Question

As a sociologist, you are interested in better understanding what factors impact personal annual income. To explore this topic, you asked participants to report their father’s income as well as their own salaries. What is the correlation between parent and personal income in the sample below?

Case	Parent Income (in thousands) (X)	Personal Income (in thousands) (Y)
1	39	68
2	62	82
3	44	72
4	44	65
5	43	77
6	75	98
7	69	65
8	62	63
9	48	94
10	38	64

   Use this table to help you calculate the correlation coefficient.

Case	X	Y	XY	X2	Y2
1
2
3
4
5
6
7
8
9
10
∑

5.      SPxy:

6.      SSx:

7.      SSy:

8.      r:

Answer 1

	X	Y	X * Y	X2	Y2	Sxx =Σ (Xi - X̅ )2	Syy = Σ( Yi - Y̅ )2	Sxy = Σ (Xi - X̅ ) * (Yi - Y̅)
	39	68	2652	1521	4624	179.56	46.24	91.12
	62	82	5084	3844	6724	92.16	51.84	69.12
	44	72	3168	1936	5184	70.56	7.84	23.52
	44	65	2860	1936	4225	70.56	96.04	82.32
	43	77	3311	1849	5929	88.36	4.84	-20.68
	75	98	7350	5625	9604	510.76	538.24	524.32
	69	65	4485	4761	4225	275.56	96.04	-162.68
	62	63	3906	3844	3969	92.16	139.24	-113.28
	48	94	4512	2304	8836	19.36	368.64	-84.48
	38	64	2432	1444	4096	207.36	116.64	155.52
Total	524	748	39760	29064	57416	1606.4	1465.6	564.8

X̅ = Σ (Xi / n ) = 524/10 = 52.4
Y̅ = Σ (Yi / n ) = 748/10 = 74.8

Sxx = 1606.4

Syy = 1465.6

Sxy = 564.8

r = Sxy / √( Sxx * Syy )
r = 564.8 / √(1606.4 * 1465.6)
r = 0.3681