Question

Out of the two regression lines x + 2y – 5 = 0 and 2x + 3y = 8, find the line of regression of y on x.

Answer 1

Given the lines of regression are

x + 2y – 5 = 0   ...(1)

and 2x + 3y = 8   ...(2)

Assume that (1) is the regression line of y on x

i.e., y = `(-1)/2x + 5/2`

`\implies` b_yx = `(-1)/2`

and line (2) is the regression line of x on y

i.e., x = `(-3)/2y + 4`

`\implies` b_xy = `(-3)/2`

Now b_yx · b_xy = `(-1)/2 xx (-3)/2 = 3/4 < 1`

Therefore, our assumption is correct and line (1)

i.e., x + 2y – 5 = 0 is the regression line of y on x.