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

Answer:

$r=\frac{9(5316)-(70)(740)}{\sqrt{[9(704) -(70)^2][9(62078) -(740)^2]}}=-0.9908$  

Step-by-step 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:

$r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}$  

For our case we have this:

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

$r=\frac{9(5316)-(70)(740)}{\sqrt{[9(704) -(70)^2][9(62078) -(740)^2]}}=-0.9908$