Question

As part of a study on stress and its effects on aging, researchers measured telomere length in blood cells of healthy premenopausal women with chronically ill children.

Here is a link to the data.

Question: What is the correlation coefficient for these variables? Calculate your answer using the function =correl(array 1, array2) in microsoft excel. Answer to three decimal places.

1	1.63
1	1.24
1	1.33
2	1.5
2	1.42
2	1.36
2	1.32
3	1.47
2	1.24
4	1.51
4	1.31
5	1.36
5	1.34
5	1.57
4	1.03
4	0.84
5	0.94
5	1.03
5	1.14
6	1.17
6	1.23
6	1.25
6	1.31
6	1.34
7	1.36
6	1.22
8	1.32
8	1.28
8	1.26
7	1.18
7	1.03
8	1.1
8	1.13
8	0.98
10	0.85
10	1.05
12	1.15
12	1.14
12	1.56

B. Based on your calculated correlation coefficient, how would you describe the correlation between the length of telomeres and and the number of years healthy pre-menopausall woman cared for chronically ill children?

		strong negative
		weak negative
		weak positive
		strong positive
		no correlation C. Based on the correlation between telomere and caring for chronically ill children, how would you expect stress to impact aging? Increased stress increases the rate of aging, as seen by shorter telomeres. Increased stress increases the rate of aging, as seen by longer telomeres. Increased stress decreases the rate of aging, as seen by shorter telomeres. The absence of a correlation between telomeric length and carying for a chronically ill child suggests that stress does not impact aging.

Answer 1

A.

X	Y	X-Mx	Y-My	(X-Mx)^2	(Y-My)^2	(X-Mx)(Y-My)
1	1.63	-4.718	0.387	22.259	0.15	-1.824
1	1.24	-4.718	-0.003	22.259	0	0.016
1	1.33	-4.718	0.087	22.259	0.008	-0.409
2	1.5	-3.718	0.257	13.823	0.066	-0.954
2	1.42	-3.718	0.177	13.823	0.031	-0.657
2	1.36	-3.718	0.117	13.823	0.014	-0.434
2	1.32	-3.718	0.077	13.823	0.006	-0.285
3	1.47	-2.718	0.227	7.387	0.051	-0.616
2	1.24	-3.718	-0.003	13.823	0	0.012
4	1.51	-1.718	0.267	2.951	0.071	-0.458
4	1.31	-1.718	0.067	2.951	0.004	-0.115
5	1.36	-0.718	0.117	0.515	0.014	-0.084
5	1.34	-0.718	0.097	0.515	0.009	-0.069
5	1.57	-0.718	0.327	0.515	0.107	-0.235
4	1.03	-1.718	-0.213	2.951	0.046	0.366
4	0.84	-1.718	-0.403	2.951	0.163	0.693
5	0.94	-0.718	-0.303	0.515	0.092	0.218
5	1.03	-0.718	-0.213	0.515	0.046	0.153
5	1.14	-0.718	-0.103	0.515	0.011	0.074
6	1.17	0.282	-0.073	0.08	0.005	-0.021
6	1.23	0.282	-0.013	0.08	0	-0.004
6	1.25	0.282	0.007	0.08	0	0.002
6	1.31	0.282	0.067	0.08	0.004	0.019
6	1.34	0.282	0.097	0.08	0.009	0.027
7	1.36	1.282	0.117	1.644	0.014	0.15
6	1.22	0.282	-0.023	0.08	0.001	-0.007
8	1.32	2.282	0.077	5.208	0.006	0.175
8	1.28	2.282	0.037	5.208	0.001	0.084
8	1.26	2.282	0.017	5.208	0	0.038
7	1.18	1.282	-0.063	1.644	0.004	-0.081
7	1.03	1.282	-0.213	1.644	0.046	-0.274
8	1.1	2.282	-0.143	5.208	0.021	-0.327
8	1.13	2.282	-0.113	5.208	0.013	-0.259
8	0.98	2.282	-0.263	5.208	0.069	-0.601
10	0.85	4.282	-0.393	18.336	0.155	-1.684
10	1.05	4.282	-0.193	18.336	0.037	-0.828
12	1.15	6.282	-0.093	39.464	0.009	-0.586
12	1.14	6.282	-0.103	39.464	0.011	-0.649
12	1.56	6.282	0.317	39.464	0.1	1.989
		Mx: 5.718	My: 1.243	Sum: 349.897	Sum: 1.392	Sum: -7.443

X Values
∑ = 223
Mean = 5.718
∑(X - M_x)² = SS_x = 349.897

Y Values
∑ = 48.49
Mean = 1.243
∑(Y - M_y)² = SS_y = 1.392

X and Y Combined
N = 39
∑(X - M_x)(Y - M_y) = -7.443

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = -7.443 / √((349.897)(1.392)) = -0.3373
B. As r is negative and less than 0.50, so it is weak and negatively correlated

So answer is weak negative

C. Increased stress decreases the rate of aging, as seen by shorter telomeres.