Discussion
The regression equation of Y on X is given by \(y = 2 - 1.2x\) and that of X on Y is given by \(x = -1 - 0.3y\). Hence the correlation coefficient between X and Y is :
Answer: C
The correlation coefficient is -0.6.
The regression coefficients are \(b_{yx} = -1.2\) and \(b_{xy} = -0.3\), and \(r^{2} = b_{yx}b_{xy}\):
\[ r^{2} = (-1.2)(-0.3) = 0.36, \quad |r| = 0.6 \]
\(r\) has the same sign as the two regression coefficients, which are both negative, so \(r = -0.6\).
0.36 is \(r^{2}\), not \(r\), and +0.6 has the wrong sign.
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