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Question
The equations of the two lines of regression are 6x + y − 31 = 0 and 3x + 2y – 26 = 0. Find the value of the correlation coefficient
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Solution
r = `+- sqrt("b"_(xy) * "b"_(yx))`
= `+- sqrt((-1)/6 xx (-3)/2)`
= `+- 1/2`
= `+- 0.5`
Since the values of bxy and byx are negative,
r is also negative.
∴ r = – 0.5
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byx = `square/square`
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∴ Regression equation of y on x is `square`
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Mean of y = 28
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Regression coefficient of x on y = – 0.3
a. r = `square`
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∴ y = `square`
c. When y = 25,
`x - square = square (25 - square)`
∴ x = `square`
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`sigma_y` = 3
r = 0.5
byx = `square`
bxy = `square`
when x = 10,
`y - square = square (10 - square)`
∴ y = `square`
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