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प्रश्न
If the regression line of x on y is, 9x + 3y − 46 = 0 and y on x is, 3x + 12y − 7 = 0, then the correlation coefficient ‘r’ is equal to:
विकल्प
`(-1)/12`
`1/12`
`(-1)/(2sqrt3)`
`1/(2sqrt3)`
उत्तर
`(-1)/(2sqrt3)`
Explanation:
Given lines of regression are:
9x + 3y − 46 = 0 ....(x on y)
9x = − 3y + 46
⇒ x = `(-3)/9"y" + 46/9`
⇒ x = `(-1)/3"y" + 46/9`
∴ bxy = `(-1)/3`
and 3x + 12y − 7 = 0 ........(y on x)
⇒ 12y = − 3x + 7
⇒ y = `(-3)/12"x" + 7/12`
⇒ y = `(-1)/4"x" + 7/12`
∴ byx = `(-1)/4`
Now, r = `sqrt("b"_"xy". "b"_"yx")`
= `sqrt(((-1)/3)((-1)/4))`
= `1/sqrt12`
⇒ r = `1/(2sqrt3)`
∴ r = `(-1)/(2sqrt3)` ......(Since bxy and byx are negative ∴ r is negative)
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