Template:ResponseSurface

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.