1. Find Correlation Coefficient from two Regression line equations X+2Y-5=0, 2X+3Y-8=0
Solution:
`x+2y-5=0`
`:.x+2y=5`
and `2x+3y-8=0`
`:.2x+3y=8`
`x+2y=5 ->(1)`
`2x+3y=8 ->(2)`
equation`(1) xx 2 =>2x+4y=10`
equation`(2) xx 1 =>2x+3y=8`
Substracting `=>y=2`
Putting `y=2` in equation`(1)`, we have
`x+2(2)=5`
`=>x=5-4`
`=>x=1`
`:.x=1" and "y=2`
`:. bar x = 1, bar y = 2`
Suppose `X+2Y-5=0` is regression equation of `y` on `x`
`=>1 x +2 y -5 = 0`
`=>2 y = -1 x +5`
`=>y = (-1)/(2) x +5/(2)`
`=>y = -0.5 x +2.5`
`:. byx = -0.5`
Suppose `2X+3Y-8=0` is regression equation of `x` on `y`
`=> 2 x +3 y -8 = 0`
`=> 2 x = -3 y +8`
`=> x = (-3)/(2) y +8/2`
`=> x = -1.5 y +4`
`:. bxy = -1.5`
`r = sqrt(byx * bxy)`
`=sqrt(-0.5 * -1.5)`
`=sqrt(0.75)`
`=-0.866`
This material is intended as a summary. Use your textbook for detail explanation.
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