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Re: Mathematica calculates RSquared wrongly?

• To: mathgroup at smc.vnet.net
• Subject: [mg112777] Re: Mathematica calculates RSquared wrongly?
• From: Darren Glosemeyer <darreng at wolfram.com>
• Date: Thu, 30 Sep 2010 04:51:09 -0400 (EDT)
• References: <i7seru$pt5$1@smc.vnet.net> <201009290815.EAA28196@smc.vnet.net>

  On 9/29/2010 3:15 AM, Ray Koopman wrote:
> On Sep 28, 3:09 am, Darren Glosemeyer<darr... at wolfram.com>  wrote:
>> On 9/27/2010 4:47 AM, Lawrence Teo wrote:
>>> [...]
>>> nlm = NonlinearModelFit[sbbBN, a*x^2 + b*x + c, {a, b, c}, x]
>>> nlm["RSquared"]
>>>
>>> The RSquared by Mathematica is 0.963173
>>> Meanwhile, Excel and manual hand calculation show that R^2 should
>>> be equal to 0.7622.
>>>
>>> Is Mathematica wrong? Thanks!
>> This is as designed. For nonlinear models, the corrected (i.e. with
>> the mean subtracted out) sum of squares is sometimes used. This is
>> consistent with comparing to a constant model, but most nonlinear
>> models do not include a constant in an additive way. For this reason,
>> NonlinearModelFit uses the uncorrected (i.e. without subtracting out
>> the mean) sum of squares.
> This information should be included in the "Goodness-of-Fit Measures"
> section of the NonlinearModelFit documentation, which should also
> point out that RSquared is computed as  1 - (Residual SS)/(Total SS),
> and that in nonlinear models this is generally different from the
> ratio (Model SS)/(Total SS) that is sometimes cited -- e.g.,
> http://reference.wolfram.com/mathematica/RegressionCommon/ref/RSquared.html
> -- as the definition of RSquared.
>

The RegressionCommon documentation is for a now obsolete standard 
package. The "RSquared" property for nonlinear models is described near 
the bottom of

http://reference.wolfram.com/mathematica/tutorial/StatisticalModelAnalysis.html

The current statement is:

"The coefficient of determination "RSquared" is the ratio of the model 
sum of squares to the total sum of squares."

I will modify this to mention that the total is the uncorrected total 
for the next version.

Darren Glosemeyer
Wolfram Research

• References:
  • Re: Mathematica calculates RSquared wrongly?
    • From: Ray Koopman <koopman@sfu.ca>