Question
Download Solution PDFIf the correlation coefficient between x and y is 0.5 and the regression coefficient of y on x is 0.5, then the regression coefficient of x on y is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFthe correlation coefficient between x and y (rxy) = 0.5
the regression coefficient of y on x (byx) = 0.5
Then, the regression coefficient of x on y (bxy) = \({r^2 \over b_{yx}}\) = \({(0.5)^2 \over 0.5} = 0.5\)
The correlation coefficient between x and y (rxy) = \(\sqrt {{b_{xy}} × {b_{yx}}}\)
or, rxy2 = bxy × byx
or, bxy = \({r^2 \over b_{yx}}\)
Hence, the required value of the regression coefficient of x on y is 0.5
Last updated on Jul 8, 2025
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