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Question
The equations of two regression lines are
2x + 3y − 6 = 0
and 3x + 2y − 12 = 0 Find
- Correlation coefficient
- `sigma_"X"/sigma_"Y"`
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Solution
The given regression equations are
2x + 3y – 6 = 0 and 3x + 2y − 12 = 0
(i) 2x + 3y = 6
3y = – 2x + 6
`y = (– 2)/3x + 2`
`b_( yx) = (-2)/3`
3x + 2y = 12
3x = – 2y = 12
`x = (-2)/3y + 4`
`b_(xy) = (-2)/3`
`b_( yx).b_(xy) = (-2)/3 xx (-2)/3 = 4/9 ∈ [0, 1]`
∴ Our assumption is correct.
∴ `r^2 = b_( yx).b_(xy)`
`r^2 = 4/9`
`r = ±2/3`
Since `b_( yx)` and `b_(xy)` are negative ∴ r =`(-2)/3`
(ii) `b_(xy) = (r . sigma_y)/sigma_x`
`(-2)/3 = (-2)/3 . sigma_x/sigma_y`
∴ `sigma_x/sigma_y = 1`
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byx = `square/square`
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Mean of y = 20
`sigma_x` = 4
`sigma_y` = 3
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bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
