Question

Use table below to analyze correlation and to develop regression equations describing the relationships between person’s height and weight. Make separate regression lines for men and women.

gender	height	weight
0	72	155
0	67	145
0	65	125
1	67	120
1	63	105
1	54	120
1	66	125
1	64	125
0	72	160
0	66	133
0	66	175
0	71	205
0	71	175
1	57	82
1	66	125
1	67	133
0	70	175
0	73	163
1	68	133
0	72	180
1	65	107
1	70	170
1	64	110
1	64	140
1	63	110
1	60	110
1	69	125
1	65	120
1	67	180
0	67	120
0	68	140
0	65	130
1	62	122
1	66	114
1	65	115
1	63	125
0	73	195
0	69	135
0	70	145
0	72	170
0	73	172
0	69	168
0	68	155
0	71	185
0	71	175
0	68	158
0	69	185
0	67	146
0	66	135
0	67	150
0	72	160
0	68	155
0	75	230
0	68	149
0	73	240
0	72	170
0	72	198
0	72	163
0	72	230
0	74	170
0	68	151
0	73	220
0	68	145
0	70	130
0	72	160
0	70	210
0	67	145
0	67	185
0	71	237
0	72	205
0	73	147
0	68	170
0	72	181
0	68	150
0	67	150
0	70	200
0	71	175
0	70	155
0	67	167
1	58	100
1	56	100

Answer 1

Soln

i)

Assuming for Males, Gender = 0

	height (Y)	weight (X)	XY	Y2	X2
	72	155	11160	5184	24025
	67	145	9715	4489	21025
	65	125	8125	4225	15625
	72	160	11520	5184	25600
	66	133	8778	4356	17689
	66	175	11550	4356	30625
	71	205	14555	5041	42025
	71	175	12425	5041	30625
	70	175	12250	4900	30625
	73	163	11899	5329	26569
	72	180	12960	5184	32400
	67	120	8040	4489	14400
	68	140	9520	4624	19600
	65	130	8450	4225	16900
	73	195	14235	5329	38025
	69	135	9315	4761	18225
	70	145	10150	4900	21025
	72	170	12240	5184	28900
	73	172	12556	5329	29584
	69	168	11592	4761	28224
	68	155	10540	4624	24025
	71	185	13135	5041	34225
	71	175	12425	5041	30625
	68	158	10744	4624	24964
	69	185	12765	4761	34225
	67	146	9782	4489	21316
	66	135	8910	4356	18225
	67	150	10050	4489	22500
	72	160	11520	5184	25600
	68	155	10540	4624	24025
	75	230	17250	5625	52900
	68	149	10132	4624	22201
	73	240	17520	5329	57600
	72	170	12240	5184	28900
	72	198	14256	5184	39204
	72	163	11736	5184	26569
	72	230	16560	5184	52900
	74	170	12580	5476	28900
	68	151	10268	4624	22801
	73	220	16060	5329	48400
	68	145	9860	4624	21025
	70	130	9100	4900	16900
	72	160	11520	5184	25600
	70	210	14700	4900	44100
	67	145	9715	4489	21025
	67	185	12395	4489	34225
	71	237	16827	5041	56169
	72	205	14760	5184	42025
	73	147	10731	5329	21609
	68	170	11560	4624	28900
	72	181	13032	5184	32761
	68	150	10200	4624	22500
	67	150	10050	4489	22500
	70	200	14000	4900	40000
	71	175	12425	5041	30625
	70	155	10850	4900	24025
	67	167	11189	4489	27889
Total	3980	9603	672962	278258	1663699

Using the above values and formula, we get:

r = 0.603

The magnitude of r indicates moderate correlation between height and weight for males and the positive sign indicates direct relationship ie as height increases, weight also increases and vice versa

Let the regression equation be: Y = a + bX

Where

Slope(b) = {n*∑XY - ∑X *∑Y}/{n*∑X² – (∑X)² } = 0.05

and a = ∑Y/n – b*∑X/n = 60.87

Hence, Height = 60.87 + 0.05 Weight

ii)

Females:

gender	height (Y)	weight (X)	XY	Y2	X2
1	67	120	8040	4489	14400
1	63	105	6615	3969	11025
1	54	120	6480	2916	14400
1	66	125	8250	4356	15625
1	64	125	8000	4096	15625
1	57	82	4674	3249	6724
1	66	125	8250	4356	15625
1	67	133	8911	4489	17689
1	68	133	9044	4624	17689
1	65	107	6955	4225	11449
1	70	170	11900	4900	28900
1	64	110	7040	4096	12100
1	64	140	8960	4096	19600
1	63	110	6930	3969	12100
1	60	110	6600	3600	12100
1	69	125	8625	4761	15625
1	65	120	7800	4225	14400
1	67	180	12060	4489	32400
1	62	122	7564	3844	14884
1	66	114	7524	4356	12996
1	65	115	7475	4225	13225
1	63	125	7875	3969	15625
1	58	100	5800	3364	10000
1	56	100	5600	3136	10000
Total	1529	2916	186972	97799	364206

Using the above values and formula, we get:

r = 0.610

The magnitude of r indicates moderate correlation between height and weight for females and the positive sign indicates direct relationship ie as height increases, weight also increases and vice versa

Let the regression equation be: Y = a + bX

Where

Slope(b) = {n*∑XY - ∑X *∑Y}/{n*∑X² – (∑X)² } = 0.12

and a = ∑Y/n – b*∑X/n = 49.02

Hence, Height = 49.02 + 0.12 Weight