Answer to Question #157828 in Statistics and Probability for Pushpak Krishna Jadhav

Question #157828

a partially destroyed laboratory data, only the equations giving the two lines of regression of x on y and y on x are available and are respectively, 7x-16y + 9 = 0, 5y - 4x-3 = 0. Calculate


the coefficient of correlation, x and y.


1
Expert's answer
2021-01-26T01:06:47-0500

The given two equation are 7x16y+9=07x-16y+9=0 ......(1) and 5y4x3=05y-4x-3=0 ........(2)

Suppose 7x16y+9=07x-16y+9=0 is regression equation of yy on xx

    7x16y+9=0\implies 7x-16y+9=0

    16y=7x+9\implies 16y=7x+9

    y=716x+916\implies y=\frac{7}{16}x+\frac{9}{16}

    y=0.4375x+0.5625\implies y=0.4375 x+0.5625

byx=0.4375\therefore byx=0.4375

Again suppose 5y4x3=05y-4x-3=0 is regression equation of xx on yy

    5y4x3=0\implies 5y-4x-3=0

    4x=5y3\implies 4x=5y-3

    x=54y34\implies x=\frac{5}{4}y-\frac{3}{4}

    x=1.25y0.75\implies x=1.25y-0.75

byx=1.25\therefore byx=1.25

So the coefficient of correlation xx and yy is ,

r=+byx.bxyr=+\sqrt{byx.bxy} [As byx>0byx>0 and bxy>0]bxy>0]

r=716.54=0.546875=0.7395\therefore r=\sqrt{\frac{7}{16}.\frac{5}{4}}=\sqrt{0.546875}=0.7395




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