Answer:
A. 0.75
Step-by-step explanation:
The formula for the correlation coefficient r is
[tex]r =\frac {n \sum{xy} - \sum{x}\sum{y}}{\sqrt{[n \sum{x^{2}}- (\sum{x})^{2}}][n \sum{y^{2}}- (\sum{y})^{2}]}[/tex]
It's easier to use a statistical calculator, but this question probably expects you to do it by hand.
Let’s write a table for easy calculation.
x y xy x² y²
15 36 540 225 1296
13 22 286 169 484
12 6 72 144 36
11 20 220 121 400
51 84 1118 659 2216
(Σx)² = 2601
(Σy)² = 7056
[tex]r =\frac{4\times1118-51\times84}{\sqrt{[4\times659-2601][4\times2216-7056]}}[/tex]
[tex]r =\frac{4472-4284}{\sqrt{[2636-2601][8864-7056]}}[/tex]
[tex]r =\frac{188}{\sqrt{35\times1808}}[/tex]
[tex]r =\frac{188}{\sqrt{63280}}[/tex]
[tex]r =\frac{188}{251.6}[/tex]
r = 0.747
The graph below shows that there is a poor correlation among the points.
