if the correlation between X and Y is r 05 do X and Y share

if the correlation between X and Y is r =0.5, do X and Y share half of their variation in common? Why?

Solution

if the correlation between X and Y is r =0.5, do X and Y share half of their variation in common? Why?

No

r =0.5

r² =0.5*0.5=0.25   or 25%

X and Y share 25% of their variation in common.

The value of r² measures the variation in common not the value of r.