A. Here is a bivariate data set. x y 25.7 52.5 29.4 64.7 21.8 54.9 35...

A. Here is a bivariate data set.

x	y
25.7	52.5
29.4	64.7
21.8	54.9
35	63.4
31.4	74.7
21.6	46.5
40.8	69.7
37.9	77.7
16.7	41.1
29.6	78.1
13.1	45.5
36.1	78.4
32.1	68.2
45.2	76.8
36.1	57.9

Find the correlation coefficient and report it accurate to three decimal places.
r =
What proportion of the variation in y can be explained by the variation in the values of x? Report answer as a percentage accurate to one decimal place.
r² = %

B. Based on the data shown below, calculate the correlation coefficient (to three decimal places)

x	y
1	4.97
2	4.04
3	3.51
4	3.78
5	5.15
6	7.22
7	6.69
8	5.76
9	6.73
10	6.6
11	9.77
12	8.24
13	6.91

Expert Solution

Ans:

a)

	x	y	xy	x^2	y^2
1	25.7	52.5	1349.25	660.49	2756.25
2	29.4	64.7	1902.18	864.36	4186.09
3	21.8	54.9	1196.82	475.24	3014.01
4	35	63.4	2219	1225	4019.56
5	31.4	74.7	2345.58	985.96	5580.09
6	21.6	46.5	1004.4	466.56	2162.25
7	40.8	69.7	2843.76	1664.64	4858.09
8	37.9	77.7	2944.83	1436.41	6037.29
9	16.7	41.1	686.37	278.89	1689.21
10	29.6	78.1	2311.76	876.16	6099.61
11	13.1	45.5	596.05	171.61	2070.25
12	36.1	78.4	2830.24	1303.21	6146.56
13	32.1	68.2	2189.22	1030.41	4651.24
14	45.2	76.8	3471.36	2043.04	5898.24
15	36.1	57.9	2090.19	1303.21	3352.41
Total	452.5	950.1	29981.01	14785.19	62521.15

Correlation coefficient,r=(15*29981.01-452.5*950.1)/SQRT((15*14785.19-452.5^2)*(15*62521.15-950.1^2))

r=0.810

r^2=0.810^2=0.656 or 65.6%

b)

	x	y	xy	x^2	y^2
1	1	4.97	4.97	1	24.7009
2	2	4.04	8.08	4	16.3216
3	3	3.51	10.53	9	12.3201
4	4	3.78	15.12	16	14.2884
5	5	5.15	25.75	25	26.5225
6	6	7.22	43.32	36	52.1284
7	7	6.69	46.83	49	44.7561
8	8	5.76	46.08	64	33.1776
9	9	6.73	60.57	81	45.2929
10	10	6.6	66	100	43.56
11	11	9.77	107.47	121	95.4529
12	12	8.24	98.88	144	67.8976
13	13	6.91	89.83	169	47.7481
Total	91	79.37	623.43	819	524.1671

correlation coefficient,r=(13*623.43-91*79.37)/SQRT((13*819-91^2)*(13*524.1671-79.37^2))

r=0.799

milcah answered 6 months ago

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