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Question
Identify the regression equations of x on y and y on x from the following equations, 2x + 3y = 6 and 5x + 7y − 12 = 0
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Solution
Given two equations are
2x + 3y = 6 and 5x + 7y – 12 = 0
Let 2x + 3y = 6 be the regression equation of Y on X.
∴ The equation becomes 2X + 3Y = 6
i.e., 3Y = 6 - 2X
i.e., Y = `(-2)/3"X" + 6/3`
Comparing it with Y = bYX X + a, we get
`"b"_"YX" = - 2/3`
Now, other equation 5x + 7y – 12 = 0 be the regression equation of X on Y.
∴ The equation becomes 5X + 7Y – 12 = 0
i.e., 5X = - 7Y + 12
∴ X = `- 7/5 "Y" + 12/5`
Comparing it with X = bXY Y + a', we get
`"b"_"XY" = - 7/5`
Now, `"b"_"XY" * "b"_"YX" = - 7/5 xx (- 2/3) = 14/15 < 1`
∴ Our assumption of regression equation is true.
∴ 2x + 3y = 6 is the regression equation of Y on X, and 5x + 7y – 12 = 0 is the regression equation of X on Y.
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