Question

It is difficult to determine a person’s body fat percentage accurately without immersing him or her in water. Researchers hoping to find ways to make a good estimate immersed 20 male subjects, then measured their waist shown in the table.

Waist (in.) Body Fat (%) 32 6 36 21 38 15 33 6 39 22 40 31 41 32 35 21 38 25 38 30 33 10 40 20 36 22 32 9 44 38 33 10 41 27 34 12 34 10 44 28

a) Treating waist as the explanatory variable, x, determine the estimates of ?1and ?0.

Answer 1

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	32	6	25.5025	189.06	69.4375
2	36	21	1.1025	1.56	-1.3125
3	38	15	0.9025	22.56	-4.5125
4	33	6	16.4025	189.06	55.6875
5	39	22	3.8025	5.06	4.3875
6	40	31	8.7025	126.56	33.1875
7	41	32	15.6025	150.06	48.3875
8	35	21	4.2025	1.56	-2.5625
9	38	25	0.9025	27.56	4.9875
10	38	30	0.9025	105.06	9.7375
11	33	10	16.4025	95.06	39.4875
12	40	20	8.7025	0.06	0.7375
13	36	22	1.1025	5.06	-2.3625
14	32	9	25.5025	115.56	54.2875
15	44	38	48.3025	333.06	126.8375
16	33	10	16.4025	95.06	39.4875
17	41	27	15.6025	52.56	28.6375
18	34	12	9.3025	60.06	23.6375
19	34	10	9.3025	95.06	29.7375
20	44	28	48.3025	68.06	57.3375
Total	741	395	276.9500	1737.75	615.2500
Mean	37.050	19.75	SSX	SSY	SXY
sample size :             n=		20
here                y̅	=	19.7500
x̅	=	37.0500
Sxx	=	'Σ(Xi-X̅)2=	276.950
Sxy                                         =		'Σ(Xi-X̅)(Yi-Y̅)=	615.250
slope=                      β̂1           =		Sxy/Sxx=	2.2215
intercept=              β̂0           =		y̅-β1x̅=	-62.5573