Question

Compute the correlation coefficient for the data set. (2,19), (3,22), (4,26), (5,20), (6,35), (7,30), (9,40), (10,42), (11,35)

Answer 1

Answer:

The correlation coefficient  of the data is 0.8679.

Step-by-step explanation:

The formula to compute the correlation coefficient is:

$r(X,Y)=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\cdot\sum X^{2}-(\sum X)^{2}}\times \sqrt{n\cdot\sum Y^{2}-(\sum Y)^{2}}}$

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:

$r(X,Y)=\frac{n\cdot \sum XY-\sum X\cdot \sum Y}{\sqrt{n\cdot\sum X^{2}-(\sum X)^{2}}\times \sqrt{n\cdot\sum Y^{2}-(\sum Y)^{2}}}$

            $=\frac{(9\times 1893)-(57\times 269)}{\sqrt{(9\times 441)-(57)^{2}}\times \sqrt{(9\times 8635)-(269)^{2}}}\\\\=\frac{1704}{\sqrt{720\times 5354}}\\\\=0.86788895\\\\\approx 0.8679$

Thus, the correlation coefficient  of the data is 0.8679.