# [R] Scaled MPSE as a test for regressors?

Zhou Fang zhou.zfang at gmail.com
Mon Mar 23 16:01:20 CET 2009

Hi,

This is really more a stats question than a R one, but....

Does anyone have any familiarity with using the mean prediction
squared error scaled by the variance of the response, as a 'scale
free' criterion for evaluating different regression algorithms.

E.g.

Generate X_train, Y_train, X_test, Y_test from true f. X_test/Y_test
are generated without noise, maybe?

Use X_train, Y_train and the algorithm to make \hat{f}

Look at var(Y_test - \hat{f}(X_test))/var(Y_test)

(Some of these var maybe should be replaced with mean squared values instead.)

It seems sort of reasonable to me. You get a number between zero and
one out of it, with 1 the solution for constant fits. Anyone seen
anything like this, or know anything about properties? Has it got a
name?

Zhou Fang