In: Statistics and Probability
Neighborhood |
Economic Conditions |
Political Participation |
1 |
36.3 |
16.4 |
2 |
29.4 |
14.8 |
3 |
45.6 |
68.7 |
4 |
65.3 |
78.8 |
5 |
66.8 |
77.4 |
6 |
98.4 |
65.1 |
7 |
41.3 |
55.4 |
8 |
12.6 |
9.6 |
9 |
9.5 |
22.1 |
10 |
89.6 |
98.6 |
11 |
62.1 |
45.6 |
12 |
45.6 |
37.3 |
13 |
68.5 |
56.4 |
14 |
72.5 |
64.1 |
15 |
39.8 |
25.7 |
16 |
25.7 |
17.5 |
17 |
61.4 |
72.1 |
18 |
55.6 |
61.8 |
19 |
44.8 |
48.8 |
20 |
48.9 |
51.5 |
21 |
51.3 |
60.1 |
22 |
55.3 |
62.7 |
Let X : Economic Conditions
Y: Political Participation
Following is the scatter plot of the data:
Following table shows the calculations for correlation coefficient:
X | Y | X^2 | Y^2 | XY | |
36.3 | 16.4 | 1317.69 | 268.96 | 595.32 | |
29.4 | 14.8 | 864.36 | 219.04 | 435.12 | |
45.6 | 68.7 | 2079.36 | 4719.69 | 3132.72 | |
65.3 | 78.8 | 4264.09 | 6209.44 | 5145.64 | |
66.8 | 77.4 | 4462.24 | 5990.76 | 5170.32 | |
98.4 | 65.1 | 9682.56 | 4238.01 | 6405.84 | |
41.3 | 55.4 | 1705.69 | 3069.16 | 2288.02 | |
12.6 | 9.6 | 158.76 | 92.16 | 120.96 | |
9.5 | 22.1 | 90.25 | 488.41 | 209.95 | |
89.6 | 98.6 | 8028.16 | 9721.96 | 8834.56 | |
62.1 | 45.6 | 3856.41 | 2079.36 | 2831.76 | |
45.6 | 37.3 | 2079.36 | 1391.29 | 1700.88 | |
68.5 | 56.4 | 4692.25 | 3180.96 | 3863.4 | |
72.5 | 64.1 | 5256.25 | 4108.81 | 4647.25 | |
39.8 | 25.7 | 1584.04 | 660.49 | 1022.86 | |
25.7 | 17.5 | 660.49 | 306.25 | 449.75 | |
61.4 | 72.1 | 3769.96 | 5198.41 | 4426.94 | |
55.6 | 61.8 | 3091.36 | 3819.24 | 3436.08 | |
44.8 | 48.8 | 2007.04 | 2381.44 | 2186.24 | |
48.9 | 51.5 | 2391.21 | 2652.25 | 2518.35 | |
51.3 | 60.1 | 2631.69 | 3612.01 | 3083.13 | |
55.3 | 62.7 | 3058.09 | 3931.29 | 3467.31 | |
Total | 1126.3 | 1110.5 | 67731.31 | 68339.39 | 65972.4 |
Sample size: n=22
Now,
The coefficient of correlation is :
Scatter plot shows that there is a strong linear relationship
between the variables and correlation coefficient also shows the
same.