Question

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

Answer 1

Let X : Economic Conditions

Y: Political Participation

Following is the scatter plot of the data:

120 100 80 60 40 20 0 100 120 20 40 0 60 80

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,

$S_{yy}=\sum y^{2}-\frac{\left (\sum y \right )^{2}}{n}=12284.37864$

$S_{xx}=\sum x^{2}-\frac{\left (\sum x \right )^{2}}{n}=10069.86955$

$S_{xy}=\sum xy-\frac{\left (\sum x \right )\left (\sum y \right )}{n}=9119.847727$

The coefficient of correlation is :

$r=\frac{S_{xy}}{\sqrt{S_{xx}S_{yy}}}=0.82$

Scatter plot shows that there is a strong linear relationship between the variables and correlation coefficient also shows the same.