Interview Question: Fitness Test

Sample Question #210 (statistics – regressions)

What does R2 from a regression measure? Can it ever be negative?

How is R2 calculated?

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One Response to Interview Question: Fitness Test

  1. Brett says:

    ANSWER
     
    R2 measures the regressions’s goodness of fit, i.e., how well the fitted line lines up with the actual data line. It can do this because it answers the question "how much of the total variation in the data can be explained by the regression?" It’s calculated by dividing explained variation (i.e., explained squared sum errors) by the total variation in the data.
     
    R2 can be negative, or even greater than 1, if the regression has restrictions. This is why in restricted least squares, it cannot be used at all. Also, it does not measure anything meaningful in most nonlinear regressions.
     

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