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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`
Solution
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`
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