Dear all,
i would like to kindly request you could you please refer attached document (comments are shown with yellow coloured text at page no. 40 & 41) for answering the current question.
Dear Mohammad,
F-value = (SSR/i)/((SSE/(n-1-i) = MSR/MSE. MSR: regression mean square; MSE: Mean square error; i: degrees of freedom for regression and (n-1-i): degrees of freedom for residual (error). The regression model is not significant if F-value < F-crit = F (α,i,n-1-i) with α = 0.05 (normally)
Increasing the numbers of model terms ( that means increasing i) leads to a decrease of MSR and an increase of MSE up to point which the F-value < F-crit and the model is no longer significant.
Therefore, I am not sure that F-value = 1.5 can be used as a critical value for the elimination of non-significant terms or not. However, from text book about RSM that I am using, I do not know how to calculate F-crit and what is mathematical formula? I want to understand clearly more than only based on the result from software.
I don't think that a critical value can be given for all cases. For example suppose F=1.51, you conclude "significant model"; and if you have F=1.49, the conclusion is "unsignificant model". The ANOVA table gives you the F values for each effect in your model, and it can be a good solution to eliminate non significant effects, for example with p-value greater than 5% (very classical value). But it's the same problem as the preceding one. Another problem can occur if effects are correlated (VIF greater than 1). In this case, F values are impacted by this colinearity between effects. Suppose you have several effects strongly correlated, these effects can be declared unsignificant, even if each of them is individually significant.
To conclude, don't focus only on F value. Look at also individual F, VIF, PRESS, residuals, ... Don't hesitate do try several models, and compare them! And remember what said GEP Box : all models are wrong, some ones are useful; so build models as simple as possible!
A F with 1 (numerator) and 10 (denominator) degrees of freedom has a p=0.75126 (the right tail probability of 75.126% which means that the probability of the null hypothesis: b11=0 would be false (parameter associated with x1^2) is 75.126%. This is not enough for declare b11 significant, but is not enough to eliminate it. That is, the response variation produced by b11x1^2 in the model MAY BE in the same order that the experimental variation. In my opinion with such p it is better to keep the quadratic term mainly because your RSM model is only valid within the factors limits imposed by experimental design. If you have doubts you can preserve the quadratic term and to solve an optimization problem (within the valid limits) and then you eliminate the quadratic term, solve again the optimization problem, and compare the results. If the results are different you must prefers the results with quadratic terms (if your F is 1.5) because you have 75.126% (or other with other degrees of freedoms) of probability that this term must be different to zero.
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