Re: Formula for Coefficient of Determination (Quadratic Regression)

From: Richard Ulrich (Rich.Ulrich_at_comcast.net)
Date: 08/25/04 

Date: Wed, 25 Aug 2004 15:35:18 -0400

On Wed, 25 Aug 2004 17:46:52 +0200, Giobibo <giobibo@yahoo.com> wrote:

> I need to calculate the "Coefficient of Determination" Rē for a
> quadratic regression.
>
> For a linear regression it is simply given by R-square.
> But how can I calculate the coefficient of Determination for a
> quadratic regression?
>

Do you mean Y= a*X +b*X^2 + c ?

Most statisticians consider that a linear regression because
it is linear in the coefficients. Its R^2 is the CD.

Many engineers (inter alia) don't call it linear, but it
is still the simple case. Here is a post from last year,
and my response -

Is this a question about computing "R-squared", or
about using the term "coefficient of determination"?

=====
On 3 Sep 2003 01:42:07 -0700, baspo@web.de (Bastian) wrote:

> I wonder if the coefficient of determination, which usually ranges
> from -1 to +1, can achieve other values for nonlinear relations. I
> read something like that in an artikel which said that this is shown
> in GREENE, W. H., Econometric analysis (1997), p. 318.
>
> Unfortunately I can't get the book the next weeks, so I'd be glad
> about any comments on the topic or some hints to other literature
> sources.

W.H. Green, Econometric analysis (1997) does not say
anything about coefficient of determination on page 318.
Or about anything that I see as relevant.

The C of D is listed in the index for page 85 and page 252.
On p. 252, Greene writes,
"The coefficient of determination is denoted R2.
As we have shown, it must be between 0 and 1,
and it measures the proportion of the total variation
in y that is accounted for by variation in the regressors."

So, I don't see the support in Greene that you mentioned.
 [ snip, stuff about no-intercept models and R^2 definitions]
===== end of googled citation.

Googling the web for <"coefficient of determination" nonlinear>
gets thousands of hits. You could narrow the search, to get
your own special area.

I know that various replacements for R^2 have been
suggested, for describing Logistic regression in particular,
but I don't think that it is ever labeled the CD. 

-- 
Rich Ulrich, wpilib@pitt.edu
http://www.pitt.edu/~wpilib/index.html

Relevant Pages

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