Question

The following data give the height in inches (X) and the weight in lb. (Y) of a random sample of 10 students from a large group of students of age 17 years:

X	61	68	68	64	65	70	63	62	64	67
Y	112	123	130	115	110	125	100	113	116	125

Estimate weight of the student of a height 69 inches.

Answer 1

Height (X)	Weight (Y)	dx = X − 65	dy = Y − 117	dx2	dy2	dxdy
61	112	− 4	− 5	16	25	20
68	123	3	6	9	36	18
68	130	3	13	9	169	39
64	115	− 1	− 2	1	4	2
65	110	0	− 7	0	49	0
70	125	5	8	25	64	40
63	100	− 2	− 17	4	289	34
62	113	− 3	− 4	9	16	12
64	116	− 1	− 1	1	1	1
67	125	2	8	4	64	16
652	1169	2	− 1	78	717	182

N = 10, ∑X = 652, ∑Y = 1169, ∑dx = 2, ∑dy = − 1, ∑dx² = 78, ∑dy² = 717, ∑dxdy = 182, `bar"X" = 652/10` = 65.2, `bar"Y" = 1169/10` = 116.9

b_yx = `("N"sum"dxdy" - (sum"dx")(sum"dy"))/("N"sum"dx"^2 - (sum"dx")^2)`

= `(10(182) - (2)(-1))/(10(78) - (2)^2)`

= `1822/776`

= 2.3479

Regression equation of Y on X

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

Y – 117 = 2.3479 (X – 65.2)

Y – 117 = 2.3479X – (2.3479)(65.2)

Y = 2.3479X – 153.08308 + 117

Y = 2.3479 – 36.08308

When the height X = 69 inches

Weight, Y = 2.3479(69) – 36.08308

= 162.0051 – 36.08308

= 125.92202

= 125.92 lb