What is MSE00 and MSE00a and R?

i have gone through Greg's many examples;

but i am not clearly understanding the significance of MSE00; MSE00a; R and R^2.

This can be applied used in classification problem?????

why this method since mse is default given in NN performance function.

Thanks in advance; and waiting for Greg's precious comment.

Answer 1

[Greg Heath]

Unfortunately, I just saw this post.

MSE00 is the MSE for a naïve constant output model that always outputs the average of the target data. MSE = SSE/Neq where Neq is the number of equations that are used to estimate the unknown weights.

MSE00a is the MSE "a"djusted for the loss in estimation degrees of freedom caused by the bias of evaluating the MSE with the same data that was used to build the model. MSEa = SSE/Ndof where Ndof is the number of estimation degrees of freedom Ndof = Neq-Nw where Nw is the number of unknown weights that are estimated.

It is not hard to show that MSE00 is the average biased target variance (divide by N)and MSE00a is the average unbiased target variance (divide by N-1).

NMSE = MSE/MSE00 is the normalized MSE for an arbitrary model

NMSEa = MSEa/MSE00a is the normalized "a"djusted MSE

R^2 = 1-NMSE and Ra^2 = 1-NMSEa are the coefficient of determination and DOF "a"djusted value.

R^2 is often interpreted as the fraction of the target variance that is "explained" by the model.

R turns out to be the slope of the output vs target linear regression line.

Look up Rsquare and coefficient-of-determination in Wikipedia and other statistics references.