Answer:
The correlation coefficient of the data is 0.8679.
Step-by-step explanation:
The formula to compute the correlation coefficient is:
[tex]r(X,Y)=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\cdot\sum X^{2}-(\sum X)^{2}}\times \sqrt{n\cdot\sum Y^{2}-(\sum Y)^{2}}}[/tex]
From the data provided compute the values of ∑ XY, ∑ X, ∑ Y, ∑ X² and ∑ Y².
The values are computed in the table below.
Compute the correlation coefficient as follows:
[tex]r(X,Y)=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\cdot\sum X^{2}-(\sum X)^{2}}\times \sqrt{n\cdot\sum Y^{2}-(\sum Y)^{2}}}[/tex]
[tex]=\frac{(9\times 1893)-(57\times 269)}{\sqrt{(9\times 441)-(57)^{2}}\times \sqrt{(9\times 8635)-(269)^{2}}}\\\\=\frac{1704}{\sqrt{720\times 5354}}\\\\=0.86788895\\\\\approx 0.8679[/tex]
Thus, the correlation coefficient of the data is 0.8679.
