Question

The two lines of regressions are 4x + 2y- 3 = 0 and 3x + 6y + 5 =0. Find the correlation co-efficient between x and y.

Answer 1

4x + 2y- 3 = 0

2y = -4x + 3

`y = -2x + 3/2`

`b_1  = -2`

and

3x + 6y + 5 =0

6y = -3x - 5

`y = -1/2x- 5/6`

`b_2 = -1/2`

`|b_2| < |b_1|`

`b_(yx) = -1/2`

`:. b_"xy" = 1/b_1 = -1/2`

`r= +- sqrt(b_"xy" xx b_"yx")`

`= - sqrt((-1/2) (-1/2))`

`r = -1/2`