In the simplest case of a simple linear regression what you wrote holds true: the explained variance is simply a sum of variance explained by the model and the residual variability that cannot be explained, and that would always lie between 0 and 1. e.g. here: https://online.stat.psu.edu/stat500/lesson/9/9.3

However, this would be quite hard to do for more complex models (even for a multivariate linear regression) thus a need for a more general definition like here: https://en.wikipedia.org/wiki/Coefficient_of_determination or here https://www.investopedia.com/terms/r/r-squared.asp. I can easily envision a situation where data has outliers (i.e. data is not clean enough to be used in modeling) that it'd render a model that performs worse than a base model of simply taking average as a prediction for each observation.

Cheers,
-Tom

On Thu, Aug 12, 2021 at 12:19 PM Samir K Mahajan <samirkmahajan1972@gmail.com> wrote:

Dear Christophe Pallier,  Reshama Saikh and Tromek Drabas, 


Thank you for your kind response.  Fair enough. I go with you R2 is not a square.  However, if you open any  book of econometrics,  it says R2 is  a ratio that lies between 0  and 1.  This is the constraint. It measures the proportion or percentage of the total variation in  response variable (Y)  explained by the regressors (Xs) in the model . Remaining proportion of variation in Y, if any,  is explained by the residual term(u) Now, sklearn.matrics. metrics.r2_score gives me a negative value lying on a linear scale (-5.763335245921777). This negative value breaks the constraint. I just want to highlight that. I think it needs to be corrected. Rest is up to you .

I find that  Reshama Saikh  is hurt by my email. I am really sorry for that. Please note I never undermine your  capabilities and initiatives. You are great people doing great jobs. I realise that I should have been more sensible. 

My regards to all of you.

Samir K Mahajan 








On Thu, Aug 12, 2021 at 12:02 PM Christophe Pallier <christophe@pallier.org> wrote:
Simple: despite its name R2 is not a square. Look up its definition.

On Wed, 11 Aug 2021, 21:17 Samir K Mahajan, <samirkmahajan1972@gmail.com> wrote:
Dear All,
I am amazed to find  negative  values of  sklearn.metrics.r2_score and sklearn.metrics.explained_variance_score in a model ( cross validation of OLS regression model) 
However, what amuses me more  is seeing you justifying   negative  'sklearn.metrics.r2_score ' in your documentation.  This does not make sense to me . Please justify to me how squared values are negative. 

Regards,
Samir K Mahajan. 

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