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प्रश्न
Identify the regression equations of X on Y and Y on X from the following equations :
2x + 3y = 6 and 5x + 7y – 12 = 0
उत्तर
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.
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∴ Y − 12 = `r.(σ_y)/(σ_x)("X" - 10)`
∴ Y − 12 = `0.6 xx 4/square ("X" - 10)`
∴ When x = 5
Y − 12 = `square(5 - 10)`
∴ Y − 12 = −4
∴ Y = `square`
