# How much should I put effort to refine a Response surface?

A response surface that I have obtained from a DOE analysis with multiple variables, show small irregularities when I plot 2D variable-vs-variable curves . like somewhere it should be exponentially and only reduce, it changes the gradient in some points.

I assuem it's from the impreciseness of the fitting of the Response surface. How much effort shouldI put to obtain a more precise curve ?

Well, this depends entirely on what you plan to do with your response surface. We have no idea what you want to do with it, so we can't answer that. Here's what you should do: ask yourself, "what is the worst thing that could happen if this response surface is not accurate enough?"

If you are building a nuclear reactor, and the answer is "hundreds of people will die" then you might want to spend another few years on it.

If you are writing the physics engine for a video game, and then answer is "the physics in the game will be slightly unrealistic" then you might not need to spend any more time on it.

Somewhere in between might be a project where the answer is "nobody gets hurt but my company could lose \$X". In that case spend time on it in proportion to the value of X versus the cost of your time in improving it.

How much effort you should put in your response surface (RS) to get better predicted values no one can tell you as mentioned in the answer above…

But I think with the RS you want to predict some points?! Predict them with the RS and check if your real measured value is in a confidence interval (e.g. 95 %) of your prediction that fits your needs.

Remind: You will never predict a value on point – therefore the confidence interval...

If you need more precise predictions think about:

• measurement system analysis (MSA)
• do repeated measures at your points and „put“ the distribution of these points in your creation of the RS
• use linear / quadratic / cubic regression formulas with interactions
• Hint: Kick out the terms that are irrelevant (see p-value)
• devide your area in multiple areas – one DOE per area
• and sure some more points...