0.014270 1.388114 0.045566 0.038706 0.006859 1.433679484
b44 -0.02233909
x4 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 0 0 0 0 0 0 2 -2 0 0 0 0 0 0 0 1.815
mc-1 0.0625
x1x2 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
x44 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0
12.407
F 0.03497
Ya 0.654 0.433 0.538 0.321 0.314 0.279 0.295 0.242 0.779 0.594 0.71 0.529 0.481 0.307 0.328 0.291 0.125 0.648 0.785 0.213 0.429 0.198 0.842 0.486 0.797 0.709 0.759 0.694 0.728 0.738 0.746
0.127
x11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
10.187
x22 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0
11.087
x33 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0
1
1
1
-1
-1
1
-1
-1
-1
1
-1
-1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
-0.051
0.137
x2x4 1 -1 1 -1 -1 1 -1 1 1 -1 1 -1 -1 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0.505
x3x4 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-0.389
结构矩阵和试验计算结 x1x3
1 1 -1 -1 1 1 -1 -1 -1 -1 1 1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -0.019
F-G
G
0.03125 0.00372
误差来源 x1 x2 x3 x4
x1x2 x1x3 x1x4 x2x3 x2x4 x3x4 x11 x22 x33 x44 回归 剩余 失拟 纯误 总误差
b2
0.13188555
b3
0.04371183
b4
0.07563105
b12 -0.0243125
b13 -0.0011875
b14 -0.0031875
b23
0.0085625
b24
0.0315625
b34
0.0079375
b11 -0.09171409
b22 -0.06358909
b33 -0.10996409
1
0.0001626 0.0570826 4.49(0.05)
1
0.0011731 0.4119122
1
0.0159391 5.5968834
1
0.0010081 0.3539737
1
0.240534 84.461731
1
0.1156298 40.602528
1
0.345785 121.41983
1
方差分析表
df
MS
F值
Fa
1
0.1648516 57.886402
1
0.4174178 146.57315 8.53(0.01)
1
0.0458537 16.10119
1
0.1372704 48.201466 3.05(0.10)
1
0.0094576 3.3209528
1
0.0001626 0.0570826
x1 1 1 1 1 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 2 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 -1.989
x2 1 1 1 1 -1 -1 -1 -1 1 1 1 1 -1 -1 -1 -1 0 0 2 -2 0 0 0 0 0 0 0 0 0 0 0 3.165
试验号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Bj
x0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 15.992
0.0142704 5.0109355
14
0.099151 34.816136 3.45(0.01)
16
0.0028478
10
0.0038706 3.3856559 4.06（0.05）
6
0.0011432
30
结构矩阵和试验计算结果
x1x4
x2x3
1
1
-1
1
1
-1
-1
-1
1
-1
-1
-1
1
1
-1
1
-1
x3 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 0 0 0 0 2 -2 0 0 0 0 0 0 0 0 0 1.049
各参数
T=∑Bjj
K
ELeabharlann Baidu
e-1
43.284 0.14286 -0.03571 0.04167
b0
0.73894548
b1 -0.08288163
SS 0.164852 0.417418 0.045854 0.137270 0.009458 0.000163 0.000163 0.001173 0.015939 0.001008 0.240534 0.115630 0.345785 0.014270 1.388114 0.045566 0.038706 0.006859 1.433679484
b44 -0.02233909
x4 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 1 -1 0 0 0 0 0 0 2 -2 0 0 0 0 0 0 0 1.815
mc-1 0.0625
x1x2 1 1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0