3 An investor obtains data about the profits of 8 randomly chosen investment accounts over two one-year periods.
The profit in the first year for each account is \(p \%\) and the profit in the second year for each account is \(q \%\).
The results are shown in the table and in the scatter diagram.
| Account | A | B | C | D | E | F | G | H |
| \(p\) | 1.6 | 2.1 | 2.4 | 2.7 | 2.8 | 3.3 | 5.2 | 8.4 |
| \(q\) | 1.6 | 2.3 | 2.2 | 2.2 | 3.1 | 2.9 | 7.6 | 4.8 |
\(n = 8 \quad \sum \mathrm { p } = 28.5 \quad \sum \mathrm { q } = 26.7 \quad \sum \mathrm { p } ^ { 2 } = 136.35 \quad \sum \mathrm { q } ^ { 2 } = 116.35 \quad \sum \mathrm { pq } = 116.70\)
\includegraphics[max width=\textwidth, alt={}, center]{bf1468d1-e02e-47d2-bf41-5bc8f5b4d7c4-3_782_1280_998_242}
- State which, if either, of the variables \(p\) and \(q\) is independent.
- Calculate the equation of the regression line of \(q\) on \(p\).
- Use the regression line to estimate the value of \(q\) for an investment account for which \(p = 2.5\).
- Give two reasons why this estimate could be considered reliable.
- Comment on the reliability of using the regression line to predict the value of \(q\) when \(p = 7.0\).