Monte Carlo Experimental Design - Revision history

Admin: /* Computing Response Surface */

2011-07-03T22:28:46Z

Computing Response Surface

← Older revision		Revision as of 22:28, 3 July 2011
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	<pre>		<pre>
	b(1) = 0.~~2183~~		b(1) = 0.2606
	b(2) = -0.~~03345~~		b(2) = -0.01793
	b(3) = 0.~~03604~~		b(3) = 0.0367
	b(4) = -0.~~003655~~		b(4) = -0.003453
	b(5) = -0.~~001308~~		b(5) = 0.0003092
	b(6) = -0.~~0003175~~		b(6) = -0.0003485
	</pre>		</pre>

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	Degree of response surface is 2.		Degree of response surface is 2.

	MSE = 0.~~02986376~~		MSE = 0.04267264
	MSE DoF = ~~9994~~		MSE DoF = 5029

	L-inf norm resid = 0.~~51267228~~		L-inf norm resid = 0.50344056

	R^2 = 0.~~74807552~~		R^2 = 0.68807653
	adjusted R^2 = 0.~~74794948~~		adjusted R^2 = 0.68776641
	---------------------------------------------------		---------------------------------------------------
	</pre>		</pre>

2011-07-03T22:00:51Z

Cubic Surface, 6 Dimensions

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 ---------------------------------------------------
 </pre>
 =References=

2011-07-03T21:29:59Z

Quadratic Surface, 6 Dimensions

← Older revision		Revision as of 21:29, 3 July 2011
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	===Quadratic Surface, 6 Dimensions===		===Quadratic Surface, 2 Dimensions===

	Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/MCResponseSurface_2dim_2deg.mat		Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/MCResponseSurface_2dim_2deg.mat

2011-07-03T21:29:27Z

Quadratic Surface, 6 Dimensions

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 R^2 =			 0.68956066
 adjusted R^2 =		 0.68788663
 ---------------------------------------------------
 </pre>

2011-07-03T08:00:35Z

Quadratic Surface, 6 Dimensions

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 b(27) = 0.0131
 b(28) = -10.72
 </pre>

2011-07-03T07:59:54Z

Cubic Surface, 6 Dimensions

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 b(83) = -3.1649e-01
 b(84) = -3.6841e+03
 </pre>

2011-07-03T07:55:38Z

Computing Response Surface

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 [[Image:MCResponseSurface_6dim_2deg.png|500px]]
 ===Cubic Surface, 6 Dimensions===
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 ** <code>response_surface</code> - structure containing information about the response surface (coefficient vector is in response_surface.beta)
 ** <code>model</code> - this is a matrix containing the polynomial powers of each variable (variable order given in section [[Composite Experimental Design#A Note on Coefficient and Variable Order]]; description of polynomial powers matrix given in section [[Composite Experimental Design#Polynomial Powers Matrix]])
 [[Image:MCResponseSurface_6dim_3deg.png|500px]]
 =References=

2011-07-03T07:46:11Z

Quadratic Surface, 6 Dimensions

← Older revision		Revision as of 07:46, 3 July 2011
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	A quadratic response surface was computed using all of the information from the Monte Carlo samples. There were 10,000 samples in total.		A quadratic response surface was computed using all of the information from the Monte Carlo samples. There were 10,000 samples in total.

			The resulting polynomial coefficient vector is:

			<pre>
			b(1) = 175.9
			b(2) = -55.47
			b(3) = -59.65
			b(4) = -75.2
			b(5) = 1.12
			b(6) = 0.1184
			b(7) = -44.47
			b(8) = 4.065
			b(9) = -0.8079
			b(10) = 5.412
			b(11) = -10.95
			b(12) = 25.88
			b(13) = 21.01
			b(14) = -0.1112
			b(15) = 0.2904
			b(16) = -0.3872
			b(17) = -0.003535
			b(18) = -0.03342
			b(19) = -0.009973
			b(20) = -0.01873
			b(21) = 0.0003347
			b(22) = -0.0003496
			b(23) = 21.21
			b(24) = 16.26
			b(25) = 21.64
			b(26) = -0.5508
			b(27) = 0.0131
			b(28) = -10.72
			</pre>

			The response surface, plotted with the non-visualized dimensions set to a constant (their means), is:

	[[Image:MCResponseSurface_6dim_2deg.png\|500px]]		[[Image:MCResponseSurface_6dim_2deg.png\|500px]]

2011-07-03T07:03:12Z

Computing Response Surface

← Older revision		Revision as of 07:03, 3 July 2011
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	A quadratic response surface was computed using all of the information from the Monte Carlo samples. There were 10,000 samples in total.		A quadratic response surface was computed using all of the information from the Monte Carlo samples. There were 10,000 samples in total.

	[[Image:~~ResponseSurface_2deg~~.png\|500px]]		[[Image:MCResponseSurface_6dim_2deg.png\|500px]]

	===Cubic Surface, 6 Dimensions===		===Cubic Surface, 6 Dimensions===
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	** <code>model</code> - this is a matrix containing the polynomial powers of each variable (variable order given in section [[Composite Experimental Design#A Note on Coefficient and Variable Order]]; description of polynomial powers matrix given in section [[Composite Experimental Design#Polynomial Powers Matrix]])		** <code>model</code> - this is a matrix containing the polynomial powers of each variable (variable order given in section [[Composite Experimental Design#A Note on Coefficient and Variable Order]]; description of polynomial powers matrix given in section [[Composite Experimental Design#Polynomial Powers Matrix]])

	[[Image:~~ResponseSurface_3deg~~.png\|500px]]		[[Image:MCResponseSurface_6dim_3deg.png\|500px]]

	=References=		=References=

2011-07-03T07:02:20Z

Computing Response Surface

← Older revision		Revision as of 07:02, 3 July 2011
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	===Quadratic Surface, 6 Dimensions===		===Quadratic Surface, 6 Dimensions===

	Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/~~ResponseSurface_6dim_2deg~~.mat		Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/MCResponseSurface_6dim_2deg.mat

	* contains 2 variables:		* contains 2 variables:
Line 106:		Line 106:

	A quadratic response surface was computed using all of the information from the Monte Carlo samples. There were 10,000 samples in total.		A quadratic response surface was computed using all of the information from the Monte Carlo samples. There were 10,000 samples in total.

			[[Image:ResponseSurface_2deg.png\|500px]]

			===Cubic Surface, 6 Dimensions===

			Download the response surface here: http://files.charlesmartinreid.com/ExperimentalDesign/MCResponseSurface_6dim_3deg.mat

			* contains 2 variables:
			** <code>response_surface</code> - structure containing information about the response surface (coefficient vector is in response_surface.beta)
			** <code>model</code> - this is a matrix containing the polynomial powers of each variable (variable order given in section [[Composite Experimental Design#A Note on Coefficient and Variable Order]]; description of polynomial powers matrix given in section [[Composite Experimental Design#Polynomial Powers Matrix]])

			[[Image:ResponseSurface_3deg.png\|500px]]

	=References=		=References=