Eight students run a \(400\)-metre race. Their race time, \(T\), and the length, \(L\), of their legs are shown in the table.
| Leg length (\(L\) cm) | \(85\) | \(82\) | \(78\) | \(91\) | \(76\) | \(84\) | \(80\) | \(88\) |
|---|---|---|---|---|---|---|---|---|
| Race time (\(T\) seconds) | \(65.2\) | \(67.3\) | \(70.0\) | \(60.8\) | \(72.5\) | \(66.1\) | \(68.9\) | \(62.4\) |
The equation of the regression line of \(T\) on \(L\) for this data can be written in the form \(T = aL + b\).
Find the value of \(a\) and the value of \(b\).
[2]Write down the value of the Pearson's product-moment correlation coefficient \(r\).
[1]Use the equation of the regression line of \(T\) on \(L\) to predict the time of a student with a leg length of \(79\) cm.
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