9 A random sample of 10 pairs of values of \(x\) and \(y\) is given in the following table.
| \(x\) | 4 | 6 | 6 | 8 | 2 | 7 | 12 | 14 | 9 | 5 |
| \(y\) | 2 | 4 | 6 | 8 | 6 | 10 | 9 | 8 | 6 | 5 |
- Find the equation of the regression line of \(y\) on \(x\).
- Find the product moment correlation coefficient for the sample.
- Find the estimated value of \(y\) when \(x = 10\), and comment on the reliability of this estimate.
- Another sample of \(N\) pairs of data from the same population has the same product moment correlation coefficient as the first sample given. A test, at the \(1 \%\) significance level, on this second sample indicates that there is sufficient evidence to conclude that there is positive correlation. Find the set of possible values of \(N\).