Maharashtra State BoardHSC Commerce 12th Board Exam
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The equations of two regression lines are2x + 3y − 6 = 0and 2x + 2y − 12 = 0 Find Correlation coefficient σXσY - Mathematics and Statistics

Sum

The equations of two regression lines are
2x + 3y − 6 = 0
and 2x + 2y − 12 = 0 Find 

  1. Correlation coefficient
  2. `sigma_"X"/sigma_"Y"`
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Solution

The given regression equations are
2x + 3y – 6 = 0 and 2x + 2y – 12 = 0

(i) Let 2x + 3y – 6 = 0 be the regression equation of Y on X

∴ The equation becomes 3Y = – 2X + 6

i.e., Y = `(-2)/3 "X" + 6/3`

Comparing it with Y = bYX X + a, we get

`"b"_"YX" = - 2/3`

Now, the other equation, i.e., 2x + 2y – 12 = 0 is the regression equation of X on Y.

∴ The equation becomes 2X = –2Y + 12

i.e., X = `- 2/2 "Y" + 12/2`

Comparing it with X = bXY Y + a' we get

`"b"_"XY" = - 2/2 = - 1`

∴ r = `+-sqrt("b"_"XY" * "b"_"YX")`

`= +- sqrt(-1 * (- 2/3)) = +-sqrt(2/3) = +- 0.82`

since bXY and bYX are negative,

r is also negative.

∴ r = - 0.82

(ii) `"b"_"XY" = "r" sigma_"X"/sigma_"Y"`

∴ `- 1 = - 0.82 xx sigma_"X"/sigma_"Y"`

∴ `sigma_"X"/sigma_"Y" = (- 1)/- 0.82`

∴ `sigma_"X"/sigma_"Y"` = 1.22

Concept: Properties of Regression Coefficients
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