Discussion
Given the two regression lines estimated from given data as under :
\(Y = 4 + 0.4X\)
\(X = -2 + 0.9Y\)
Then coefficient of correlation between X and Y will be
Answer: C
The coefficient of correlation is 0.6, the third option. The slope of the regression of Y on X is \(b_{yx} = 0.4\) and the slope of the regression of X on Y is \(b_{xy} = 0.9\), and the coefficient of correlation is the geometric mean of the two slopes:
\[ r = \sqrt{b_{yx} \, b_{xy}} \]
\[ r = \sqrt{0.4 \times 0.9} = \sqrt{0.36} \]
\[ r = 0.6 \]
The sign is positive because both slopes are positive. The values 0.4 and 0.8 are not the root of the product, and 0.5 would need a product of 0.25.
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