Re: Mathematica calculates RSquared wrongly?

*To*: mathgroup at smc.vnet.net*Subject*: [mg112785] Re: Mathematica calculates RSquared wrongly?*From*: Lawrence Teo <lawrenceteo at yahoo.com>*Date*: Thu, 30 Sep 2010 04:52:37 -0400 (EDT)*References*: <i7seru$pt5$1@smc.vnet.net>

With reference to the following statement, > 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. Is this the standard practice in mathematics world? It seems to me that this takes away the common comparison ground between linear and nonlinear regression. I always get unrealistically high R^2 (>0.9) from NonlinearModelFit function, even though the fit might be awfully off. This makes me think if the so called uncorrected R^2 is right. Any explanation? Thanks PC On Sep 28, 6:09 pm, Darren Glosemeyer <darr... at wolfram.com> wrote: > 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