Question

For a certain bivariate data of a group of 10 students, the following information gives the internal marks obtained in English (X) and Hindi (Y):

	X	Y
Mean	13	17
Standard Deviation	3	2

If r = 0.6, Estimate x when y = 16 and y when x = 10

Answer 1

Given, `barx` = 13, `bary` = 17, `sigma_x` = 3, `sigma_y` = 2, r = 0.6

b_yx = `"r" sigma_y/sigma_x = 0.6 xx 2/3` = 0.4

b_xy = `"r" sigma_x/sigma_y = 0.6 xx 3/2` = 0.9

The regression equation of X on Y is given by `("X" - barx) = "b"_(xy)  ("Y" - bary)`

(X – 13) = 0.9(Y – 17)

X – 13 = 0.9Y – 15.3

X = 0.9Y – 15.3 + 13

X = – 2.3 + 0.9Y    ......(i)

For Y = 16, from equation (i) we get

X = – 2.3 + (0.9)(16)

= – 2.3 + 14.4

= 12.1

The regression equation of Y on X is given by `("Y" - bary) = "b"_(yx)  ("X" - barx)`

(Y – 17) = 0.4(X – 13)

Y – 17 = 0.4X – 5.2

Y = 0.4X – 5.2 + 17

Y = 11.8 + 0.4X    .....(ii)

For X = 10, from equation (ii) we get

Y = 11.8 + 0.4(10)

= 11.8 + 4

= 15.8