I think this may be of some help... http://udel.edu/~mcdonald/statcurvreg.html

I have briefly gone through it and it talks mainly about increasing the order of the model. I think I may need to redesign my experiment design points.

One question in general. If I am not wrong, higher the value of Rsq, we can say better the model will be able to predict the values of the output. Therefore we are to iterate and improve the model by adding/removing terms which will increase the value of R sq.

Dear Deewajar

If you add parameters to a model its Rsq always grows. This is the reason behind the adjusted Rsq. You can use Rsq to compare linear models of the same number of parameters, but if you have two models of different number of parameters it is best to use other measures like the adjusted Rsq or the Cp of Mallows.

if your problem is on selection of the model using R-sqr, you may go through the paper http://www.pjsor.com/index.php/pjsor/article/view/427.

The main problem with r-sqr is, inclusion of variables in the model results a higher value of R-sqr and also if the sample size (n) is less than the number of parameters (p) in the model, which results a higher value for Rsqr (=1). So, you include the curvature by looking at the scatter plot for which the family of models suitable to the given data using non-linear least squares methods.

In my experience, I never got expected model in an experiment or two. I need to repeat experiments for precision and validity. After triplicate or tetraplicate, we will reach ultimate model.

Dear Deewakar, the model you've presented here has no interaction effect in it. Its obvious you didn't get the expected results. A 3 factorial design has 4 interaction terms which you didn't include them in the model. Whole model is:

y=a+b*x1+c*x2+d*x3+e*(x1*x2)+f*(x1*x3)+g*(x2*x3)+h*(x1*x2*x3)

hope it helps

This model only and only works when levels of your factors are quantitative and not names or order scaled.

Dear Deewakar, If I understand it right you stated wrongly the question…

In fact, the reason why you performed central point experiments was to test (statistically) if the response you are studying could be described by a first-order model or if you needed to include higher-order terms. The r-sqr or the r-adjusted do not allow concluding if the model is suitable or if there is LOF (lack-of-fit --> "wrong model"). A low r-sqr can be due to low precision, not to a wrong model.

Both situations (wrong model and low precision) lead to a “high” residual variance which in turn lowers the r-sqr value. If the “problem” is a “to simple model”, increasing the number of levels in your design will help. If the problem is “low precision” there is no gain in increasing the number of levels (and model terms – quadratic, interactions etc) because the r-sqr will not increase.

Are you using any DOE statistic software or performing calculations “by hand” (using excel, for instance)?

Is simple, for example:

y=a+a*x1+b*x2+c*x3+d*x1^2+e*x^2, and so on, if Quadratic is significant,

y=a+a*x1+b*x2+c*x3+d*x1^2+e*x^2+f*x1^3+g*x^3, if Cubic, ...

You may create te new terms as new variables, e.g. "XCuad"=x^2 ,...

Go into the Minitab DOE menu and add in some axial points. This will allow you to fit a quadratic model after you run the samples. Until then, you can't add a quadratic term to your model.They are all confounded among each other. So, you can;t tell which factor(s) have a true quadratic effect.