If the correlation coefficient 'r' is 0.6 and the regression coefficient of x on y is 0.18, then the regression coefficient of y on x is:
2
The correlation coefficient \(r\) and the two regression coefficients are related by the identity:
\(r^2 = b_{xy} \cdot b_{yx}\)
Given: \(r = 0.6\) and \(b_{xy} = 0.18\) (regression coefficient of x on y).
Substituting into the identity:
\((0.6)^2 = 0.18 \times b_{yx}\)
\(0.36 = 0.18 \times b_{yx}\)
\(b_{yx} = \dfrac{0.36}{0.18} = 2\)
Therefore the regression coefficient of y on x is 2, which matches option 4.
Note: The formula \(b_{yx} = r \times b_{xy}\) is incorrect. The correct relation between r and the two regression coefficients is \(r = \pm\sqrt{b_{xy} \cdot b_{yx}}\).
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