10 Delegates who travelled to a conference were asked to report the distance, \(y \mathrm {~km}\), that they had travelled and the time taken, \(x\) minutes. The values reported by a random sample of 8 delegates are given in the following table.
| Delegate | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) | \(G\) | \(H\) |
| \(x\) | 90 | 46 | 72 | 98 | 52 | 65 | 105 | 82 |
| \(y\) | 90 | 55 | 69 | 85 | 45 | 50 | 110 | 74 |
$$\left[ \Sigma x = 610 , \Sigma x ^ { 2 } = 49682 , \Sigma y = 578 , \Sigma y ^ { 2 } = 45212 , \Sigma x y = 47136 . \right]$$
Find the equations of the regression lines of \(y\) on \(x\) and of \(x\) on \(y\).
Estimate the time taken by a delegate who travelled 100 km to the conference.
Calculate the product moment correlation coefficient for this sample.