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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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