Question

For the lines of regression 4x – 2y = 4 and 2x – 3y + 6 = 0, find the mean of ‘x’ and the mean of ‘y’.

Answer 1

Given: Lines of regression are,

4x – 2y = 4   ...(i)

And 2x – 3y + 6 = 0

⇒ 2x – 3y = – 6   ...(ii)

Multiplying equation (ii) by 2 and then subtracting equation (i) from it,

  4x – 6y = – 12
  4x – 2y = 4
–     +      –         
       – 4y = – 16
⇒ `y = 16/4`

⇒ y = 4

Putting y = 4 in equation (i), we get 4x – 2 × 4 = 4

⇒ 4x = 4 + 8

⇒ 4x = 12

⇒ `x = 12/4`

⇒ x = 3

∴ `barx = 3` and `bary = 4`