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in simple linear regression

R-squared is equal to the squared correlation coefficient between the actual y and the predicted y (i.e. 𝑦 hat )

how to prove this relationship?



marked as duplicate by gung regression Dec 21 '15 at 14:08

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.


The usual way of interpreting the coefficient of determination R^{2} is to see it as the percentage of the variation of the dependent variable y (Var(y)) can be explained by our model.

For the proof we have to know the following (taken from OLS theory and general statistics):


Proof for the relationship between R2 and correlation coefficient

I hope this answer clears your doubt.

  • 2
    $\begingroup$ +1. Welcome to our site, Dinesh. You would likely find it easier to write mathematical expressions (and we would find them easier to read) using the built-in $\TeX$ markup: just enclose them between dollar signs \$. Further help is available.. $\endgroup$ – whuber Dec 21 '15 at 13:07
  • $\begingroup$ @Dinesh, can you please explain why Cov(y_hat, e)=0 ? $\endgroup$ – Mvkt Jul 10 '18 at 1:17

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