4 The table shows the load a lorry was carrying, \(x\) tonnes, and the fuel economy, \(y \mathrm {~km}\) per litre, for 8 different journeys. You should assume that neither variable is controlled.
| 5.1 | 5.8 | 6.5 | 7.1 | 7.6 | 8.4 | 9.5 | 10.5 |
| Fuel economy | | \(( y \mathrm {~km}\) per litre \()\) |
| 6.2 | 6.1 | 5.9 | 5.6 | 5.3 | 5.4 | 5.3 | 5.1 |
$$n = 8 \quad \sum x = 60.5 \quad \sum y = 44.9 \quad \sum x ^ { 2 } = 481.13 \quad \sum y ^ { 2 } = 253.17 \quad \sum x y = 334.65$$
- Calculate the equation of the regression line of \(y\) on \(x\).
- Estimate the fuel economy for a load of 9.2 tonnes.
- An analyst calculated the equation of the regression line of \(x\) on \(y\). Without calculating this equation, state the coordinates of the point where the two regression lines intersect.
- Describe briefly the method required to estimate the load when the fuel economy is 5.8 km per litre.