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Identify the Regression Equations of X on Y and Y on X from the Following Equations : 2x + 3y = 6 and 5x + 7y – 12 = 0 - Mathematics and Statistics

Sum

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

Let the regression eqn. of y on x is  

2x + 3y = 6 

3y = -2x + 6

y = `(-2)/3x + 6`

From 5x + 7y - 12 = 0

7y = -5x + 12

y = `(-5)/7 x + 12/7`

b2 = `(-5)/7`

Let b1 = `(-2)/3`

`therefore |b_1|<|b_2|`

`therefore b_1 = b_yx = (-2)/3`

`therefore b_xy = 1/b_2 = (-7)/5`

2x + 3y = 6 is regression line of y on x

5x + 7y - 12 = 0 is regression line of x on y.

Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
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