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Re: R^2 for linearized regression
Posted:
Jan 31, 2013 5:18 PM
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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
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