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

0.87

Explanation:

round up

Answer 2

The correlation coefficient of the data is 0.8679.

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)}* \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)}* \sqrt{n\cdot\sum Y^(2)-(\sum Y)^(2)}}`

`=\frac{(9* 1893)-(57* 269)}{\sqrt{(9* 441)-(57)^(2)}* \sqrt{(9* 8635)-(269)^(2)}}\\\\=(1704)/(√(720* 5354))\\\\=0.86788895\\\\\approx 0.8679`

Thus, the correlation coefficient of the data is 0.8679.