2. 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. The bank codes the data using variables \(x = \frac { u - 100 } { 3 }\) and \(y = \frac { h - 20 } { 7 }\) The results for the 12 months of 2009 are summarised below.
$$\sum x = 477 \quad S _ { x x } = 5606.25 \quad \sum y = 480 \quad S _ { y y } = 4244 \quad \sum x y = 23070$$
- Calculate the value of the product moment correlation coefficient for \(x\) and \(y\).
- Write down the product moment correlation coefficient for \(u\) and \(h\).
The bank claims that an increase in unemployment among its customers is associated with an increase in house repossessions.
- State, with a reason, whether or not the bank's claim is supported by these data.