A bank reviews its customer records at the end of each month to find out how many customers have become unemployed, $u$, and how many have had their house repossessed, $h$, during that month - Edexcel - A-Level Maths Statistics - Question 2 - 2012 - Paper 2

To calculate the product moment correlation coefficient $r$, use the formula:

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

Where:

• $n = 12$ (the number of months)
• $\sum x = 477$
• $\sum y = 480$
• $\sum x^2 = 5606.25$
• $\sum y^2 = 23070$
• $\sum xy = 3990$ (calculated as $n \sum xy = 12 * 3990$)

Substituting these values gives:

$r = \frac{12 \times 3990 - 477 \times 480}{\sqrt{(12 \times 5606.25 - 477^2)(12 \times 23070 - 480^2)}}$

Calculating the individual components:

• $12 \times 3990 = 47880$
• $477 \times 480 = 228960$
• $12 \times 5606.25 = 67275$
• $12 \times 23070 = 276840$

So,

$r = \frac{47880 - 228960}{\sqrt{(67275 - 227529)(276840 - 230400)}}$

After further calculations:

• $67275 - 227529 = -160254$
• $276840 - 230400 = 46440$

Finally, we find that:

• The correlation coefficient $r \approx 0.818$.