Question

Use the following data to calculate and record the correlation coefficient, r.

Height (in.)	Foot Length (in.)
63	10
66	12
62.5	9.4
74	10.5
70	11.3
72	11.3
71	12.5
64	9.1
72	10.9
71	10
74	12.1
67	10
69	11.1
65	9.6
62.8	9
72	11.3
68.8	10.5
69	10
65.3	9
53	7
71	10.3
74	11.7
70	10
72	10.6
72.5	12.8
67	9.5
69	10.9
74	11.6
68	9
70.1	10.1
62	8
77	11.4
63	9.5
64.5	9.4
71	9.8

Answer 1

X-Mx	Y-My	(X-Mx)^2	(Y-MY)^2	(X-Mx)(Y-MY)
-5.471	-0.32	29.937	0.102	1.751
-2.471	1.68	6.108	2.822	-4.152
-5.971	-0.92	35.658	0.846	5.494
5.529	0.18	30.565	0.032	0.995
1.529	0.98	2.337	0.96	1.498
3.529	0.98	12.451	0.96	3.458
2.529	2.18	6.394	4.752	5.512
-4.471	-1.22	19.994	1.488	5.455
3.529	0.58	12.451	0.336	2.047
2.529	-0.32	6.394	0.102	-0.809
5.529	1.78	30.565	3.168	9.841
-1.471	-0.32	2.165	0.102	0.471
0.529	0.78	0.279	0.608	0.412
-3.471	-0.72	12.051	0.518	2.499
-5.671	-1.32	32.165	1.742	7.486
3.529	0.98	12.451	0.96	3.458
0.329	0.18	0.108	0.032	0.059
0.529	-0.32	0.279	0.102	-0.169
-3.171	-1.32	10.058	1.742	4.186
-15.471	-3.32	239.365	11.022	51.365
2.529	-0.02	6.394	0	-0.051
5.529	1.38	30.565	1.904	7.629
1.529	-0.32	2.337	0.102	-0.489
3.529	0.28	12.451	0.078	0.988
4.029	2.48	16.229	6.15	9.991
-1.471	-0.82	2.165	0.672	1.207
0.529	0.58	0.279	0.336	0.307
5.529	1.28	30.565	1.638	7.077
-0.471	-1.32	0.222	1.742	0.622
1.629	-0.22	2.652	0.048	-0.358
-6.471	-2.32	41.879	5.382	15.014
8.529	1.08	72.737	1.166	9.211
-5.471	-0.82	29.937	0.672	4.487
-3.971	-0.92	15.772	0.846	3.654
2.529	-0.52	6.394	0.27	-1.315
Mx: 68.471	My: 10.320	Sum: 772.351	Sum: 53.416	Sum: 158.830

X Values
∑ = 2396.5
Mean = 68.471
∑(X - M_x)² = SS_x = 772.351

Y Values
∑ = 361.2
Mean = 10.32
∑(Y - M_y)² = SS_y = 53.416

X and Y Combined
N = 35
∑(X - M_x)(Y - M_y) = 158.83

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

r = 158.83 / √((772.351)(53.416)) = 0.782