How to improve regression model?

Hi, I have a request about Minitab.
I have 3 factors on 2 level (8 experiments) and 1 response variable. I would like to improve the regression equation obtained with Factorial design with new series of targeted experiments suggested by Minitab, hence varying factors of the experiments without adding another level.

Maybe with RSM? Which are your suggestions?

Thanks for your help, have a nice day!

In your first design, did you use center points? Did they indicate curvature?

If they did indicate curvature, RSM would definitely be a good approach. If you ran center points in your first design, you can easily augment your first experiment by adding and running axial points plus another set of center points. The two sets of center points allow you to block on two experiments run at different times. If you did not use center points, other approaches might be better until you have indications of curvature.

If you had no curvature, did you have any interactions? If no interactions do you want to expand the design space or move it in a specific direction?

I have no center points in my original design, because all factors are on 2 levels (minimum and maximum).
The original set is this (experiments in double). A,B,C factors. Y is the response.

A.....B.......C........Y
1,0 20 2,0 89,1339
1,0 20 2,0 93,8583
1,0 20 0,5 65,5118
1,0 20 0,5 68,6614
1,0 10 2,0 72,7559
1,0 10 2,0 80,6299
1,0 10 0,5 71,1811
1,0 10 0,5 71,8110
0,5 20 2,0 77,4803
0,5 20 2,0 81,5748
0,5 20 0,5 54,1732
0,5 20 0,5 54,8031
0,5 10 2,0 62,8346
0,5 10 2,0 57,0079
0,5 10 0,5 58,7402
0,5 10 0,5 58,7402

What is your goal? To maximize Y? To hit a target?

You have an excellent model with R^2 (adj.) = 95%
All three main effects and one interaction are statistically significant, and the low lack of fit means there is little chance of curvature, so I would not recommend RSM. It would gain you little. If your goal is to maximize Y, I would relocate the center of a new design to the "best corner" (i.e., A=1, B=20, C=2) and run using center points.

I forgot to mention that after running the second design, you can combine both designs together as two different blocks and analyze it using GLM.

Thanks. Actually, I'm not interested in maximizing/minimizing or fixing a target value of Y.
You did factorial design if I'm not wrong, I've just tried it. My purpose is perform additional experiments suggested by Minitab in order to fit as well as the last case, but evaluating other type of interactions between factors or quadratic relations. Because B*C interaction is strange from the experimental point of view (chemical experiments), so the actual model is not so representative neverthless his high R^2

If you are performing chemical experiments, you may need to use a Mixture design.

Miner said:

If you are performing chemical experiments, you may need to use a Mixture design.

Click to expand...

"Sum of the components must be the same for each row". I can't use Mixture design. My factors are Concentration, Contact Time and Ratio between liquid solid. So, they are not defined in fixed proportions because are physically different, and their sum has no sense.