# Regression Equation for Multiple Outputs?

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• #31557

JB
Participant

I’m having trouble with a DOE scenario it goes something like this.
We are measuring 3 different outputs that are all important to the customer. Some factors are significant for more than one output, so when you try to set up a regression how do you do it? Do you end up with 3 equations, one for each output or can you somehow get one equation that represents all three outputs?

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#83254

clb1
Participant

Treat each output separately.  When you are done you will have an equation for each response (output).  There are a number of statistical packages that will take your final equations and do an optimum search for you. If your package doesn’t have this capability you will have to do the search manually.
In this case, you should put the equations in a spread sheet and run a “what if” analysis to identify optimum factor combinations.  If you don’t have a lot of variables or if the equations do not share a lot of common terms you may be able to do the optimization simply by inspecting the final equations.

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#83255

mcleod
Member

Do you have minitab?  If so you should look at the use of the multiple response optimizer.  The tool is great for doing this.  I have used it on several DOEs where cycle time and torque out force were my CTQ’s.  You can then set up different scenarios in the program to optimize your inputs to give you the optimal output.

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#83257

Chip Hewette
Participant

I assume the results are something like this:y1 = ax1 + bx2 + cx3 + 0*x4y2 = 0*x1 + bx2 + cx3 + 0*x4y3 = 0*x1 + 0*x2 + cx3 + dx4Please keep in mind that for a factor “x” to be significant does not automatically mean that it has a massive effect on the output.  If the measure y can be evaluated closely, and you have done enough replication, you may have some significant terms that have large coefficients and some that have small coefficients.  Evaluate the impact of the factors within each equation first.Now, consider interactive effects.  If you have two factors that are significant, can they interact?  Have you tested for interactive effects?  Perhaps you have a simple situation where factor a is only important when factor b is at a certain level.  Such interactions will go a long way in setting the better level or concentration of each factor.With additional info, you can evaluate the second and third y measurement equations.  Perhaps some of the combinations will be defined and your search for optima will be simplified.Often outside information is brought to bear on troubling questions.  Perhaps the cost of factor A is exorbitant?  Maybe it should be minimized, even though it affects measure y1, so that a cheaper factor b can be used to boost y1 to an acceptable level.

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#83258

JB
Participant

That is somewhat where we are. We have three equations looking to form them into one. However, two equations have the same variable in them, so how can you combine them? Example:
The regression equation is
Bitterness = – 7.90 + 2.75 Hops – 3.10 Sugar + 1.42 Ferm time – 0.201 Mash temp
The regression equation is
Color = – 27.1 + 5.67 Deg.Barley + 0.146 Mash temp
How do you combine when both have mash temp in the equation?

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#83259

JB
Participant

Scott,
I tried using the optimizer but it would only choose either my low, mid, and high points and nothing in between. Am I doing something wrong? I thought you could adjust it to any point b/w your low and your high.

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#83260

Opey
Participant

First off let me speak for all of us and say that you have the best job in the world.  There is no more humanitarian occupation than trying to make better beer.
Now, correct me if I’m wrong, but it sounds like the only problem you have is two CTQs (bitterness and color) that share one significant factor (mash temp).  If this is true, then why not set mash temp to whatever level is most desirable for you, and then adjust the other factors to get the right bitterness and color?
Opey

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#83273

mcleod
Member

Make sure you have all of the right targets and the assigned weights to everything.  The other thing to worry about is in your DOE was there any curvature in the design?  Watch out using the linear regression formulas for optimization unless you are pretty sure there is no curvature.  Otherwise you may want to use the coefficients from your DOE ANOVA tables instead.  Other than that I am not sure why the optimizer is not working.  I have had good luck with it and being able to move it around to optimize.  Make sure you can move your lines on the optimizer.  There may be something that is set up that is only allowing Minitab to select it and not you.  You do have the freedom to move or type in what settings you want them at.

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#83278

JB
Participant

Scott,
When I use the optimizer (Stat, DOE, Factorial, response optimizer) I choose all three responses (bitterness, color, CO2). Go into setup and fill in my low, target, and high values for each variable. Then go to options and give starting values for each. When the optimizer comes up it only allows me to move to the high, mid, or low points and nothing in between. AND when I move one variables setting they all move to that same setting (high,mid, or low). Is this what happens to you too? I sure thought that you could choose any setting between your low and your high.

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#83302

mcleod
Member

No not at all.  When I set it up and move the lines to optimize the outputs it allows me to move to any setting.  Actually the last DOE I did it allowed me to move to such small settings (.001) that I had to remember I couldn’t set my process up to that fine.
Have you tried  to contact minitab and maybe their help line or some techs at the company?  Sounds like there is some funny setting set up wrong somewhere.

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#83338

Minitab Tech Support
Participant

Hi JB,
If you have center points in your design, and you analyze including the center points in the model, you will not have a continuous response line on the optimizer graph.  You will only get fits at isolated points.
Here is the reasoning:  In a factorial design with center points, it’s possible to detect curvature by comparing the fit at the center point with what would be expected if there were no curvature.  But you don’t have enough data to model how that curvature is distributed over the design space away from the center point.  Therefore, we don’t have a model that would allow us to compute and plot fitted values anywhere but the cube points and the center point.
Note that a central composite design, used for response surface DOE, consists of a (fractional) factorial design with center points and additional axial points. The axial points are added so that the curvature can be modeled with quadratic terms across the whole response surface. The factorial design points alone are not sufficient.
If curvature is not significant in your model (you can check for significance by looking at the p-value for Curvature in the Analysis of Variance table), you can re-analyze the design without checking the box for “Include center points in the model” (this check box appears under the Terms button in the Analyze Factorial Design dialog box).  By doing this, you will be able to get a continuous fitted response line on the optimizer graph.  MINITAB will assume a flat surface with no curvature.
I hope this explanation answers your question.   If not, please feel free to email me at [email protected].  It would be helpful if you could attach your MINITAB project file to the email.
Sincerely,
Annie on behalf of Minitab Tech Support

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#83379

Frank Serafini
Participant

Continuous data, Muiltiple Y’s, Multiple X’s = Multivariate Analysis.
Very special stuff. See your MBB. I’m interested in the outcome.

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