You can find the formula for RMSE easily enough. Here for example:
https://en.wikipedia.org/wiki/Root-mean-square_deviation
It is simply the sqrt of the mean of the squares of the errors, which is what polyfitn computes, as you can see:
polymodel.RMSE = sqrt(mean((depvar - yhat).^2));
So, you may have chosen a different formula for RMSE. I suppose there are others one might define, but the one in polyfitn is what seems to be standard.
I have no idea what you are asking about if it is safe to use the RMSE that polyfitn returns.
As a simple test:
M = rand(10,3);
y = rand(10,1)*10 + 10;
P = polyfitn(M,y,1);
pred = polyvaln(P,M);
sqrt(mean((pred - y).^2))
ans =
1.9747
P.RMSE
ans =
1.9747
I'm not sure what form you might have chosen here otherwise.
