G Mohanty et al./ Materials Research Bulletin 43(2008)1814-1828 freedom for evaluation Residuals Lack of fit Pure error Corr total Standard deviation of 0.004 suggested low deviation associated with the experiment(Table 5). Mean is overall average of all the response data. CV.(coefficient of variation) measures the unexplained or residual variability of the data as the percentage of the mean of the response variable. Low C.V. value of 2.24 indicated that the proportion of variability unexplained by the model was extremely low. In other words, the model was able to explain most of the variability of the data. Predicted residual error sum of squares(PRESS)is a measure of how the model fits each point in the design. Low PRESS value of 1. 27 indicated that the observations did not highly influence the model which is desirable. R gives a measure of the amount of variation around the mean explained by the model. This model was able to explain more than 99% of the variability in the weight of alumina deposited Adj r is a measure of the amount of variation around the mean explained by the model, adjusted for the number of terms in the model. The adjusted R- decreases as the number of terms in the model increases if those additional terms do not add value to the model. The adjusted R2-value of 0.9974 indicated that all the selected terms contributed significantly to the model Predicted R2 gives some indication of the predictive capability of the regression model. Predicted R of 0.9904 indicated that the model can be expected to explain more than 99%o of the variability in predicting new observations in the design space The overall predictive capability of the model based on this criterion can be considered to be extremely satisfactory Adeq precision measures the signal to noise ratio. Adeq precision ratio of 97.388 indicated an adequate signal for proper model discimination. Since the noise in the system was insignificant compared to the signal as measured from the"adeq precision", it was decided not to replicate the design. Besides replication would have resulted in increased costs The regression equation for the alumina deposit obtained in terms of actual factors is Sqrt(weight of deposit) +0.0738191+0.000828180 x concentration.0204777 X electrode separation-667949E-007 X applied potential -0.0222254 x deposition time +0.000390049x concentration x electrode separation +8.46254E-006x concentration x applied potential+ 0.00268953 x concentration x deposition time +0.00701612 x electrode separation x deposition time+9.27401E 005 x applied potential x deposition time.000523226 x concentration x electrode separation x deposition time The regression equation in terms of coded factors is Sart +0.194030+00679850×A-0.0195735×B+0.0265547×C+0.0455348×D-0.00656404×A B+0.00634691×A×C+0.0164307×AxD-0.00344841×B×D+0.00695551×C×D 0.00523226×AxB×D 2.8. Model adequacy testing Residuals analysis is the primary diagnostic tool for checking violations of the basic assumptions, like normality, and model adequacy. The examination of the residuals from an unreplicated 2 design can also provide informationStandard deviation of 0.004 suggested low deviation associated with the experiment (Table 5). Mean is overall average of all the response data. C.V. (coefficient of variation) measures the unexplained or residual variability of the data as the percentage of the mean of the response variable. Low C.V. value of 2.24 indicated that the proportion of variability unexplained by the model was extremely low. In other words, the model was able to explain most of the variability of the data. Predicted residual error sum of squares (PRESS) is a measure of how the model fits each point in the design. Low PRESS value of 1.27 indicated that the observations did not highly influence the model which is desirable. R2 gives a measure of the amount of variation around the mean explained by the model. This model was able to explain more than 99% of the variability in the weight of alumina deposited. Adj R2 is a measure of the amount of variation around the mean explained by the model, adjusted for the number of terms in the model. The adjusted R2 decreases as the number of terms in the model increases if those additional terms do not add value to the model. The adjusted R2 -value of 0.9974 indicated that all the selected terms contributed significantly to the model. Predicted R2 gives some indication of the predictive capability of the regression model. Predicted R2 of 0.9904 indicated that the model can be expected to explain more than 99% of the variability in predicting new observations in the design space. The overall predictive capability of the model based on this criterion can be considered to be extremely satisfactory. Adeq precision measures the signal to noise ratio. Adeq precision ratio of 97.388 indicated an adequate signal for proper model discimination. Since the noise in the system was insignificant compared to the signal as measured from the ‘‘adeq precision’’, it was decided not to replicate the design. Besides replication would have resulted in increased costs. The regression equation for the alumina deposit obtained in terms of actual factors is Sqrtðweight of depositÞ ¼ þ0:0738191 þ 0:000828180 concentration 0:0204777 electrode separation 6:67949E 007 applied potential 0:0222254 deposition time þ 0:000390049 concentration electrode separation þ 8:46254E 006 concentration applied potential þ 0:00268953 concentration deposition time þ 0:00701612 electrode separation deposition time þ 9:27401E 005 applied potential deposition time 0:000523226 concentration electrode separation deposition time The regression equation in terms of coded factors is Sqrtðweight of depositÞ ¼ þ0:194030 þ 0:0679850 A 0:0195735 B þ 0:0265547 C þ 0:0455348 D 0:00656404 A B þ 0:00634691 A C þ 0:0164307 A D 0:00344841 B D þ 0:00695551 C D 0:00523226 A B D 2.8. Model adequacy testing Residuals analysis is the primary diagnostic tool for checking violations of the basic assumptions, like normality, and model adequacy. The examination of the residuals from an unreplicated 2k design can also provide information G. Mohanty et al. / Materials Research Bulletin 43 (2008) 1814–1828 1821 Table 6 Degrees of freedom for evaluation Model 10 Residuals 9 Lack of fit 6 Pure error 3 Corr total 19