Recovering the correlation from R-squared and slope sign

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In a simple regression with one predictor, the report says R^2 = 0.49 and notes that the slope is positive. What is the correlation between x and y?

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In a simple (one-predictor) regression there is a tidy link: R-squared is just the correlation squared, R^2 = r^2. So to get the correlation back, take the square root: r = \pm\sqrt{R^2} = \pm\sqrt{0.49} = \pm 0.7. The square root leaves two candidates, +0.7 and -0.7, because squaring erased the sign. That is where the extra clue comes in: the correlation always carries the same sign as the slope. The slope here is positive, so r = +0.7. This is the key subtlety, R-squared measures strength but throws away direction; you need the slope's sign (or the sign of the correlation itself) to recover…

Recovering the correlation from R-squared and slope sign

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