This template creates/organizes information about response surfaces.
The usage is like this:
{{{ResponseSurface
|title =
|link=
|comments1=
|polynomial_coefficient_vector=
|polynomial_powers_matrix=
|comments2=
|image=
|comments3=
|statistics=
|comments4=
|text=
}}}
Example
| Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/MCResponseSurface_Yp_exit_6dim_4deg.mat
|
| Some thoughts about this response surface?
|
The polynomial coefficient vector is given by:
b(1) = 9.4335e+04
b(2) = -7.1360e+04
b(3) = -1.3930e+04
b(4) = 2.4439e+04
b(5) = 6.3177e+01
b(6) = -7.3399e-01
b(7) = -4.7962e+04
b(8) = 2.5084e+04
b(9) = 1.2428e+04
b(10) = 9.7792e+02
b(11) = -9.2480e+03
b(12) = -5.1276e+03
b(13) = -5.7739e+03
b(14) = -1.3153e+02
b(15) = 1.5852e+01
b(16) = -1.7894e+01
b(17) = 7.7344e-01
b(18) = -1.1606e+00
b(19) = -1.8691e+00
b(20) = 5.6333e+00
b(21) = 5.4130e-02
b(22) = -3.5192e-03
b(23) = 1.7109e+03
b(24) = -1.8055e+03
b(25) = -6.1622e+03
b(26) = 9.2918e+01
b(27) = 2.2992e+00
b(28) = 2.4321e+04
b(29) = -3.2712e+03
b(30) = -2.0094e+03
b(31) = -8.4970e+02
b(32) = 6.7127e+02
b(33) = 5.4902e+02
b(34) = 1.6649e+03
b(35) = 3.9418e+01
b(36) = -8.6106e+01
b(37) = 2.8060e+03
b(38) = 8.4698e+02
b(39) = 4.0922e+01
b(40) = -4.1602e+01
b(41) = 3.6996e+01
b(42) = 2.7639e+01
b(43) = -3.6318e+01
b(44) = 1.9221e+01
b(45) = -1.3503e-01
b(46) = 4.1899e-01
b(47) = 3.5445e-02
b(48) = 3.4742e-03
b(49) = 1.0020e-01
b(50) = 9.6863e-01
b(51) = 1.0226e-01
b(52) = -1.0614e+00
b(53) = -7.4942e-01
b(54) = -6.7971e-01
b(55) = -2.5682e-02
b(56) = 1.6590e-03
b(57) = 6.0159e-04
b(58) = -3.3300e-04
b(59) = 6.4587e-04
b(60) = 4.1078e-04
b(61) = 8.1751e-04
b(62) = -4.3508e-06
b(63) = 1.0649e-05
b(64) = 1.0716e+03
b(65) = -3.1054e+02
b(66) = -9.7221e+02
b(67) = 2.0289e+03
b(68) = -9.5553e+02
b(69) = 2.5068e+02
b(70) = -1.2136e+01
b(71) = -2.9474e+00
b(72) = -8.2761e+00
b(73) = -5.5199e-01
b(74) = -1.3527e-01
b(75) = -2.5765e-01
b(76) = -6.1860e-01
b(77) = 4.1224e-03
b(78) = -3.8697e-04
b(79) = -1.8981e+03
b(80) = 1.5007e+03
b(81) = 5.7488e+02
b(82) = -1.3082e+01
b(83) = -3.1649e-01
b(84) = -3.6841e+03
|
The polynomial powers matrix corresponding to the polynomial coefficient vector is given by:
0 0 0 0 0 0
0 0 0 0 0 1
0 0 0 0 1 0
0 0 0 1 0 0
0 0 1 0 0 0
0 1 0 0 0 0
1 0 0 0 0 0
0 0 0 0 0 2
0 0 0 0 1 1
0 0 0 0 2 0
0 0 0 1 0 1
0 0 0 1 1 0
0 0 0 2 0 0
0 0 1 0 0 1
0 0 1 0 1 0
0 0 1 1 0 0
0 0 2 0 0 0
0 1 0 0 0 1
0 1 0 0 1 0
0 1 0 1 0 0
0 1 1 0 0 0
0 2 0 0 0 0
1 0 0 0 0 1
1 0 0 0 1 0
1 0 0 1 0 0
1 0 1 0 0 0
1 1 0 0 0 0
2 0 0 0 0 0
0 0 0 0 0 3
0 0 0 0 1 2
0 0 0 0 2 1
0 0 0 0 3 0
0 0 0 1 0 2
0 0 0 1 1 1
0 0 0 1 2 0
0 0 0 2 0 1
0 0 0 2 1 0
0 0 0 3 0 0
0 0 1 0 0 2
0 0 1 0 1 1
0 0 1 0 2 0
0 0 1 1 0 1
0 0 1 1 1 0
0 0 1 2 0 0
0 0 2 0 0 1
0 0 2 0 1 0
0 0 2 1 0 0
0 0 3 0 0 0
0 1 0 0 0 2
0 1 0 0 1 1
0 1 0 0 2 0
0 1 0 1 0 1
0 1 0 1 1 0
0 1 0 2 0 0
0 1 1 0 0 1
0 1 1 0 1 0
0 1 1 1 0 0
0 1 2 0 0 0
0 2 0 0 0 1
0 2 0 0 1 0
0 2 0 1 0 0
0 2 1 0 0 0
0 3 0 0 0 0
1 0 0 0 0 2
1 0 0 0 1 1
1 0 0 0 2 0
1 0 0 1 0 1
1 0 0 1 1 0
1 0 0 2 0 0
1 0 1 0 0 1
1 0 1 0 1 0
1 0 1 1 0 0
1 0 2 0 0 0
1 1 0 0 0 1
1 1 0 0 1 0
1 1 0 1 0 0
1 1 1 0 0 0
1 2 0 0 0 0
2 0 0 0 0 1
2 0 0 0 1 0
2 0 0 1 0 0
2 0 1 0 0 0
2 1 0 0 0 0
3 0 0 0 0 0
|
|
|
| The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):
MCResponseSurface_Yp_exit_6dim_4deg.png
|
| Some comments about the image
|
Some key statistics for this response surface are given below:
---------------------------------------------------
Response surface summary of information:
Number of variables in response surface is 6.
Number of terms in polynomial is 210.
Degree of response surface is 4.
MSE = 0.02069806
MSE DoF = 9790
L-inf norm resid = 0.37829408
R^2 = 0.85452284
adjusted R^2 = 0.85141715
---------------------------------------------------
|
| Comments about the statistics?
|
| Some final thoughts here.
|
|