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How to make sure the right order of the general Polynomial fit?

altenbach
Thanks for your advice! You advise that It should be very important to fit the data on the base of physical meanings , it is very useful!
But what I want to get is a strict description of goodness of fit in mathmatics.
Now I think mse is enough, In your nonlinear fit vi , why use [ (mse * covariance)^0.5 ]*fitted coefficient *100 to decibe the error?
Would you please tell me your math theory?
 
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