Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.stat.math.independent

Topic: R^2 for linearized regression
Replies: 3   Last Post: Jan 31, 2013 5:18 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ] Topics: [ Previous | Next ]
Richard Ulrich

Posts: 2,860
Registered: 12/13/04
Re: R^2 for linearized regression
Posted: Jan 31, 2013 5:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


By the way, this post by David Jones is fine, and my post does not
contradict anything in it. I offered a slightly different angle on
the same advice.

In the final paragraph, where he says, "From a theoretical
point of view," I don't have a better single word for
"theoretical," but I would prefer some statement like, "From
a theoretical point of view that focuses on the validity and
robustness of the statistical tests ...". His next sentence
fixes that tiny problem.

--
Rich Ulrich


On Thu, 31 Jan 2013 15:29:42 -0000, "David Jones"
<dajhawk@hotmail.co.uk> wrote:

[snip, original post]
>======================================
>
>It is important to be clear about how the value of R^2 that you use is
>calculated when you use it. Just using values from individual fitting
>modules may well not be enough.
>
>See http://en.wikipedia.org/wiki/Coefficient_of_determination
>
>You should try calculating R^2 directly from the sets of observed and
>corresponding values predicted values, where
>(i) "observed" is the original observations and "predicted" is either the
>predictions from linear regression or the exponential of the predictions
>from the regression model for the log-ed data (it is also possible to
>include a "bias adjusted" version of the latter)
>and
>(ii) "observed" is the log-ed original observations and "predicted" is
>either the predictions from linear regression on the log-ed data or the
>logarithm of the predictions from the regression model for the original
>data.
>
>This gives at least 4 values to compare. You can also try introducing an
>additional linear regression step, for example where in (i) you could fit a
>linear model for the observed data based on the exponentiated predictions
>from the linear model for the log-ed observations.
>
>If you have time you could construct a pair of scatter plots of observed
>versus predicted values in both original and transformed spaces.
>
>But there is no definite generally applicable answer to your question,
>except hat you should definitely have a comparison of R^2 values calculated
>for the same transformation of the observed data. From a theoretical point
>of view , if the usual model-checks for regression models suggest that the
>transformed model is better then you should be using the R^2 calculated for
>the log-ed data. But, if practical/real-world considerations suggest that
>the "importance" of errors of prediction is equal on the non-transformed
>scale, then R^2 calculated for the untransformed observations may be more
>closely aligned to what you are trying to use the predictions for.
>
>David Jones




Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.