2 The director of a concert hall wishes to investigate if the price of the most expensive concert tickets affects attendance. The director collects data about the price, \(\pounds P\), of the most expensive tickets and the number of people in the audience, \(H\) hundred (rounded to the nearest hundred), for 20 concerts. For each price there are several different concerts. The results are shown in the table.
| \(P\) (£) | 75 | 65 | 55 | 45 | 35 |
| \multirow[t]{5}{*}{\(H\) (hundred)} | 27 | 27 | 27 | 26 | 15 |
| 27 | 27 | 20 | 21 | 12 |
| | 22 | 18 | 16 | 9 |
| | 19 | 18 | 13 | |
| | 12 | 16 | 9 | |
\(\mathrm { n } = 20 \quad \sum \mathrm { p } = 1080 \quad \sum \mathrm {~h} = 381 \quad \sum \mathrm { p } ^ { 2 } = 61300 \quad \sum \mathrm {~h} ^ { 2 } = 8011 \quad \sum \mathrm { ph } = 21535\)
- Calculate the equation of the regression line of \(h\) on \(p\).
- State what change, if any, there would be to your answer to part (a) if \(H\) had been measured in thousands (to 1 decimal place) rather than in hundreds.
For a special charity concert, the most expensive tickets cost \(\pounds 50\).
- Use your answer to part (b) to estimate the expected size of the audience for this concert. Give your answer correct to \(\mathbf { 1 }\) decimal place.
- Comment on the reliability of your answer to part (c). You should refer to
- the value of the product-moment correlation coefficient for the data, which is 0.642
- the value of \(\pounds 50\)
- any one other relevant factor that should be taken into account.