Polyfitn Function calculate the RMS value

When I use 'polyfitn' function to fit 3D data, should I use 'polyvaln' function and calculate the RMS error? OR Can I directly consider the RMSE value from the function 'polyfitn' to be the RMS error. In both the cases, the values are different. But for all the cases I checked, the minima occurs at the same point for both the values. Is it safe to consider RMSE value?

Answer 1

[John D'Errico]

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.

[jupiter]

Thank you John, while I was also doing the same thing but calculating the sum and then dividing it by the number of elements (Old school way :)), only a factor of cube at the denominator was causing the difference in the result. Now everything is working fine.