Design of Experiments with existing data

#1
Hello, I have an experiment generated by CFD (Computational Fluid Dynamics) that includes 3 input factors that are varied to obtain 1 response.
I wish to use DOE (Design of Experiments) to determine how much the variation in the response can be explained by varying the 3 input factors.
I realize I can use the 2 or 3K factorial design to determine this but I already have a specific set of data I want to run the experiment on.

What method could I use to perform this analysis? I've attached the data set below.
I'm currently using Minitab for my analysis but I'm willing to try other software.

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#5
@GretaGarbo @Miner The model that generated that data is non-linear so when I ran the linear regression on the data, the results didn't make much sense to me. For example, these are the coefficients calculated by the regression model:
Coefficients

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Let's take the coefficient for X2 for example, it's equal to -4.02. If I'm not mistaken this means that a one-unit change in X2 will result in a 4.02% reduction in the response Y.

However, if we look at designs 7 and 8 in the original data I posted, the only difference between the two designs is a one-unit change in X2, while X1 and X3 are kept constant. But the percent change in Y between designs 7 and 8 is 40%, not 4.02 or something closer. This is reflected throughout the data which is why the linear regression model didn't make sense to me.

These are some more results from the linear regression
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I've edited the original post to include the acronyms.
 

Dason

Ambassador to the humans
#7
Let's take the coefficient for X2 for example, it's equal to -4.02. If I'm not mistaken this means that a one-unit change in X2 will result in a 4.02% reduction in the response Y.
You are mistaken. It means that a one unit change in X2 will reduce the expected value by 4.02.
 
#8
You are mistaken. It means that a one unit change in X2 will reduce the expected value by 4.02.
Thanks for the correction.

Perhaps X2 wasn't the best choice to investigate because it's not a significant predictor.
You could also try putting an interaction in your regression.
Ok, since X3 is the only significant predictor, does the coefficient of X3 make sense if you compare it to the original data?
 

katxt

Active Member
#9
Sort of. A graph of Y vs X3 has a slope of about -1 which matches your table. It doesn't help that most of the points are on 34.
 
#10
I see. Most of the points are on 34 because I was performing a local sensitivity analysis by changing one parameter at a time to examine the effect on the response.

So the conclusion from this analysis is that the X1 and X2 are not significant predictors of the response, however, X3 is?
 

Dason

Ambassador to the humans
#11
Just fyi for the future if you come here (or to a statistician) before you actually conduct the experiment we can help you design something that will optimize power for a set sample size.
 

Miner

TS Contributor
#12
I see. Most of the points are on 34 because I was performing a local sensitivity analysis by changing one parameter at a time to examine the effect on the response.

So the conclusion from this analysis is that the X1 and X2 are not significant predictors of the response, however, X3 is?
One factor at a time experiments are inefficient and often unable to detect interactions.
 
#13
Just fyi for the future if you come here (or to a statistician) before you actually conduct the experiment we can help you design something that will optimize power for a set sample size.
Alright so maybe I should explain the experiment from scratch. I performed an optimization experiment that included modifying 3 input parameters (X1,X2,X3) to achieve a response (Y). I generated 50 of such experiments (attached below). My goal is to figure out which of the 3 input parameters has the biggest effect on the response. So I took one of the 50 experiments and performed local sensitivity analysis by varying one factor at a time, which is the data I posted in the original post.

One factor at a time experiments are inefficient and often unable to detect interactions.
I read as much.
 

Attachments

katxt

Active Member
#14
The Y vs X1 has an interesting hook. Try multiple regression as before on your 50 experiments but with an X1squared term included.
 

katxt

Active Member
#20
OK. You really need both the X1 and the X1squared terms in the model.
Something like this. Note the minimum about 100. Both the X1 and the X1squared terms are significant.
 

Attachments