> This issue that traces back to the very unfortunate use

> of R-squared as the name of a tool to simply compare a model to the model

> that

> is a single number (the mean). The mean can be shown to be the optimal

> choice

> for a model that is a single number, so it makes sense to try to do better.

>

> The OP has the correct form -- and I find no matter what the software, when

> working with models that do NOT have a constant in them (i.e., nonlinear

> models, regression through the origin) it pays to do the calculation

> "manually". In R it is really easy to write the necessary function, so

> why take a chance that a software developer has tried to expand the concept

> using a personal choice that is beyond a clear definition.

>

> I've commented elsewhere that I use this statistic even for nonlinear

> models in my own software, since I think one should do better than the

> mean for a model, but other workers shy away from using it for nonlinear

> models because there may be false interpretation based on its use for

> linear models.

>

> JN

>

>

> On 2018-09-27 06:56 AM, Patrick Barrie wrote:

> > I have a query on the R-squared correlation coefficient for linear

> > regression through the origin.

> >

> > The general expression for R-squared in regression (whether linear or

> > non-linear) is

> > R-squared = 1 - sum(y-ypredicted)^2 / sum(y-ybar)^2

> >

> > However, the lm function within R does not seem to use this expression

> > when the intercept is constrained to be zero. It gives results different

> > to Excel and other data analysis packages.

> >

> > As an example (using built-in cars dataframe):

> >> cars.lm=lm(dist ~ 0+speed, data=cars) # linear regression through

> > origin

> >> summary(cars.lm)$r.squared # report R-squared [1] 0.8962893 >

> > 1-deviance(cars.lm)/sum((cars$dist-mean(cars$dist))^2) # calculates

> > R-squared directly [1] 0.6018997 > # The latter corresponds to the value

> > reported by Excel (and other data analysis packages) > > # Note that we

> > expect R-squared to be smaller for linear regression through the origin

> > > # than for linear regression without a constraint (which is 0.6511 in

> > this example)

> >

> > Does anyone know what R is doing in this case? Is there an option to get

> > R to return what I termed the "general" expression for R-squared? The

> > adjusted R-squared value is also affected. [Other parameters all seem

> > correct.]

> >

> > Thanks for any help on this issue,

> >

> > Patrick

> >

> > P.S. I believe old versions of Excel (before 2003) also had this issue.

> >

>

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