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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.
Solution
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`
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