4. A second hand car dealer has 10 cars for sale. She decides to investigate the link between the age of the cars, \(x\) years, and the mileage, \(y\) thousand miles. The data collected from the cars are shown in the table below.
| 2 | 2.5 | 3 | 4 | 4.5 | 4.5 | 5 | 3 | 6 | 6.5 |
| Mileage, \(y\) | | (thousands) |
| 22 | 34 | 33 | 37 | 40 | 45 | 49 | 30 | 58 | 58 |
[You may assume that \(\sum x = 41 , \sum y = 406 , \sum x ^ { 2 } = 188 , \sum x y = 1818.5\) ]
- Find \(S _ { x x }\) and \(S _ { x y }\).
- Find the equation of the least squares regression line in the form \(y = a + b x\). Give the values of \(a\) and \(b\) to 2 decimal places.
- Give a practical interpretation of the slope \(b\).
- Using your answer to part (b), find the mileage predicted by the regression line for a 5 year old car.
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