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Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X^{2 }= 1680, ∑Y^{2} = 320 and ∑XY = 480.

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#### Solution

N = 20, ∑X = 80, ∑Y = 40, ∑X^{2 }= 1680, ∑Y^{2} = 320 and ∑XY = 480

`bar"X" = (sum"X")/"N" = 80/20` = 4

`bar"Y" - (sum"Y")/"N" = 40/20` = 2

b_{yx} = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`

= `(20(480) - (80)(40))/(20(1680) - (80)^2)`

= `(9600 - 3200)/(33600 - 6400)`

= `6400/27200`

= 0.235

= 0.24

Regression line of Y on X

`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`

Y − 2 = 0.24 (X − 4)

Y = 0.24X − 0.96 + 2

Y = 0.24X + 1.04

b_{xy} = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"Y"^2 - (sum"Y")^2)`

= `(20(480) - (80)(40))/(20(320) - (40)^2)`

= `(9600 - 3200)/(6400 - 1600)`

= `6400/4800`

= 1.33

Regression line of X on Y

`"X" - bar"X" = "b"_"xy"("Y" - bar"Y")`

X – 4 = 1.33 (Y – 2)

X = 1.33Y – 2.66 + 4

X = 1.33Y + 1.34

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