Why am I seeing a negative R^2 value?

R^2 is defined as:  

R^2 = 1 - mean(e_1^2)/var(y_1)

where mean(e_1^2) is the mean of the squares of the residuals, and var(y_1) is the variance of the dependent variable that is being regressed. It isn't actually the square of any quantity!

R^2 can take values between 1 and -Infinity, and it will be negative whenever the residuals are larger than the residuals would be for the model y_1 ~ m.

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  • 0
    James Rothman

    Is not mean(e_1^2) <= to the variance of e? If so it is possible to show that it has to be less than var(y_1) and that R^2 has to be positive.

  • 0
    Tobias Cunningham

    You can’t do it

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