To extract the coefficients use the "fit" function....
[fitobject,gof,output]=fit([x, y], z, 'poly22');
fitobject.p00, fitobject.p10, etc contain all of the coefficients. For more info type
doc fit
In terms of which coefficient influences the model most, it is better to ask which term influence the model most (e.g., p00, or p10*x, or p01*y, or p20*x^2, etc). Not sure if MATLAB has a specific tool to do this, but a simple approach would be to remove each term one by one and assess the fit. So something like...
coeffs = fieldnames(fitobject);
n=length(coeffs);
for ii=1:n
dummy_fit = fitobject; % copy to dummy variable
dummy_fit.(coeffs{ii}) = 0; % set desired coefficient to zero
zhat = dummy_fit(x, y); % get the model estimate
residual(ii) = norm(z-zhat) % get the residual
end
This loops through all the coefficients and gets the residual when each one is set to zero. Note, that overriding a coefficient value in the fit object spits out a warning, for your purposes this is not important. There may be a smarter way of doing this, but this should work OK.
