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Choose the correct option.
If the regression line of x on y is, 9x + 3y - 46 = 0 and y on x is, 3x + 12y - 7 = 0, then the…
If the regression line of $x$ on $y$ is, $9x + 3y - 46 = 0$ and $y$ on $x$ is, $3x + 12y - 7 = 0$, then the correlation coefficient ‘r’ is equal to:
- (a)$-\frac{1}{12}$
- (b)$\frac{1}{12}$
- (c)$-\frac{1}{2\sqrt{3}}$
- (d)$\frac{1}{2\sqrt{3}}$
Answer
Answer
Correct option: (c)
Answer: (c) $-\frac{1}{2\sqrt{3}}$
$x$ on $y$: $x = -\frac13 y + \frac{46}{9}$, so $b_{xy} = -\frac13$; $y$ on $x$: $y = -\frac14 x + \frac{7}{12}$, so $b_{yx} = -\frac14$.
$r^2 = b_{xy}b_{yx} = \frac{1}{12}$, and both coefficients are negative, so $r = -\frac{1}{2\sqrt3}$.