Question

Scroll the bottom arrows to see the whole table. if I make it any smaller you will not be able to see the numbers clearly: Is there a relationship between the relative-change* in weight and the relative-change* in Cholesterol level from screening to follow up for patients taking Drug A?

* Relative Change = (Follow up - Initial) / Initial

Patient ID	Drug	Stomach Pain	Sex	Age	Height	Systolic BP	Diastolic BP	Exercise	Coffee Consumption	Alcohol Consumption	Weight	Weight3	Cholesterol	Cholesterol3	Triglycerides	Triglycerides3	HDL	HDL3	LDL	LDL3
1	B	Yes	F	22	67.13	124	78	180	1	> 2	138	145	197	182	152	135	43	34	151.6	145.8
2	B	Yes	M	22	63	122	70	0	2	< 2	115	122	181	151	59	57	60	48	120.1	102.1
3	B	No	F	22	72	124	80	90	0	< 2	190	190	190	169	117	86	41	37	147.1	130.6
4	A	Yes	M	22	69	120	70	120	5	> 2	115	105	131	133	54	72	58	67	72.1	64.8
5	B	Yes	M	25	73	138	92	40	2	> 2	160	165	172	166	93	139	49	40	121.5	123.8
6	B	Yes	M	22	67.5	100	72	0	0	< 2	150	165	233	229	176	144	42	38	188.2	188.7
7	A	Yes	M	23	73	128	78	0	2	< 2	154	150	194	148	79	80	49	26	143.7	120.7
8	A	No	M	24	71.5	128	74	90	0	< 2	185	187	155	148	89	73	45	50	108.6	96.8
9	A	Yes	F	23	73.5	124	82	60	1	> 2	178	166	234	175	307	88	28	28	201.1	145.6
10	A	Yes	M	22	72.25	130	88	40	0	0	158	163	201	203	88	112	50	40	149.6	161.2
11	A	No	M	26	73	130	86	0	1	< 2	188	195	258	276	299	199	30	21	223.2	251.8
12	A	No	M	22	64.25	120	74	0	0	> 2	150	150	212	228	52	61	69	60	142.2	167
13	B	Yes	M	22	64.25	120	74	0	4	0	123	131	137	165	158	147	29	39	105.5	123.6
14	B	No	F	27	65	100	68	180	2	> 2	138	133	285	229	98	89	69	61	214.4	166.6
15	A	No	M	22	59	124	84	180	0	> 2	143	140	218	172	101	96	46	21	170.4	149.5
16	B	Yes	F	24	67.5	122	68	210	1	< 2	139	151	167	152	71	91	51	37	114.9	113.5
17	A	Yes	F	22	71.5	118	70	60	0	< 2	156	155	170	158	81	91	42	40	126.7	116.5
18	A	Yes	M	22	69	125	76	180	0	< 2	150	154	157	140	86	88	37	34	118.6	104.6
19	A	Yes	M	24	68	122	74	100	5	> 2	135	128	215	176	71	53	62	46	151.9	129.2
20	A	No	M	25	74	134	88	180	0	< 2	219	220	194	207	71	130	40	33	152.9	171.9
21	A	No	F	28	71	110	80	60	2	> 2	173	173	207	231	107	145	53	47	152.3	181.7
22	A	Yes	M	22	68.5	116	84	280	0	0	151	165	198	199	80	126	44	46	152.7	151
23	A	Yes	M	23	75.5	124	73	60	1	0	182	183	189	262	47	230	50	31	138.2	227.3
24	A	Yes	M	24	70	124	72	360	0	< 2	161	163	216	203	95	121	35	28	179.5	173.1
25	B	Yes	F	22	72	126	88	120	0	0	176	173	212	173	140	88	43	35	166.8	136.6
26	B	Yes	F	26	72.5	138	82	0	0	< 2	177	175	175	169	77	78	46	52	127.8	115.8
27	B	Yes	F	23	72	120	68	60	1	< 2	174	197	158	172	57	126	34	30	123.1	140
28	B	No	F	20	74	118	76	0	2	0	234	217	115	146	95	110	26	33	87.5	111.2
29	B	No	F	28	66	138	82	120	0	0	150	160	228	224	480	373	29	28	191.3	190
30	A	Yes	F	23	74	124	76	60	0	< 2	149	150	164	164	94	92	43	44	119.5	118.5
31	B	Yes	M	22	70	118	72	0	0	< 2	156	160	149	149	155	65	37	29	109.5	119
32	A	Yes	F	23	71.5	124	70	180	3	< 2	168	170	211	183	63	60	52	44	158	138
33	B	Yes	F	22	73	122	76	0	0	< 2	182	170	191	185	99	101	39	39	150.4	144.4
34	B	No	F	40	75	128	80	0	5	> 2	217	230	277	243	240	218	71	28	202.2	211.5
35	B	No	M	22	65	128	82	120	1	< 2	190	201	178	191	52	77	41	56	136.2	133.8
36	A	Yes	F	25	69	124	78	150	5	< 2	159	154	157	112	93	71	41	38	114.5	72.9
37	A	No	M	22	73	126	73	180	0	0	191	199	151	155	44	94	42	44	108.3	109.5
38	A	No	M	24	59.5	122	72	100	0	0	140	140	209	165	71	71	41	42	166.9	121.9
39	B	No	F	23	71	116	72	120	0	0	183	186	209	147	95	124	37	29	170.5	116
40	B	Yes	F	26	71	132	78	90	0	0	162	167	197	216	47	64	43	43	153.2	172
41	B	No	M	29	69.5	130	82	0	3	< 2	181	169	226	208	126	86	38	36	186	170.6
42	B	No	F	30	70	112	72	0	5	< 2	196	199	127	139	116	69	32	31	93.1	106.9
43	A	No	M	25	65.5	120	72	180	2	> 2	141	143	180	162	85	93	41	46	137.6	114.5
44	B	No	F	25	74	117	77	0	2	0	230	217	117	146	95	110	25	33	87.5	111.2
45	A	Yes	M	24	70	122	76	100	5	> 2	135	128	215	177	71	53	62	46	151.9	129.2

