r2_score returns r correlation coefficient not R2 coefficient of determination

[lkettle]

r2_score returns r correlation coefficient not r2 coefficient of determination.

Your documentation indicates in
http://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html

that r2_score can return negative results with examples. This means you are actually producing the r , or correlation coefficient, indicating negative and positive correlation.

an R2 is between 0-1 and is never negative.

[jnothman]

You're incorrect that it is the correlation coefficient. In the doctest example, r2_score([1,2,3], [3,2,1]) is calculated as -3. The correlation coefficient would be -1.

Notes in the API docs you cite explicitly contradict your assertions:

Unlike most other scores, R^2 score may be negative (it need not actually be the square of a quantity R).

See Wikipedia

Important cases where the computational definition of R2 can yield negative values, depending on the definition used, arise where the predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data, and where linear regression is conducted without including an intercept. Additionally, negative values of R2 may occur when fitting non-linear functions to data

Related: #5570

[WalidGharianiEAGLE]

Why r2_score is returning this result ?

print(r2_score([1,2,3],[4,5,7]))
-16.0