6. A travel agent sells flights to different destinations from Beerow airport. The distance \(d\), measured in 100 km , of the destination from the airport and the fare \(\pounds f\) are recorded for a random sample of 6 destinations.
| Destination | \(A\) | \(B\) | \(C\) | \(D\) | \(E\) | \(F\) |
| \(d\) | 2.2 | 4.0 | 6.0 | 2.5 | 8.0 | 5.0 |
| \(f\) | 18 | 20 | 25 | 23 | 32 | 28 |
$$\text { [You may use } \sum d ^ { 2 } = 152.09 \quad \sum f ^ { 2 } = 3686 \quad \sum f d = 723.1 \text { ] }$$
- Using the axes below, complete a scatter diagram to illustrate this information.
- Explain why a linear regression model may be appropriate to describe the relationship between \(f\) and \(d\).
- Calculate \(S _ { d d }\) and \(S _ { f d }\)
- Calculate the equation of the regression line of \(f\) on \(d\) giving your answer in the form \(f = a + b d\).
- Give an interpretation of the value of \(b\).
Jane is planning her holiday and wishes to fly from Beerow airport to a destination \(t \mathrm {~km}\) away. A rival travel agent charges 5 p per km.
- Find the range of values of \(t\) for which the first travel agent is cheaper than the rival.
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