A) \[-\frac{2}{3}\]
B) \[\frac{2}{7}\]
C) \[\frac{4}{9}\]
D) none of these
Correct Answer: B
Solution :
Let us assume that line of regression of\[x\] on \[y\]is \[2x-7y+6=0\] or \[2x=7y-6\] ?(i) and line of regression of y on \[x\]is \[7x-2y+1=0\] or \[2y=7x+1\] ?(ii) From Eqs. (i) and (ii) \[{{b}_{xy}}=\frac{7}{2}\]and \[{{b}_{yx}}=\frac{7}{2}\] Now \[\sqrt{{{b}_{xy}}.{{b}_{yx}}}=\sqrt{\frac{7}{2}.\frac{7}{2}}\] \[\Rightarrow \] \[r=\frac{7}{2}>1\] \[\therefore \] Our assumption is wrong. \[\Rightarrow \]Eq. (i) is of \[y\]on \[x\]and Eq. (ii) is of\[x\] on y \[\therefore \] \[r=\sqrt{\frac{2}{7}.\frac{2}{7}}=\frac{2}{7}\] Note: The regression coefficient does not depend upon the change of origin, but depend only change of scale.
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