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
