Flat-screen TV Sales Study
Refer to the management scenario of Example 12.1. Find the sample correlation coefficient, r, between the number of ads placed and flat-screen TV sales. Comment on the strength of the linear relationship.
Table 12.4 shows the calculations for Pearson’s sample correlation coefficient, r.
Table 12.4 gives ∑x=44, ∑y=346, ∑x2=174, ∑xy=1324, ∑y2=10336 and n=12.
Then: r = [12(174)−(44)2][12(10336)−(346)2]12(1324)−(44)(346)=(152)(4316)664
= 0.8198 (Formula 12.5)
Table 12.4 Pearson’s correlation coefficient for the flat-screen TV sales study
Ads (x) | Sales (y) | x2 | xy | y2 |
4 | 26 | 16 | 104 | 676 |
4 | 28 | 16 | 112 | 784 |
3 | 24 | 9 | 72 | 576 |
2 | 18 | 4 | 36 | 324 |
5 | 35 | 25 | 175 | 1225 |
2 | 24 | 4 | 48 | 576 |
4 | 36 | 14 | 144 | 1296 |
3 | 25 | 9 | 75 | 625 |
5 | 31 | 25 | 155 | 961 |
5 | 37 | 25 | 185 | 1369 |
3 | 30 | 9 | 90 | 900 |
4 | 32 | 16 | 128 | 1024 |
44 | 346 | 174 | 1324 | 10336 |