I have a data set consisting of 3 columns: $x$, $y$ and $z$. I am analyzing the influence of $x$ and $y$ on $z$: image of the scattered data and fit
I have managed to find a surface fit of the form $z=10^{a+bx+cx^2+d\log{y}}$ in Matlab, which should represent a mean. I would like to find a new surface of a similar form that represents the 95% confidence interval and another one that represents the 5% confidence interval. More specific: I want to find a function $f(x,y)$ that represents the values for which $z$ is smaller than $f(x,y)$ with a confidence level of 95%, and the same for the 5% confidence level. Is this possible and how? Specific ways in Matlab are appreciated, but I'm looking for a general method.
Thank you