Hi

In order to interpret the analysis of a Box-Wilson Central Composite Design, please see the websites:

1.http://help.synthesisplatform.net/doe9/central_composite_designs__analysis_results.htm

2.http://documentation.statsoft.com/STATISTICAHelp.aspx?path=Experimental/Doe/Examples/Example5CentralCompositeResponseSurfaceDesigns

Regards,

Zuhair

R2 measures the fraction of total sum of squares about mean( SSTOT ) that is explained by the Regression model you have estimated the parameters for ( the fitted Regression model), R2 do not involve the degrees of freedom associated with the Regression and Residual space, and hence do not indicate the efficiency of your prediction model, adjusted R2 is the statistic which takes into account these degrees of freedom contributions in calculation. I would suggest you to calculate both the R2 and Adjusted R2 for your dataset and see if they are significantly different in which case this indicate a strong overfitting problem.

F ratio gives the ratio of Mean Squared Regression and Mean Squared Residual , and under Standard model assumptions follows a non-central F distribution( if your model is statistically significant otherwise a central F distribution) with regression and residuals degrees of freedom respectively. I believe in your case the SSREG/SSTOT is coming out to be 0.6 but (1-(MSR/MSTOT)) is significantly smaller which results in FRATIO=MSREG/MSR less than that of the central F distribution threshold value , for given degrees of freedom of regression and residual, at 95% Confidence level.

Hello Hamida, if your model's p-value is not significant, then it is not significant. It means the model does not adequately explain data variations in the region of experimentation. Although your R2 is 60% which implies that 60% of the events that led to the responses were mediated by the input factors, i suggest you take what Debopam said seriously. R2 has a tendency to mislead, so the adjusted form which takes care of the degrees of freedom corrected for the number of predictor variables in the model is employed for more reliable statistical explanations. Please also look at the F-statistic and p-value of the Lack-of-fit (LOF) error. If the p-value is significant, then i suggest you re-model. Please read the suggested links.Article Response surface modeling and optimization of major medium v...

Article Utilization of response surface methodology to optimize the ...

Thank you so much : Mr Z. A. Al-Hemyari , Mr Debopam Ghosh and Mr Maurice Ekpenyong for your answers