R-squared from a strong negative correlation

Question

A simple regression has a correlation of r = -0.9 between x and y. What is the model's R-squared?

Accepted Answer

Square the correlation: R^2 = r^2 = (-0.9)^2 = 0.81. The minus sign disappears when you square, which is the whole reason R-squared cannot tell positive from negative relationships. A correlation of -0.9 and one of +0.9 both produce the same R^2 = 0.81: the model explains about 81\% of the variation in y either way. So direction and strength are two separate facts. The correlation (-0.9) holds both: strong, and negative. R-squared (0.81) keeps only the strength. If someone hands you an R-squared and asks for the sign of the relationship, you must look elsewhere (the slope, the correlation, or…

R-squared from a strong negative correlation

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