How does REGSTATS compute mse?

I have a very simple and seemingly silly question, but I can't figure it out. I am trying to understand why MATLAB returns a mean square error (mse) value of Inf for a perfect regression fit. Shouldn't MSE for a perfect fit be zero?

For example if I have x = [1, 3, 5] and say y = exp(x) = [2.7183 20.0855 148.4312].

Now, just for the sake of it if I do a regression using regstat as: stats = regstat(y,x,'quadratic'), it gives a perfect fit to the function (as expected, since there are 3 points) and stats.yhat are the same values as y.

stats.rsquare = 1 , which makes sense... but stats.mse = Inf. Why so ? According to the traditional formula shouldn't mse be equal to zero, since it is a perfect fit?

Any clarifications will be appreciated. Thanks!

Answer 1

[dpb]

DOF = 0 so the denominator is zero--> inf for the mse.

Try with

x = [1:2:N];
y = x.^2;

instead, for example, for N=[5 7] to illustrate.