# Optimize One Response with Three Variables

C

#### Cenderze

Hello!

I'm intending to do a response optimization of one response, y, having three variables x1, x2, x3. These variables are coded in the following manor:

A B C y
-1,00000 -1,00000 -1,00000 66
1,00000 -1,00000 -1,00000 80
-1,00000 1,00000 -1,00000 78
1,00000 1,00000 -1,00000 100
-1,00000 -1,00000 1,00000 70
1,00000 -1,00000 1,00000 100
-1,00000 1,00000 1,00000 60
1,00000 1,00000 1,00000 75
-1,68179 0,00000 0,00000 100
1,68179 0,00000 0,00000 80
0,00000 -1,68179 0,00000 68
0,00000 1,68179 0,00000 63
0,00000 0,00000 -1,68179 65
0,00000 0,00000 1,68179 82
0,00000 0,00000 0,00000 113
0,00000 0,00000 0,00000 100
0,00000 0,00000 0,00000 118
0,00000 0,00000 0,00000 88
0,00000 0,00000 0,00000 100
0,00000 0,00000 0,00000 85

I dont know how to perform this optimization. I've tried to "Define Custom Surface Response Design" and choosing the Optimize Response option under Stat -> DOE -> Response Surface

I receive a value though which has only desirability = 0,7 (hence not an optimum -the highest value in my set of y i 118) and using x1 = -0,5 which is not in the range of my valid values for it.

When I've googled all I see is people who merely makes surface plots and conclude in what path the response is optimized - however using three variables I do not know how to perform this.

Any help really appreciated!

Regards,
Cenderze

Last edited by a moderator:

#### Miner

##### Forum Moderator
Include the actual response values and I'll take a look at it.

C

#### Cenderze

Sure I can add the response values. I believe adding a column after the x1, x2, x3 columns in my question makes it too difficult to copy everything as intended, so I merely write out the response column as a whole.

It is the following

y
66
70
78
60
80
70
100
75
100
75
100
80
68
63
65
82
113
100
118
88
100
85

It is desirable to have high values on y.

C

#### Cenderze

Include the actual response values and I'll take a look at it.
Thanks again for writing. Just wanted to make sure you noticed that the whole data set was edited. I saw a 1 in the wrong place.

Doing the exercise as

Stat -> DOE -> Define Custom Response Surface

And choosing 3 responses, 6 center points, 1 replicate and alpha 1,682 and subsequently choosing to

Stat -> DOE -> Optimize Response variable

and choosing Maximize and lowest 100 and target 118 I got that the max y is

101,711

and D=0,41

but A=0,6 B = -0,11 and C=0,15

which, if I've understood correct is invalid for this design.

So, basicially, I stil need help even though I've found an error in my original data set.

Hmm.. guess this became more of an update than an actual response

#### Miner

##### Forum Moderator
The data in post 3 has two more entries than in post 1.

C

#### Cenderze

Thank you for replying. The "main" post has been edited now so it should be correct size and correct data.

#### Miner

##### Forum Moderator
I'll take a look on Monday. You might want to bump it again Sunday night.

#### Miner

##### Forum Moderator
I see your problem. Response Optimizer is only as good as the predictive model that you develop. If the predictive model is poor, the Optimizer results will also be poor.

I analyzed your experimental data as a response surface design and found the two quadratic terms BB and CC to be significant. The R^2(adj) was low (34.7%) and R^2(pred) was very low (15.7%). Since Minitab's DOE analysis is heirarchical (meaning you must include the non-significant B and C terms), I reanalyzed the data using General Regression and included only the quadratic terms. This improved the model slightly to a R^2(pred) of 33.4%. However, this is still far from a good model.

The error partitioning did not indicate a Lack of Fit issue. All of the error was in the Pure Error category. This would indicate that you potentially have an issue with your measurement variation or your experimental setup variation.

Can you tell us any more about the factors and responses as well as the process? That would enable us to offer better advice.

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