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Question
Obtain the two regression lines from the following data N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480.
Solution
N = 20, ∑X = 80, ∑Y = 40, ∑X2 = 1680, ∑Y2 = 320 and ∑XY = 480
`bar"X" = (sum"X")/"N" = 80/20` = 4
`bar"Y" - (sum"Y")/"N" = 40/20` = 2
byx = `("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
bxy = `("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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