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महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90, Σxy = 76 Find the regression equation of x on y

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प्रश्न

If n = 5, Σx = Σy = 20, Σx2 = Σy2 = 90, Σxy = 76 Find the regression equation of x on y

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उत्तर

Given, Σx = 20, Σy = 20, Σx2 = 90, Σy2 = 90, Σxy = 76, n = 5

Now,

`barx = (sumx)/"n" = 20/5` = 4

`bary = (sumy)/"n" = 20/5` = 4

bxy = `(sumxy - "n" bar(x)  bar(y))/(sum y^2 - "" bar(y)^2`

= `(76 - 5 xx 4 xx 4)/(90 - 5(4)^2`

= `(76 - 80)/(90 - 80)`

= – 0.4

The regression equation of X on Y is given by `("X" - barx) = "b"_(xy)  ("Y" - bary)`

∴ (X – 4) = – 0.4(Y – 4)

∴ X + 0.4Y = 5.6

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पाठ 2.3: Linear Regression - Q.4

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