[jira] [Created] (SPARK-12331) R^2 for regression through the origin

["Imran Younus (JIRA)" <ji...@apache.org>]

Imran Younus created SPARK-12331:
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             Summary: R^2 for regression through the origin
                 Key: SPARK-12331
                 URL: https://issues.apache.org/jira/browse/SPARK-12331
             Project: Spark
          Issue Type: Improvement
          Components: ML
            Reporter: Imran Younus
            Priority: Minor


The value of R^2 (coefficient of determination) obtained from LinearRegressionModel is not consistent with R and statsmodels when the fitIntercept is false i.e., regression through the origin. In this case, both R and statsmodels use the definition of R^2 given by eq(4') in the following review paper:

https://online.stat.psu.edu/~ajw13/stat501/SpecialTopics/Reg_thru_origin.pdf

Here is the definition from this paper:
R^2 = \sum(\hat(y)_i^2)/\sum(y_i^2)

The paper also describes why this should be the case. I've double checked that the value of R^2 from statsmodels and R are consistent with this definition. On the other hand, scikit-learn doesn't use the above definition. I would recommend using the above definition in Spark.




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