In article <000d01c0183c$63fe79e0$93716395@sprint>,
Jineshwar Singh <[EMAIL PROTECTED]> wrote:
>I am aware that the standard error of the estimate (regression line) cannot
>be used as an absolute measure of a single model utility. Is there any
>guideline about its value? The ratio of standard error of the estimate and
>the average of y values does help to decide when we evaluate more than one
>model. Is there any particular value of this ratio that can be used ? Any
>help will be appreciated.
I think you have some misconceptions here.
For starters, you should avoid the term "standard error of the
estimate". I don't know who came up with this bizzare term, but it's
utterly misleading. This quantity is NOT the standard error of an
estimator. It's an estimate for a population parameter, namely the
standard deviation of the residuals. It's better called the "residual
standard deviation" or more long-windedly (and more correctly) the
"estimated standard deviation of the residuals".
Whatever you call it, it comes in two forms - one adjusted for the
number of predictors in the regression equation, the other not. The
unadjusted form will get smaller and smaller as you add predictors,
and so can't be used to decide whether to add a predictor to the model
or not. But the adjusted form is a reasonable indicator of model
utility, though of course there may be better ones.
Computing the ratio of the residual standard deviation and the mean of
the y values will be meaningful only if there is a natural zero point
for y values. Even then, its meaning will be specific to the
application. There is no value for either this ratio, or for the
residual standard deviation itself, or for R-squared, that indicates
that a model is "good" or "bad". One can't expect the model to
predict y perfectly, and how imperfect one would expect a good model's
predictions to be is entirely dependent on the application.
Radford Neal
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Radford M. Neal [EMAIL PROTECTED]
Dept. of Statistics and Dept. of Computer Science [EMAIL PROTECTED]
University of Toronto http://www.cs.utoronto.ca/~radford
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