5 The table shows some of the values of the seasonally adjusted Unemployment Rate (UR), \(x \%\), and the Consumer Price Index (CPI), \(y \%\), in the United Kingdom from April 2008 to July 2010.
| Date | April 2008 | July 2008 | October 2008 | January 2009 | April 2009 | July 2009 | October 2009 | January 2010 | April 2010 | July 2010 |
| UR, \(x \%\) | 5.2 | 5.7 | 6.1 | 6.8 | 7.5 | 7.8 | 7.8 | 7.9 | 7.8 | 7.7 |
| CPI, \(y \%\) | 3.0 | 4.4 | 4.5 | 3.0 | 2.3 | 1.8 | 1.5 | 3.5 | 3.7 | 3.1 |
These data are summarised below.
$$n = 10 \quad \sum x = 70.3 \quad \sum x ^ { 2 } = 503.45 \quad \sum y = 30.8 \quad \sum y ^ { 2 } = 103.94 \quad \sum x y = 211.9$$
- Calculate the product moment correlation coefficient, \(r\), for the data, showing that \(- 0.6 < r < - 0.5\).
- Karen says "The negative value of \(r\) shows that when the Unemployment Rate increases, it causes the Consumer Price Index to decrease." Give a criticism of this statement.
- (a) Calculate the equation of the regression line of \(x\) on \(y\).
(b) Use your equation to estimate the value of the Unemployment Rate in a month when the Consumer Price Index is 4.0\%.