Question

It is given that $\overline{X}=10,\overline{Y}=90,{\sigma }_X=3,{\sigma }_Y=12$ and $r_{XY}=0.8$. The regression equation of $X$ on $Y$ is

• A. $Y=3.2X+58$
• B. $X=3.2Y+58$
• C. $X=-8+0.2Y$
• D. $Y=-8+0.2X$

Answer 1

Answer: (C)

$X=-8+0.2Y$

Regression equation of X on Y:

$X-\overline{X}=r_{XY}\frac{{\sigma }_X}{{\sigma }_Y}(Y-\overline{Y})$

Given that

$\overline{X}=10$

$\overline{Y}=90$

$r_{XY}=0.8$

${\sigma }_X=3$

${\sigma }_X=12$

$\therefore X=10+0.8\times \frac{3}{12}(Y-90)$

$\therefore X=0.2Y-8$