2. An estate agent recorded the price per square metre, \(p \pounds / \mathrm { m } ^ { 2 }\), for 7 two-bedroom houses. He then coded the data using the coding \(q = \frac { p - a } { b }\), where \(a\) and \(b\) are positive constants. His results are shown in the table below.
| \(p\) | 1840 | 1848 | 1830 | 1824 | 1819 | 1834 | 1850 |
| \(q\) | 4.0 | 4.8 | 3.0 | 2.4 | 1.9 | 3.4 | 5.0 |
- Find the value of \(a\) and the value of \(b\)
The estate agent also recorded the distance, \(d \mathrm {~km}\), of each house from the nearest train station. The results are summarised below.
$$\mathrm { S } _ { d d } = 1.02 \quad \mathrm {~S} _ { q q } = 8.22 \quad \mathrm {~S} _ { d q } = - 2.17$$
- Calculate the product moment correlation coefficient between \(d\) and \(q\)
- Write down the value of the product moment correlation coefficient between \(d\) and \(p\)
The estate agent records the price and size of 2 additional two-bedroom houses, \(H\) and \(J\).
| House | Price \(( \pounds )\) | Size \(\left( \mathrm { m } ^ { 2 } \right)\) |
| \(H\) | 156400 | 85 |
| \(J\) | 172900 | 95 |
- Suggest which house is most likely to be closer to a train station. Justify your answer.