Question

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If two regression lines are x + 3y = 7 and 2x + 5y = 12 then
regression coefficient of Y and X is
(a)1/3
(b)-1/3
(c)5/2
(d)-5/2
a
Ob
OC
Od​

Answer 1

We need to recall the following definition of a regression coefficient.

For a regression line $ax+by=c$

• The regression coefficient of $y$ on $x$ : $b_{yx}=-\frac{a}{b}$
• The regression coefficient of $x$ on $y$ : $b_{xy}=-\frac{b}{a}$

Given:

The equations of regression lines are:

$x+3y=7$                 .......$(1)$

$2x+5y=12$             ........$(2)$

From the equation $(1)$, we get

$3y=-x+7$

 $y=\frac{-1}{3} x+\frac{7}{3}$

So, the regression coefficient of $y$ on $x$ is,

$b_{yx}=\frac{-1}{3}$

From the equation $(2)$, we get

$2x=-5y+12$

 $x=\frac{-5}{2} y+6$

So, the regression coefficient of $x$ on $y$ is,

$b_{xy}=\frac{-2}{5}$

Hence, the correct option is (b) $-1/3$ .