Stat 3005 Correlation Example Handout Spring 2010
1
Example 3.3: A student wonders if tall women tend to date taller men than shorter women do. Here
are the heights of 6 randomly selected couples.
Couple (i) 1 2 3 4 5 6
Women (x) 66 64 66 65 70 65
Men (y) 72 68 70 68 71 65
Compute the correlation and interpret!
๐๐=1
๐๐โ1๏ฟฝ๐ง๐ง๐ฅ๐ฅ๐๐๐ง๐ง๐ฆ๐ฆ๐๐
๐๐
๐๐=1
๐ง๐ง๐ฅ๐ฅ๐๐=๐ฅ๐ฅ๐๐โ๐ฅ๐ฅ๎ชง
๐ ๐ ๐ฅ๐ฅ ๐๐๐๐๐๐ ๐ง๐ง๐ฆ๐ฆ๐๐=๐ฆ๐ฆ๐๐โ๐ฆ๐ฆ๏ฟฝ
๐ ๐ ๐ฆ๐ฆ
Step 1: We need to compute both ๐ง๐ง๐ฅ๐ฅ๐๐ and ๐ง๐ง๐ฆ๐ฆ๐๐ for ๐๐= 1, 2, 3, 4, 5,6. From Minitab:
So ๐ฅ๐ฅ1=66 ๐๐๐๐๐๐ ๐ฆ๐ฆ1=72. Then ๐ง๐ง๐ฅ๐ฅ1=๐ฅ๐ฅ1โ๐ฅ๐ฅ๎ชง
๐ ๐ ๐ฅ๐ฅ=66โ66
2.098 = 0 and ๐ง๐ง๐ฆ๐ฆ1=๐ฆ๐ฆ1โ๐ฆ๐ฆ
๏ฟฝ
๐ ๐ ๐ฆ๐ฆ=72โ69
2.53 = 1.186. The rest of
the ๐ง๐ง๐ฅ๐ฅ๐๐
โฒ๐ ๐ and ๐ง๐ง๐ฆ๐ฆ๐๐
โฒ๐ ๐ are calculated in this manner and can be seen in the table below.
๐๐
Women (x) Men(y)
๐ง๐ง๐ฅ๐ฅ
๐ง๐ง๐ฆ๐ฆ
1 66 72 0 1.186
2 64 68 -0.953
-0.395
3
66
70
0
0.395
4 65 68 -0.477
-0.395
5 70 71 1.907 0.791
6 65 65 -0.477
-1.581
53.2098.26966 ==== yx ssyx
