The regression line of \(y\) on \(x\) obtained from a random sample of five pairs of values of \(x\) and \(y\) is
$$y = 2.5 x - 1.5$$
The data is given in the following table.
| \(x\) | 1 | 2 | 4 | 2 | 6 |
| \(y\) | 2 | 3 | 6 | \(p\) | \(q\) |
- Show that \(p + q = 19\).
- Find the values of \(p\) and \(q\).
- Determine the value of the product moment correlation coefficient for this sample.
- It is later discovered that the values of \(x\) given in the table have each been divided by 10 (that is, the actual values are \(10,20,40,20,60\) ). Without any further calculation, state
(a) the equation of the actual regression line of \(y\) on \(x\),
(b) the value of the actual product moment correlation coefficient.