Question

Help appreciated.

I don't have a graphing calculator, no explanation needed.​

Answer 1

r = 0.58

Explanation:

One formula for the correlation coefficient is

`r = \frac{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]}}`

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

`r = \frac{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]}}\\\\= \frac{12* 58049.07 - 444.4* 1451.0}{\sqrt{[12* 17522.58 -{444.4}^(2)][12*226967.6 - 1451.0^(2)]}}\\\\= (696589 - 644824)/(√([210271 - 197491][2723611 - 2105401]))\\\\= (51764)/(√(12780*618210))\\\\= (51764)/(√(7900480000))\\\\= (51764)/(88885)\\\\= \mathbf{0.58}`