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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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Given:`n=8,sum(x_i-barx)=36,sum(y_i-bary)^2=40,sum(x_i-barx)(y_i-bary)=24`
∴ `b_(yx)=(sum(x_i-barx)(y_i-bary))/(sum(x_i-barx)^2)=square`
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