Re: r-Squared Question



Jerry Dallal wrote:
> I wrote:
>
> > It depends how you defined R2. If you define it as the square of the
> > correlation between observed and predicted, then it's a weakness.

What do you mean "a weakness"?

For OLS fitted regression, R^2 is ALWAYS the correlation between
the observed Y and the fitted Y.

What a tangled web we weave, when we stray from the standard linear
model methods in statistics to nonstatistical methods such as the
"arbitrary model fitting procedure" as measuring errors orthogonal
to the fitted line? What good is the new-gangled-or-mangled R^2
from a statistical point of view? A NEGATIVE value for R^2 is
second only to the "expected sign" fallacy in regression abuses.

-- Bob.


> > However if you define it as 1 - ResSS/TSS, then, for an arbitrary model
> > fitting procedure, R2 isn't even constrained to the interval [0,1],
> > since ResSS might exceed TSS.
> >
> > Here
> > > X Y YHat Y-Yhat
> > > 1 101 97 4
> > > 2 102 99 3
> > > 3 103 101 2
> > > 4 104 103 1
> > > 5 105 105 0
> > > 6 106 107 -1
> > > 7 107 109 -2
> > > 8 108 111 -3
> > > 9 109 113 -4
> > > 10 110 115 -5
> >
> > Here, TSS=82.5 and ResSS=85, so R^2 = 1-85/82.5 = -0.03, and the fitted
> > line predicts worse than always using the sample mean.
>
> I should have added that there was an earlier version of this post that
> was in error, claiming that ResSS=TSS. We don't want the corrected SS,
> but the actual SS, which differs here because the mean of the residuals
> is not 0. I've canceled my earlier post, but given the way cancels
> propagate, some copies of the original will survive. So, for the
> record, keep this post and the one with R^2= -0.03, and ignore the one
> with R^2=0.

.

Relevant Pages

  • Re: Some quotes for RH
    ... What you mean is that *you* only use a correlation when it ... "From Association to Causation: ... History of Statistics", Statistical Science, vol 14, no.3, pp 243-258, ... As Hume pointed out causation cannot be demonstrated. ...
    (uk.sport.cricket)
  • Reality Check Desired: Rank Order Correlations in IQ Testing (long, sorry)
    ... I appreciated the helpful responses I received from this group the last time I wanted to check my understanding of statistics, ... As part of preparation, I'm trying to learn how to formulate concepts about IQ test construction and validation in a way that will be informative and helpful to parents in our association. ... A lot of people have heard the term "correlation," but use that term in conversation basically as a synonym for correspondence, or agreement with theory. ... Let's initially suppose that a friendly omniscient observer has first rank-ordered all of the 456,976 individuals into their "true" rank order by intelligence, so that we can designate the test subjects in alphabetical order thus: ...
    (sci.stat.edu)
  • Re: Multidimensional Scaling
    ... > reducing intertextual distances to two dimensions), ... > Groenen (using the name product moment correlation) and was only used ... > by myself to choose between isoMDS() and my own iterative majorisation ... That is Applied Statistics at its WORST. ...
    (sci.stat.math)
  • Re: Critical t-values in large samples
    ... What if my test statistics are measured using a consistent ... values of my statistics already account for possible correlation? ... about the distribution of the residuals, ... If you have used a consistent variance-covariance matrix of the ...
    (sci.stat.edu)
  • Re: Critical t-values in large samples
    ... What if my test statistics are measured using a consistent ... values of my statistics already account for possible correlation? ... You should ask yourself, specificaly, are the standard errors being ... about the distribution of the residuals, ...
    (sci.stat.edu)