5 Craig uses his car to travel regularly from his home to the area hospital for treatment. He leaves home at \(x\) minutes after 7.30 am and then takes \(y\) minutes to arrive at the hospital's reception desk.
His results for 11 mornings are shown in the table.
| \(\boldsymbol { x }\) | 0 | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| \(\boldsymbol { y }\) | 31 | 42 | 32 | 58 | 47 | 56 | 79 | 68 | 89 | 95 | 85 |
- Explain why the time taken by Craig between leaving home and arriving at the hospital's reception desk is the response variable.
- Calculate the equation of the least squares regression line of \(y\) on \(x\), writing your answer in the form \(y = a + b x\).
- On a particular day, Craig needs to arrive at the hospital's reception desk no later than 9.00 am . He leaves home at 7.45 am .
Estimate the number of minutes before 9.00 am that Craig will arrive at the hospital's reception desk. Give your answer to the nearest minute.
- Use your equation to estimate \(y\) when \(x = 85\).
- Give one statistical reason and one reason based on the context of this question as to why your estimate in part (d)(i) is unlikely to be realistic.埗