7 [Figure 1, printed on the insert, is provided for use in this question.]
Stan is a retired academic who supplements his pension by mowing lawns for customers who live nearby.
As part of a review of his charges for this work, he measures the areas, \(x \mathrm {~m} ^ { 2 }\), of a random sample of eight of his customers' lawns and notes the times, \(y\) minutes, that it takes him to mow these lawns. His results are shown in the table.
| Customer | \(\mathbf { A }\) | \(\mathbf { B }\) | \(\mathbf { C }\) | \(\mathbf { D }\) | \(\mathbf { E }\) | \(\mathbf { F }\) | \(\mathbf { G }\) | \(\mathbf { H }\) |
| \(\boldsymbol { x }\) | 360 | 140 | 860 | 600 | 1180 | 540 | 260 | 480 |
| \(\boldsymbol { y }\) | 50 | 25 | 135 | 70 | 140 | 90 | 55 | 70 |
- On Figure 1, plot a scatter diagram of these data.
- Calculate the equation of the least squares regression line of \(y\) on \(x\). Draw your line on Figure 1.
- Calculate the value of the residual for Customer H and indicate how your value is confirmed by your scatter diagram.
- Given that Stan charges \(\pounds 12\) per hour, estimate the charge for mowing a customer's lawn that has an area of \(560 \mathrm {~m} ^ { 2 }\).