Question

In: Statistics and Probability

Researchers are often interested in the rate of political participation based on neighborhood economic conditions. Create...

  1. Researchers are often interested in the rate of political participation based on neighborhood economic conditions. Create a scatter plot of the variables and estimate the correlation between these two variables (assume each is continuous).

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

Solutions

Expert Solution

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.


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