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Re: Mathematica calculates RSquared wrongly?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112729] Re: Mathematica calculates RSquared wrongly?
  • From: Darren Glosemeyer <darreng at wolfram.com>
  • Date: Tue, 28 Sep 2010 06:06:24 -0400 (EDT)

  On 9/27/2010 4:47 AM, Lawrence Teo wrote:
> sbbBN = {{-0.582258428`, 0.49531889`}, {-2.475512593`,
>      0.751434565`}, {-1.508540016`, 0.571212292`}, {2.004747546`,
>      0.187621117`}, {1.139972167`, 0.297735572`}, {-0.724053077`,
>      0.457858443`}, {-0.830992757`, 0.313642502`}, {-3.830561204`,
>      0.81639874`}, {-2.357296433`, 0.804397821`}, {0.986610836`,
>      0.221932888`}, {-0.513640368`, 0.704999208`}, {-1.508540016`,
>      0.798426867`}};
>
> 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.

Because the model you are using is a linear model, you could instead use 
LinearModelFit, which uses corrected sums of squares if a constant term 
is present and assumes a constant term is present unless it is told 
otherwise.


In[1]:= sbbBN = {{-0.582258428`, 0.49531889`}, {-2.475512593`,
             0.751434565`}, {-1.508540016`, 0.571212292`}, {2.004747546`,
             0.187621117`}, {1.139972167`, 0.297735572`}, {-0.724053077`,
             0.457858443`}, {-0.830992757`, 0.313642502`}, {-3.830561204`,
             0.81639874`}, {-2.357296433`, 0.804397821`}, {0.986610836`,
             0.221932888`}, {-0.513640368`, 0.704999208`}, {-1.508540016`,
             0.798426867`}};

In[2]:= nlm = NonlinearModelFit[sbbBN, a*x^2 + b*x + c, {a, b, c}, x];

In[3]:= nlm["RSquared"]

Out[3]= 0.963173

In[4]:= lm = LinearModelFit[sbbBN, {x, x^2}, x];

In[5]:= lm["RSquared"]

Out[5]= 0.762242


Darren Glosemeyer
Wolfram Research


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