3. The table shows data on the number of visitors to the UK in a month, \(v\) (1000s), and the amount of money they spent, \(m\) ( \(\pounds\) millions), for each of 8 months.
| Number of visitors | | \(v ( 1000 \mathrm {~s} )\) |
| 2450 | 2480 | 2540 | 2420 | 2350 | 2290 | 2400 | 2460 |
| Amount of money spent | | \(m ( \pounds\) millions \()\) |
| 1370 | 1350 | 1400 | 1330 | 1270 | 1210 | 1330 | 1350 |
You may use
\(S _ { v v } = 42587.5 \quad S _ { v m } = 31512.5 \quad S _ { m m } = 25187.5 \quad \sum v = 19390 \quad \sum m = 10610\)
- Find the product moment correlation coefficient between \(m\) and \(v\).
- Give a reason to support fitting a regression model of the form \(m = a + b v\) to these data.
- Find the value of \(b\) correct to 3 decimal places.
- Find the equation of the regression line of \(m\) on \(v\).
- Interpret your value of \(b\).
- Use your answer to part (d) to estimate the amount of money spent when the number of visitors to the UK in a month is 2500000
- Comment on the reliability of your estimate in part (f). Give a reason for your answer.