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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