Answer 1

There is no linear relationship between relative-change* in weight and the relative-change* in Cholesterol level from screening to follow up for patients taking Drug A at 5% level of significance.

here initial and followup is not mentioned and we assumed that weight3 is followp and weight is initial

similarly for cholesterol3 is followup and cholesterol is initial

The correlation between  relative-change* in weight and the relative-change* in Cholesterol level from screening to follow up for patients taking Drug A is = r=0.3925

now we use t-test for its significance with

Null hypothesis H0:ρ=0 Vs Alternate hypothesis Ha:ρ≠0

ρ is population correlation coefficient.

since the two critical t=1.9556 is less than typical critical t=2.0796 at 5% level of significance, so we fail to reject H0 (or accept H0) and conclude that there is no linear relationship between relative-change* in weight and the relative-change* in Cholesterol level from screening to follow up for patients taking Drug A. ( generally 5% level of significance is taken if it is not mentioned)

n=	23
r=	0.3925
t =r/sqrt((1—r2)/(n—2))=	1.9556
two tailed critical t(0.05, n-2)=	2.0796
two tailed p-value =	0.0639

following information has been generated using the given data

Patient ID	Drug	Weight(intial)	Weight3 (followup)	Cholesterol(initial)	Cholesterol3(followup)	relative change in weight	relative change in cholesterol
4	A	115	105	131	133	-0.0870	0.0153
7	A	154	150	194	148	-0.0260	-0.2371
8	A	185	187	155	148	0.0108	-0.0452
9	A	178	166	234	175	-0.0674	-0.2521
10	A	158	163	201	203	0.0316	0.0100
11	A	188	195	258	276	0.0372	0.0698
12	A	150	150	212	228	0.0000	0.0755
15	A	143	140	218	172	-0.0210	-0.2110
17	A	156	155	170	158	-0.0064	-0.0706
18	A	150	154	157	140	0.0267	-0.1083
19	A	135	128	215	176	-0.0519	-0.1814
20	A	219	220	194	207	0.0046	0.0670
21	A	173	173	207	231	0.0000	0.1159
22	A	151	165	198	199	0.0927	0.0051
23	A	182	183	189	262	0.0055	0.3862
24	A	161	163	216	203	0.0124	-0.0602
30	A	149	150	164	164	0.0067	0.0000
32	A	168	170	211	183	0.0119	-0.1327
36	A	159	154	157	112	-0.0314	-0.2866
37	A	191	199	151	155	0.0419	0.0265
38	A	140	140	209	165	0.0000	-0.2105
43	A	141	143	180	162	0.0142	-0.1000
45	A	135	128	215	177	-0.0519	-0.1767
						correlation=r=	0.3925
						n=	23