Question

# As a sociologist, you are interested in better understanding what factors impact personal annual income. To...

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

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

5.      SPxy:

6.      SSx:

7.      SSy:

8.      r:

 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