4 Every year, usually during early June, the Isle of Man hosts motorbike races. Each race consists of three consecutive laps of the island's course. To compete in a race, a rider must first complete at least one qualifying lap.
The data refer to the lightweight motorbike class in 2012 and show, for each of a random sample of 10 riders, values of
$$u = x - 100 \quad \text { and } \quad v = y - 100$$
where
\(x\) denotes the average speed, in mph, for the rider's fastest qualifying lap and
\(y\) denotes the average speed, in mph, for the rider's three laps of the race.
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\multicolumn{1}{c|}{} | Rider |
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\multicolumn{1}{c|}{} | \(\mathbf { A }\) | \(\mathbf { B }\) | \(\mathbf { C }\) | \(\mathbf { D }\) | \(\mathbf { E }\) | \(\mathbf { F }\) | \(\mathbf { G }\) | \(\mathbf { H }\) | \(\mathbf { I }\) | \(\mathbf { J }\) | |
| \(\boldsymbol { u }\) | 7.88 | 13.02 | 4.29 | 2.88 | 6.26 | 7.03 | 3.60 | 11.78 | 13.15 | 11.69 | |
| \(\boldsymbol { v }\) | 6.63 | 10.16 | 3.63 | 0.47 | 5.70 | 8.01 | 3.30 | 7.31 | 13.08 | 11.82 | |
- Calculate the value of \(r _ { u v }\), the product moment correlation coefficient between \(u\) and \(v\).
- Hence state the value of \(r _ { x y }\), giving a reason for your answer.
- Interpret your value of \(r _ { x y }\) in the context of this question.