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Question

If the two lines of regression are x+4y=3 & 3x+y=15, then the value of 'x' for given value of y=3 is

A
-9
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B
4
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C
5
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D
None of these
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Solution

The correct option is B 4
Given lines are x+4y=3 (i)
& 3x+y=15 (ii)
We first check which of the line (i) & (ii) is line of regression y
on x and x on y. Let line x+4y=3 be the line of regression x on y, then
other be the line of regression y on x.
From (i) i.e. line of regression x on y we have x=4y+3
bxy=regression coefficient x on y=4 and 3x+y=15
y=3x+15
byx=regression coefficient y on x=-3
Now count r2=byxbxy=(4)(3)=12
|r|=23
which is not possible as 0r21. So our assumption is wrong
and line x+4y=3 is line of regression y on x & 3x+y=15 is line of
regression x on y.
3x+y=15
x=15y3
x=1533=4 (By putting y=3)

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