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Question
Find the equation of the regression line of Y on X, if the observations (Xi, Yi) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).
Solution
| X | Y | X2 | Y2 | XY |
| 1 | 4 | 1 | 16 | 4 |
| 2 | 8 | 4 | 64 | 14 |
| 3 | 2 | 9 | 4 | 6 |
| 4 | 12 | 16 | 144 | 48 |
| 5 | 10 | 25 | 100 | 50 |
| 6 | 14 | 36 | 196 | 84 |
| 7 | 16 | 49 | 256 | 112 |
| 8 | 6 | 64 | 36 | 48 |
| 9 | 18 | 81 | 324 | 162 |
| 45 | 90 | 285 | 1140 | 530 |
N = 9, ΣX = 45, ΣY = 90, ΣX2 = 285, ΣY2 = 1140, ΣXY = 530, `bar"X" = (sum"X")/"N" = 45/9` = 5, `bar"Y" = (sum"Y")/"N" = 90/9` = 10
byx = `("N"sum"XY" - (sum"X")(sum"Y"))/("N"sum"X"^2 - (sum"X")^2)`
= `(9(530) - (45)(90))/(9(285) - (45)^2)`
= `(4770 - 4050)/(2565 - 2025)`
= `720/540`
= 1.33
Regression line of Y on X:
`"Y" - bar"Y" = "b"_"yx"("X" - bar"X")`
Y – 10 = 1.33 (X – 5)
Y = 1.33X – 6.65 + 10
Y = 1.33X + 3.35
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