Question

The equations of the two regression lines are 2x + 3g - 6 = 0 and 5x + 7g - 12 = 0
Find: (a) Correlation coefficient. 
        (b) `sigma_x/sigma_y`

Answer 1

 Equations of regression lines are 2x + 3g - 6 = 0 and 5x + 7g - 12 = 0 
i.e. `y = (-2)/3x - 2` and `y = (-5)/7x + 12/7`

`|(-2)/3| = 2/3  "and"  |(-5)/7| = 5/7`

`|(-2)/3| < |(-5)/7|`

∴ `b_(xy) = (-2)/3`

`1/b_(yx) = (-5)/7`

`b_(yx) = (-7)/5`

(a) Correlation coefficient 

`r = sqrt(b_(xy).b_(yx))`

= `sqrt((-2)/3 xx (-7)/5)`

= `sqrt(14/15) = ±sqrt(0.9333)`

`therefore r = -0.9661`                  .......(∵ `b_(xy).b_(xy) < 0`)

(b) `b_(xy) = rσ_x/σ_y`

`(-2)/3 = (-0.9661)σ_x/σ_y`

`therefore σ_x/σ_y = (-2/3) xx (1/-0.9661)`

`σ_x/σ_y = 0.6901`