Question

The data below are the number of absences and the final grades of 9 randomly selected students from a statistics class. Calculate the correlation coefficient, r.

x = 2, 5, 8, 6, 11, 4, 17, 10, 7. y = 100, 88, 82, 84, 73, 94, 57, 78, 84

Answer 1

`r=(9(5316)-(70)(740))/(√([9(704) -(70)^2][9(62078) -(740)^2]))=-0.9908`

Explanation:

Previous concepts

The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.

Solution to the problem

In order to calculate the correlation coefficient we can begin doing the following table:

n x y xy x*x y*y

1 2 100 200 4 10000

2 5 88 440 25 7744

3 8 82 656 64 6724

4 6 84 504 36 7056

5 11 73 803 121 5329

6 4 94 376 16 8836

7 17 57 969 289 3249

8 10 78 780 100 6084

9 7 84 588 49 7056

And in order to calculate the correlation coefficient we can use this formula:

`r=(n(\sum xy)-(\sum x)(\sum y))/(√([n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]))`

For our case we have this:

n=9
`\sum x = 70, \sum y = 740, \sum xy = 5316, \sum x^2 =704, \sum y^2 =62078`

`r=(9(5316)-(70)(740))/(√([9(704) -(70)^2][9(62078) -(740)^2]))=-0.9908`