Using Response Surface Data

Once you download the .mat file associated with a response surface, you will see two variables:

model
- matrix of size $N_{vars}\times N_{polynomialterms}$
- number of columns is equal to the number of input variables $N_{vars}$
- number of rows is equal to the number of terms in the polynomial response surface $N_{polynomialterms}$
- variable order is as follows:
  - Mass flowrate ${\dot {m}}$
  - Reaction rate $k(T)$
  - Mixing length $L_{mix}$
  - Measurement location 1 $z_{1}$
  - Measurement location 2 $z_{2}$
  - Measurement location 3 $z_{3}$

response_surface
- cell object that results from Matlab's regstats() function
- polynomial coefficients corresponding to each row of model object are contained in response_surface.beta
- covariance matrix is stored in response_surface.covb
- R-squared and adjusted R-squared values stored in response_surface.rsquare and response_surface.adjrsquare, respectively
- mean square error is contained in response_surface.mse

See the Matlab regstats() help page for more information: http://www.mathworks.com/help/toolbox/stats/regstats.html

Example of how to use this information to compute the value of a response surface is here: EvaluateResponseSurface.m

Composite Design Response Surfaces

Yp at X1

Quadratic Response, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x1_6dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 28. 
Degree of response surface is 2.

MSE =			 0.00080509 
MSE DoF = 		 17 

L-inf norm resid = 	 0.05454099 

R^2 =			 0.99052326 
adjusted R^2 =		 0.97547197 
---------------------------------------------------

Quadratic Response, 2 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x1_2dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

Some key statistics for this response surface are given below:

---------------------------------------------------
Response surface summary of information:
Number of variables in response surface is 2. 
Number of terms in polynomial is 6. 
Degree of response surface is 2.

MSE =			 0.00037084 
MSE DoF = 		 39 

L-inf norm resid = 	 0.04927581 

R^2 =			 0.98998584 
adjusted R^2 =		 0.98870197 
---------------------------------------------------

Cubic Response Surface, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x1_6dim_3deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 37. 
Degree of response surface is varied, deg is a matrix. Max degree = 3.

MSE =			 0.00000010 
MSE DoF = 		 8 

L-inf norm resid = 	 0.00069080 

R^2 =			 0.99999947 
adjusted R^2 =		 0.99999709 
---------------------------------------------------

Yp at X2

Quadratic Response, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x2_6dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 28. 
Degree of response surface is 2.

MSE =			 0.01492871 
MSE DoF = 		 17 

L-inf norm resid = 	 0.19955474 

R^2 =			 0.93864060 
adjusted R^2 =		 0.84118743 
---------------------------------------------------

Quadratic Response, 2 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x2_2dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

Some key statistics for this response surface are given below:

---------------------------------------------------
Response surface summary of information:
Number of variables in response surface is 2. 
Number of terms in polynomial is 6. 
Degree of response surface is 2.

MSE =			 0.00690353 
MSE DoF = 		 39 

L-inf norm resid = 	 0.13735696 

R^2 =			 0.93490530 
adjusted R^2 =		 0.92655983 
---------------------------------------------------

Cubic Response Surface, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x2_6dim_3deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 37. 
Degree of response surface is varied, deg is a matrix. Max degree = 3.

MSE =			 0.00000006 
MSE DoF = 		 8 

L-inf norm resid = 	 0.00020206 

R^2 =			 0.99999989 
adjusted R^2 =		 0.99999941 
---------------------------------------------------

Yp at X3

Quadratic Response, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x3_6dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 28. 
Degree of response surface is 2.

MSE =			 0.03224452 
MSE DoF = 		 17 

L-inf norm resid = 	 0.30852831 

R^2 =			 0.88596596 
adjusted R^2 =		 0.70485306 
---------------------------------------------------

Quadratic Response, 2 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x3_2dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

Some key statistics for this response surface are given below:

---------------------------------------------------
Response surface summary of information:
Number of variables in response surface is 2. 
Number of terms in polynomial is 6. 
Degree of response surface is 2.

MSE =			 0.01514132 
MSE DoF = 		 39 

L-inf norm resid = 	 0.20318228 

R^2 =			 0.87715488 
adjusted R^2 =		 0.86140551 
---------------------------------------------------

Cubic Response Surface, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_x3_6dim_3deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 37. 
Degree of response surface is varied, deg is a matrix. Max degree = 3.

MSE =			 0.00000005 
MSE DoF = 		 8 

L-inf norm resid = 	 0.00033261 

R^2 =			 0.99999992 
adjusted R^2 =		 0.99999957 
---------------------------------------------------

Yp at X Out

Quadratic Response, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_out_6dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 28. 
Degree of response surface is 2.

MSE =			 0.03845480 
MSE DoF = 		 17 

L-inf norm resid = 	 0.34272386 

R^2 =			 0.86371957 
adjusted R^2 =		 0.64727417 
---------------------------------------------------

Quadratic Response, 2 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_out_2dim_2deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

Some key statistics for this response surface are given below:

---------------------------------------------------
Response surface summary of information:
Number of variables in response surface is 2. 
Number of terms in polynomial is 6. 
Degree of response surface is 2.

MSE =			 0.01817059 
MSE DoF = 		 39 

L-inf norm resid = 	 0.23540351 

R^2 =			 0.85227039 
adjusted R^2 =		 0.83333069 
---------------------------------------------------

Cubic Response Surface, 6 Dimensions

Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/CDResponseSurface_Yp_out_6dim_3deg.mat

The following is a visualization of the response surface (non-visualized dimensions are kept constant at their mean value):

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 37. 
Degree of response surface is varied, deg is a matrix. Max degree = 3.

MSE =			 0.00000000 
MSE DoF = 		 8 

L-inf norm resid = 	 0.00000000 

R^2 =			 1.00000000 
adjusted R^2 =		 1.00000000 
---------------------------------------------------

Composite Design Response Surfaces

From charlesreid1

Contents

Using Response Surface Data

Composite Design Response Surfaces

Yp at X1

Quadratic Response, 6 Dimensions

Quadratic Response, 2 Dimensions

Cubic Response Surface, 6 Dimensions

Yp at X2

Quadratic Response, 6 Dimensions

Quadratic Response, 2 Dimensions

Cubic Response Surface, 6 Dimensions

Yp at X3

Quadratic Response, 6 Dimensions

Quadratic Response, 2 Dimensions

Cubic Response Surface, 6 Dimensions

Yp at X Out

Quadratic Response, 6 Dimensions

Quadratic Response, 2 Dimensions

Cubic Response Surface, 6 Dimensions