Question

Find the equation of the regression line of Y on X, if the observations (X_i, Y_i) are the following (1, 4) (2, 8) (3, 2) (4, 12) (5, 10) (6, 14) (7, 16) (8, 6) (9, 18).

Answer 1

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

b_yx = `("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