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can anyone give me the proof that the RMS error for the regression of y on x will always be the square root of 1 minus the correlation of y on x, times the SD of y? I know the intuition behind it. like when the r value is equal to 1 the rmse is 0 cuz all points lie on a straight line, and when r is zero then the rmse is the same as the sd because there is no correlation between the x and v values. what I want is the algebraic proof of the relationship

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I know its too late, but if someone stumbles on this question here is the answer.

https://studylib.net/doc/8740342/proof-of-the-rms-error-of-regression-formula

Or

https://www.coursehero.com/file/7236053/hw3solutions/

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  • $\begingroup$ If these links go dead your answer will be useless. Can you edit it to include the proofs which the OP asked for? $\endgroup$
    – mdewey
    Commented Jan 20, 2019 at 15:22

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