Answer:
r = 0.58
Step-by-step explanation:
One formula for the correlation coefficient is
[tex]r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{n\left [\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}[/tex]
The calculation is not difficult, but it is tedious.
1. Calculate the intermediate numbers
We can display them in a table.
x y xy x² y²
48.9 167.0 8 116.30 2 391.21 27 889.00
24.8 157.4 3 903.52 615.04 24 774.76
39.2 63.7 2 497.04 1 536.84 4 057.69
40.0 144.7 5 788.00 1 600.00 20 938.09
41.5 143.2 5 942.80 1 722.25 20 506.24
29.1 149.2 4 341.72 846.81 22 260.64
40.8 90.8 3 704.64 1 664.64 8 244.64
41.9 173.6 7 273.84 1 755.61 30 136.96
46.2 150.1 6 934.62 2 134.44 22 530.01
23.7 -51.7 -1 225.29 561.69 2 672.89
47.6 196.2 9 339.12 2 265.76 38 494.44
20.7 66.8 1 382.75 428.49 4 462.24
444.4 1451.0 58 049.07 17 522.58 226 967.60
2. Calculate the correlation coefficient
[tex]r = \dfrac{n\sum{xy} - \sum{x} \sum{y}}{\sqrt{\left [n\sum{x}^{2}-\left (\sum{x}\right )^{2}\right]\left [n\sum{y}^{2}-\left (\sum{y}\right )^{2}\right]}}\\\\= \dfrac{12\times 58049.07 - 444.4\times 1451.0}{\sqrt{[12\times 17522.58 -{444.4}^{2}][12\times226967.6 - 1451.0^{2}]}}\\\\= \dfrac{696589 - 644824}{\sqrt{[210271 - 197491][2723611 - 2105401]}}\\\\= \dfrac{51764}{\sqrt{12780\times618210}}\\\\= \dfrac{51764}{\sqrt{7900480000}}\\\\= \dfrac{51764}{88885}\\\\= \mathbf{0.58}[/tex]
