![]() ![]() Also the presence of an extra-parameter eventually makes the calculus less robust. But the more the scatter is important the more the optimization differs from the cases $(1)$ and $(2)$. The number of independent parameters in the equation $(2)$ of the particular quadratic surface is six while the number of parameters in the original equation $(1)$ is five. If the data was scattered the result would be not so accurate due to several causes : This is certainly because the data doesn't come from experiment but comes from numerical simulation without scatter. This result is unusually excellent for a regression problem. One can see that the result is quite exactly the result expected by the OP : This is applied in the numerical example below, with the data from the OP. All the cases are not detailed but the method is the same. This kind of regression is roughly considered in the paper But not a general quadratic surface since the equation doesn't includes all coefficients of the general quadratic surface. So, this is a problem of regression to fit a quadratic surface. I have a pretty straightforward regression problem I need to solve within the.
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