A) \[\frac{2}{3}\]
B) \[-9\]
C) \[~-4\]
D) none of these
Correct Answer: A
Solution :
Let us assume line of regression y on X is \[x+4y=3\]or \[4y=-x+3\] ?(i) and X on Y is \[3x+y=5\] or\[~3x=-\text{ }y+5\] ...(ii) \[\Rightarrow \] \[{{b}_{YX}}=-\frac{1}{4}\]and \[{{b}_{XY}}=-\frac{1}{3}\] Now, \[r=-\sqrt{\left( -\frac{1}{4} \right)\left( -\frac{1}{3} \right)}=-\frac{1}{\sqrt{12}}>-1\] \[\therefore \] Our assumption is true. Since, \[y=3\]is given, we have to find the value of \[x,\] now we take Eq. (ii) \[3x=-3+5\Rightarrow x=\frac{2}{3}\] Note: If two regression lines are given, then we assume any of y on x and x on y. If the square root of the product of regression coefficient lies between\[-1\]to 1, then the our assumption is true, otherwise it is opposite.
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