Question

The equations of two lines of regression are 4x + 3y + 7 = 0 and 3x + 4y + 8 = 0. Find the mean value of x and y.

Answer 1

The two regression lines are:

4x + 3y + 7 = 0   ...(i)

3x + 4y + 8 = 0  ...(ii)

We solve these equations simultaneously because the point `(barx, bary)` is on both regression lines.

Multiplying equation (i) by 4 and equation (ii) by 3 and subtracting both equations, we get

16x + 12y + 28 = 0
  9x + 12y + 24 = 0
 –   –         –            
             7x + 4 = 0

`x = -4/7`

Putting the value of x into equation (i), we get

`4 xx (-4/7) + 3y + 7 = 0`

`\implies -16/7 + 7 + 3y = 0`

`\implies 3y = 16/7 - 7`

= `(16 - 49)/7`

= `-33/7`

`\implies y = -11/7`

Hence, `barx = -4/7` and `bary = -11/7`