Question

From the two regression equations y = 4x – 5 and 3x = 2y + 5, find `bar x and bar y`.

Answer 1

Given two regression equations are

y = 4x - 5

i.e., – 4x + y = –5      …(i)

and 3x = 2y + 5

i.e., 3x – 2y = 5        …(ii)

By (i) × 2 + (ii), we get

- 8x + 2y = - 10
+ 3x - 2y = 5   
- 5x = - 5

∴ x = 1

Substituting x = 1 in (i)

-4(1) + y = - 5

∴ y = 4 - 5 = - 1

Since the point of intersection of two regression lines is `(bar x, bar y)`,

`bar x = 1 and bar y = - 1`