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:

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KollegeApply · Accepted Answer

(-1)/(2sqrt3) Explanation: Given lines of regression are: 9x + 3y − 46 = 0 ....(x on y) 9x = − 3y + 46 $\Rightarrow$ x = (-3)/9"y" + $\frac{46}{9}$ $\Rightarrow$ x = (-1)/3"y" + $\frac{46}{9}$ $\therefore$ bxy = (-1)/3 and 3x + 12y − 7 = 0 ........(y on x) $\Rightarrow$ 12y = − 3x + 7 $\Rightarrow$ y = (-3)/12"x" + $\frac{7}{12}$ $\Rightarrow$ y = (-1)/4"x" + $\frac{7}{12}$ $\therefore$ byx = (-1)/4 Now, r = sqrt("b"_"xy". "b"_"yx") = sqrt(((-1)/3)((-1)/4)) = 1/sqrt12 $\Rightarrow$ r = 1/(2sqrt3) $\therefore$ r = (-1)/(2sqrt3) ......(Since bxy and byx are negative $\therefore$ r is negative)

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